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PMC11276230_p0
|
PMC11276230
|
sec[0]/p[0]
|
1. Introduction
| 4.039063 |
biomedical
|
Review
|
[
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[
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The first magnetic resonance imaging (MRI) systems developed for clinical use had a magnetic field intensity of less than 0.35 T . With the gradual development of MRI systems, significant advances have been made, one of which was the improvement in static magnetic field, with conventional 1.5 T and 3 T MRI systems becoming conventional systems used for clinical applications, replacing Low-Field MRI (LF MRI) . High-field systems have gained a dominant market share due to higher resolution, higher SNR (Signal to Noise Ratio) per unit of time, greater contrast sensitivity, and more advanced sequence . This review focuses on LF MRI, which is defined as a system with a magnetic field strength below 1 Tesla .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p1
|
PMC11276230
|
sec[0]/p[1]
|
1. Introduction
| 3.099609 |
biomedical
|
Other
|
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[
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Although commercial lower-field devices were available, many were rarely used or have been discontinued altogether. However, commercial interest has led to the FDA (Food and Drug Administration) approval of several low-field systems. Hyperfine was the first to market its device, the MRI 0.064 T Hyperfine Swoop (head examination), followed by the MRI 0.066 T Promaxo (prostate examination), the MRI 0.5 T Synaptive Evry (intraoperative MRI), and the MRI 0.55 T Siemens Magnetom Free.Max (whole-body) . While high-field devices have gained market dominance based on the parameters already mentioned, there are two main factors that create opportunities for current low-field systems. One factor is the lower acquisition costs, and the other is technological innovations that lead to improved image quality .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p2
|
PMC11276230
|
sec[0]/p[2]
|
1. Introduction
| 3.146484 |
biomedical
|
Other
|
[
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[
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Due to the development in MRI device hardware and software, including, for example, new coils or rather innovative pulse sequences and advanced processing of measured signals (using Deep Learning and Denoising Techniques), it is possible to reduce noise in the image by methods other than increasing magnetic induction and to improve the overall quality of the resulting image .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p3
|
PMC11276230
|
sec[0]/p[3]
|
1. Introduction
| 4.023438 |
biomedical
|
Study
|
[
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The aim of this article is to assess the diagnostic efficacy and capability of clinically available LF MRI technology in the obtaining of clinically relevant results in comparison with 1.5 T MRI devices in imaging the nervous system (brain, spinal cord, spine), musculoskeletal system (joints, bones, muscles) and organs of the chest, abdomen, and pelvis. To achieve this goal, studies comparing these technologies according to their diagnostic outcomes, their impact on decision-making in clinical settings, and their subsequent impact on the treatment process and its clinical outcomes were analysed.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999995 |
PMC11276230_p4
|
PMC11276230
|
sec[0]/p[4]
|
1. Introduction
| 2.958984 |
biomedical
|
Review
|
[
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0.0018548965454101562,
0.002719879150390625
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[
0.265380859375,
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The manuscript provides current evidence of the diagnostic performance of LF MRI, although it is limited. The findings may offer valuable insights for clinical practice and contribute to a better understanding of the appropriateness and effectiveness of LF MRI in diagnostic practice.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p5
|
PMC11276230
|
sec[0]/p[5]
|
1. Introduction
| 2.140625 |
biomedical
|
Study
|
[
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[
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The manuscript has the following structure. Elementary steps of systematic review are described in Materials and Methods. The list of studies that were completely read and evaluated are summarised in Results. Limitations and perspectives are discussed in the Discussion.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p6
|
PMC11276230
|
sec[1]/p[0]
|
2. Materials and Methods
| 3.279297 |
biomedical
|
Study
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[
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The analysis of studies was carried out in the form of a systematic review; the recommended Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) procedure was used for this analysis . The study is not registered in PROSPERO. Within the specific methods and procedures, the recommendations of the Cochrane Collaboration were also taken into account . Publications from 2018 to January 2023 were included in the analysis, the reason being the novelty of the technology. Several LF MRIs were cleared by the FDA in 2018 .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
PMC11276230_p7
|
PMC11276230
|
sec[1]/p[1]
|
2. Materials and Methods
| 3.945313 |
biomedical
|
Review
|
[
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[
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0.953125,
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] |
For conducting the systematic review, a key question was established: What evidence exists regarding the diagnostic efficacy of clinically available whole-body scanners with low magnetic inductance compared to 1.5 T MRI devices in imaging the nervous system (brain, spinal cord, spine), musculoskeletal system (joints, bones, muscles), and organs of the chest, abdomen, and pelvis?
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
PMC11276230_p8
|
PMC11276230
|
sec[1]/p[2]
|
2. Materials and Methods
| 4.050781 |
biomedical
|
Review
|
[
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0.0012884140014648438
] |
[
0.10211181640625,
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] |
The diagnostic efficacy of imaging technologies is a complex issue, and it is influenced by many factors. The hierarchical model proposed by Fryback and Thornbury is often used to assess it . This model describes the individual steps that should be considered when assessing the clinical value of diagnostic imaging methods. According to this model, the diagnostic efficacy of an imaging technology can be viewed at several levels: Level 1: technical quality of the test; Level 2: diagnostic accuracy, sensitivity and specificity of the test, interpretation; Level 3: whether the test result leads to a change in the diagnostic thinking of the physician; Level 4: impact of the test on the patient’s treatment plan; Level 5: impact of the test on patient outcomes; Level 6: societal costs and benefits of the diagnostic test.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p9
|
PMC11276230
|
sec[1]/p[3]
|
2. Materials and Methods
| 1.829102 |
biomedical
|
Study
|
[
0.68798828125,
0.0019741058349609375,
0.31005859375
] |
[
0.57861328125,
0.32666015625,
0.09222412109375,
0.002353668212890625
] |
The analysis of the literature was primarily focused on levels 2 to 5 of the Fryback and Thornbury model, as this level is directly related to the terms of reference of the study .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p10
|
PMC11276230
|
sec[1]/sec[0]/p[0]
|
2.1. Sources and Search Strategies
| 3.966797 |
biomedical
|
Review
|
[
0.9951171875,
0.00222015380859375,
0.00254058837890625
] |
[
0.02435302734375,
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] |
A systematic review was performed in the MEDLINE, PubMed, CENTRAL, Web of Science and Scopus databases to identify studies comparing the accuracy, reliability, and diagnostic efficacy of currently available LF MRI technologies. The search was conducted once at the end of 2023. Two researchers conducted independent data extraction and quality assessment. Papers in English and German language have been analysed.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p11
|
PMC11276230
|
sec[1]/sec[0]/p[1]
|
2.1. Sources and Search Strategies
| 2.183594 |
biomedical
|
Review
|
[
0.96435546875,
0.0031986236572265625,
0.032379150390625
] |
[
0.253173828125,
0.1016845703125,
0.64306640625,
0.002056121826171875
] |
Searches were conducted using standard MeSH terms as well as specific free terms and their combinations related to the key questions of the review. A detailed description of the search strategies and a list of the search terms used is provided in Table S1 .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p12
|
PMC11276230
|
sec[1]/sec[0]/p[2]
|
2.1. Sources and Search Strategies
| 2.238281 |
biomedical
|
Study
|
[
0.9873046875,
0.0006837844848632812,
0.01181793212890625
] |
[
0.77392578125,
0.2091064453125,
0.0162506103515625,
0.0009851455688476562
] |
PubMed searches were limited to records that were not indexed in the MEDLINE database. Searches in the Web of Science and Scopus databases, due to their multidisciplinary nature, were limited to publications on diagnostic accuracy of tests according to the comprehensive version of the search strategy of Bachmann et al. .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p13
|
PMC11276230
|
sec[1]/sec[1]/p[0]
|
2.2. Inclusion and Exclusion Criteria
| 4.0625 |
biomedical
|
Review
|
[
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[
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] |
The review sought to identify all primary studies comparing these technologies, namely randomised controlled trials, cohort studies, and case-control studies. Case studies, casuistries, simulation studies, etc., have not been analysed. An indirect comparison of two technologies (i.e., based on studies assessing the diagnostic characteristics of each technology without directly comparing them) would be associated with heterogeneity in estimated diagnostic accuracy across studies, and this could bias the results of the final comparison. This systematic review was based on studies that made direct comparisons between LF MRI and 1.5 T MRI technologies, either by applying both tests to each individual or by dividing subjects into groups to be tested with one technology.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p14
|
PMC11276230
|
sec[1]/sec[1]/p[1]
|
2.2. Inclusion and Exclusion Criteria
| 1.94043 |
biomedical
|
Study
|
[
0.96826171875,
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0.029022216796875
] |
[
0.82763671875,
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] |
The criteria for inclusion and exclusion of publications were established in advance using the objectives of this assessment and the key questions identified.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p15
|
PMC11276230
|
sec[1]/sec[1]/sec[0]/p[0]
|
2.2.1. Inclusion Criteria
| 2.787109 |
biomedical
|
Study
|
[
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[
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] |
All studies comparing the diagnostic performance of LF MRI technology and currently available 1.5 T MRI technologies were considered for inclusion. Publications from 2018 onwards were included in the analysis since the assessed technology is quite new. Studies were included in the subsequent analysis if
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
PMC11276230_p16
|
PMC11276230
|
sec[1]/sec[1]/sec[1]/p[0]
|
2.2.2. Exclusion Criteria
| 1.891602 |
biomedical
|
Study
|
[
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[
0.6748046875,
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0.0256500244140625,
0.0021076202392578125
] |
The following types of studies or publications were excluded: Overview articles, reviews, casuistries, letters to the editor, commentaries, case studies; Studies with less than 5 patients; Animal, in vitro or cadaver studies; Abstracts from conferences that did not result in a peer-reviewed publication.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p17
|
PMC11276230
|
sec[1]/sec[2]/p[0]
|
2.3. Screening and Assessment of Studies
| 2.826172 |
biomedical
|
Study
|
[
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[
0.93310546875,
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0.0004343986511230469
] |
Publication lists were imported into EndNote X6 (Thomson Reuters, Toronto, ON, Canada), and duplicate articles were removed. Subsequently, the remaining publications were exported to the Rayyan web-based software for screening purposes. Screening consisted of analysing the title, abstract, and other parameters of the publications. The aim of this step was to exclude obviously irrelevant publications from further analysis based on exclusion criteria.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p18
|
PMC11276230
|
sec[1]/sec[2]/p[1]
|
2.3. Screening and Assessment of Studies
| 2.886719 |
biomedical
|
Study
|
[
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] |
[
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] |
For the records not excluded in the screening, their full texts were retrieved, and these articles proceeded to a detailed assessment of their relevance in terms of predefined inclusion and exclusion criteria. At the same time, the reference lists for these articles were manually analysed to identify any relevant studies that may have been missed in the search. The excluded publications with the reason for exclusion are listed in Supplementary Materials .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p19
|
PMC11276230
|
sec[1]/sec[3]/p[0]
|
2.4. Data Extraction
| 3.259766 |
biomedical
|
Study
|
[
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[
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A standardised procedure was used to obtain data from each of the included studies. The following information was obtained from the included studies: year of publication, study design, number of subjects, characteristics of the study population, imaging area, diagnostic outcomes assessed, information on the procedures used to measure them, information on test results, and other relevant information.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999999 |
PMC11276230_p20
|
PMC11276230
|
sec[1]/sec[4]/p[0]
|
2.5. Critical Assessment
| 3.960938 |
biomedical
|
Study
|
[
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[
0.9853515625,
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] |
The included studies assessed the diagnostic properties of magnetic resonance imaging in organ imaging. Some studies achieved this by assessing the technical quality of the images and the reproducibility of individual measurements, while others assessed the diagnostic accuracy of the technologies. The risk of bias was assessed using the QUADAS-2 (Quality Assessment of Diagnostic Accuracy Studies 2) tool ( Table S3 ) . Two independent reviewers conducted the assessment. The search was conducted once at the end of 2023.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999999 |
PMC11276230_p21
|
PMC11276230
|
sec[1]/sec[5]/p[0]
|
2.6. Data Analysis
| 2.132813 |
biomedical
|
Study
|
[
0.99072265625,
0.0024662017822265625,
0.00669097900390625
] |
[
0.96484375,
0.0200042724609375,
0.01409912109375,
0.0008411407470703125
] |
The studies included in the final analysis differed significantly in their design and clinical outcomes analysed. For this reason, a formal meta-analysis of their results was not performed.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p22
|
PMC11276230
|
sec[1]/sec[5]/p[1]
|
2.6. Data Analysis
| 2.574219 |
biomedical
|
Study
|
[
0.99658203125,
0.0003809928894042969,
0.0032749176025390625
] |
[
0.94287109375,
0.052398681640625,
0.004375457763671875,
0.0003905296325683594
] |
For studies aimed at comparing the results of continuous parameter measurements, it was not possible to calculate inter-rater reliability parameters (agreement among observers), inter-method reliability (agreement between the individual methods of measurement) and other key parameters.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p23
|
PMC11276230
|
sec[1]/sec[5]/p[2]
|
2.6. Data Analysis
| 3.148438 |
biomedical
|
Study
|
[
0.99853515625,
0.0005927085876464844,
0.000766754150390625
] |
[
0.99853515625,
0.0009369850158691406,
0.00035381317138671875,
0.00009143352508544922
] |
The results of the study were used to calculate the diagnostic characteristics of the test (sensitivity and specificity), which were then recalculated in relation to the gold standard.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999995 |
PMC11276230_p24
|
PMC11276230
|
sec[2]/p[0]
|
3. Results
| 3.96875 |
biomedical
|
Study
|
[
0.9990234375,
0.0004589557647705078,
0.0005578994750976562
] |
[
0.9990234375,
0.0005602836608886719,
0.0004429817199707031,
0.00006753206253051758
] |
The export from the databases took place on 14 January 2023. The total number of results obtained from the above-defined databases was 1275 publications. From this set, 650 duplicates were removed, and the remaining 625 records were examined as part of the Phase 1 screening. From this sample, 586 non-relevant publications were removed based on titles and abstracts, and the remaining 39 proceeded to the next phase. The full texts of these 39 publications were thoroughly analysed as part of a detailed assessment of the relevance of the publications. The most common reason for exclusion from subsequent analysis was the use of an inappropriate comparator. Other reasons were inappropriate publication type or inappropriate technology. The entire selection process is illustrated by the PRISMA diagram in the following Figure 1 , with the excluded studies and the reason for their exclusion listed in Supplementary Materials . Finally, 2 studies were selected that met all the predefined inclusion criteria.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p25
|
PMC11276230
|
sec[2]/sec[0]/p[0]
|
3.1. Excluded Studies
| 4.023438 |
biomedical
|
Study
|
[
0.99951171875,
0.0003554821014404297,
0.0002951622009277344
] |
[
0.99755859375,
0.0007557868957519531,
0.0014314651489257812,
0.00008106231689453125
] |
During the assessment of suitability, a total of 37 studies were excluded ( Table 1 ). The reasons for the exclusion of each study are detailed in Table 1 . The most common reason for exclusion was inappropriate comparators, such as not comparing an LF MRI technology to a 1.5 T MRI scanner or the use of unsuitable technology, such as studies conducted on a prototype 0.55 LF MRI or MRI with induction adjustment to 0.55 T. It is worth noting that studies excluded due to inappropriate technology have served as comparative studies on so-called prototype 0.55 T MRI prior to market introduction. Comparative studies on prototypes were excluded because these prototypes represented experimental devices, were not commercially available, and had different technical parameters compared to the commercially available devices.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p26
|
PMC11276230
|
sec[2]/sec[1]/p[0]
|
3.2. Characteristics of the Studies
| 2.501953 |
biomedical
|
Study
|
[
0.99755859375,
0.00150299072265625,
0.0009493827819824219
] |
[
0.95849609375,
0.01441192626953125,
0.0257720947265625,
0.0010967254638671875
] |
The following table ( Table 2 ) summarises the basic characteristics of the included studies . All studies were single-centre with a small number of patients. Both studies focused on imaging of the brain region, one on imaging of intracranial aneurysms and the other on stroke diagnosis.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999999 |
PMC11276230_p27
|
PMC11276230
|
sec[2]/sec[1]/p[1]
|
3.2. Characteristics of the Studies
| 4.097656 |
biomedical
|
Study
|
[
0.9990234375,
0.0006213188171386719,
0.00016820430755615234
] |
[
0.9990234375,
0.0003304481506347656,
0.0007648468017578125,
0.00011670589447021484
] |
The study by Osmanodja et al. had the main objective to assess the performance of 0.55 T MRI technology in the diagnosis of intracranial aneurysms compared with digital subtraction angiography. As part of the partial results, the authors of the study also focused on the comparison of Siemens Free.Max technology with 1.5 T MRI devices. Nine patients were included in the comparison (1.5 T vs. 0.55 T) who were suspected of having intracranial aneurysms based on previous 1.5 T MRI images. These patients subsequently underwent examination on a 0.55 T MRI machine by TOF (time-of-flight) MRI angiography. The resulting images were evaluated by two raters using Syngo.via software (Siemens Healthineers AG, Erlangen, Germany). The evaluation consisted of measuring the size of the aneurysms. The results of the measurements were averaged between raters and compared using the Wilcoxon matched-pairs test. The results of this test showed no statistically significant differences in measured aneurysm sizes between the two technologies.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p28
|
PMC11276230
|
sec[2]/sec[1]/p[2]
|
3.2. Characteristics of the Studies
| 3.787109 |
biomedical
|
Study
|
[
0.99951171875,
0.00024199485778808594,
0.0003905296325683594
] |
[
0.98388671875,
0.0024280548095703125,
0.01331329345703125,
0.00019180774688720703
] |
This study is characterised by a very small number of patients. In addition, there is a discrepancy in the description of the number of patients: at the beginning, the authors state that there were only two men in the initial cohort, but in the results, they state that there were three. It should also be noted that not all examinations on the 1.5 T MRI machine were performed at the same facility; only 3 of the 9 examinations were performed at the same hospital as the 0.55 T MRI examination. In the section dedicated to the comparison of 1.5 T and 0.55 T MRI technologies, the authors of the study did not perform a detailed analysis of the agreement among image raters or a comprehensive analysis of the agreement between the results of the measurements of the two technologies (e.g., using intraclass correlation analysis and similar approaches). At the conclusion of the study, the authors state that a further blinded study with a larger sample size is needed to confirm their results.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p29
|
PMC11276230
|
sec[2]/sec[1]/p[3]
|
3.2. Characteristics of the Studies
| 4.089844 |
biomedical
|
Study
|
[
0.9990234375,
0.0006399154663085938,
0.00016427040100097656
] |
[
0.9990234375,
0.0003254413604736328,
0.0005650520324707031,
0.00011557340621948242
] |
Rusche et al. published a study in 2022 to assess the outcomes of imaging patients with strokes using a low-induction MRI device. A total of 24 patients were included in the study (14 stroke patients, 10 control patients). Patients first underwent a 1.5 T MRI scan and then a 0.55 T scan. Imaging was performed using DWI/ADC (diffusion-weighted image—apparent diffusion coefficient) and FLAIR (fluid-attenuated inversion recovery) sequences. On the images, two neuroradiologists independently and blinded evaluated the presence of the stroke, number, and localisation of lesions. The acquired images were also scored using a 10-point scale by two neuroradiologists, unblinded, in five dimensions: overall image quality, resolution, noise, contrast, and diagnostic quality. The authors did not provide a more detailed definition of each dimension. Subsequently, segmentation of lesion volumes was also performed by two additional radiologists.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999999 |
PMC11276230_p30
|
PMC11276230
|
sec[2]/sec[1]/p[4]
|
3.2. Characteristics of the Studies
| 4.101563 |
biomedical
|
Study
|
[
0.9990234375,
0.0006875991821289062,
0.00023627281188964844
] |
[
0.9990234375,
0.000286102294921875,
0.000499725341796875,
0.00009053945541381836
] |
The results of the image quality ratings from 17 patients using a 10-point scale were averaged among raters in each dimension and compared using the Wilcoxon test. Subsequently, inter-reader reliability was compared using the intraclass correlation coefficient (ICC). For the DWI/ADC sequence, the overall image quality, resolution, contrast, and diagnostic quality were significantly better for the 1.5 T MRI device, and the noise rating for the 0.55 T MRI device was significantly better than that of the 1.5 T MRI device. For the FLAIR sequence, overall image quality, noise and diagnostic quality were significantly better for the 1.5 T MRI technology, and no significant differences were observed between technologies for resolution and contrast. There was moderate to high agreement among raters in the results (ICC 0.64 to 0.87).
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p31
|
PMC11276230
|
sec[2]/sec[1]/p[5]
|
3.2. Characteristics of the Studies
| 4.125 |
biomedical
|
Study
|
[
0.99853515625,
0.0014181137084960938,
0.00024211406707763672
] |
[
0.99853515625,
0.0005097389221191406,
0.0006914138793945312,
0.00014126300811767578
] |
The results of stroke diagnosis were presented for 24 patients (14 in the stroke group and 10 in the control group). For the DWI/ADC sequence, rater 1 achieved similar sensitivity (92.9% [95% CI 66.1–99.8%]) and specificity (100% [95% CI 69.2–100.0%]) values for both technologies compared. Rater 2 had a lower sensitivity for the 0.55 T MRI technology (85.7% [95% CI 57.2–98.2%] vs. 100% [76.8–100.0%]) and the same specificity (100% [95% CI 69.2–100.0%]) for the compared technologies. For the FLAIR sequence, the study authors did not provide sufficiently detailed results to compare the sensitivity and specificity of the technologies in question. No significant differences were found between the 0.55 T and 1.5 T technologies in the measurement of lesion volumes.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p32
|
PMC11276230
|
sec[2]/sec[1]/p[6]
|
3.2. Characteristics of the Studies
| 3.900391 |
biomedical
|
Study
|
[
0.99951171875,
0.0003173351287841797,
0.00039505958557128906
] |
[
0.9912109375,
0.0009717941284179688,
0.00746917724609375,
0.0001323223114013672
] |
This study suffers from some methodological flaws. Patients with poor image quality for any technology were excluded from the study. The authors do not provide the criteria for assessing image quality or the number of patients excluded because of poor image quality. Furthermore, patients were excluded from the study due to a significant time difference between examinations on 0.55 T and 1.5 T devices, and patients were not excluded at the beginning of the study but only at the stage of comparing the diagnostic efficacy of the technologies (detection of stroke, etc.). In the conclusion of the study, the authors point out that a so-called convenient sample was used with limited representativeness in relation to the general population. The study also did not adequately describe the approach to selecting patients for the control group. All the above limitations of the study may result in a high risk of bias in the results of this study.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p33
|
PMC11276230
|
sec[2]/sec[1]/p[7]
|
3.2. Characteristics of the Studies
| 2.060547 |
biomedical
|
Study
|
[
0.98388671875,
0.001514434814453125,
0.01474761962890625
] |
[
0.9521484375,
0.024444580078125,
0.022430419921875,
0.0007677078247070312
] |
The summary results of all included studies are presented in the following Table 3 .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
PMC11276230_p34
|
PMC11276230
|
sec[2]/sec[2]/p[0]
|
3.3. Quality Assessment
| 4.023438 |
biomedical
|
Study
|
[
0.9990234375,
0.0004737377166748047,
0.0003199577331542969
] |
[
0.99853515625,
0.00044274330139160156,
0.0010709762573242188,
0.00008302927017211914
] |
The QUADAS tool was employed to assess the risk of bias ( Table S3 ). Two studies were evaluated, wherein, in line with the research question, one study was assessed to have a high risk in the patient selection domain. The other exhibited a risk in the flow and timing domain. For instance, in the study Rusche 2022 , the patient selection process for the control group needed to be more adequately described. In the study Osmanodja 2023 , although the same reference standard (1.5 T) was utilised, not all examinations were conducted at the same facility. These are factors that could introduce bias into the outcomes.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p35
|
PMC11276230
|
sec[3]/p[0]
|
4. Discussion
| 3.748047 |
biomedical
|
Study
|
[
0.99951171875,
0.0002028942108154297,
0.0005030632019042969
] |
[
0.92626953125,
0.00383758544921875,
0.069580078125,
0.00025653839111328125
] |
We found only two papers that directly compare the quality of images acquired with a full-body scanner with low magnetic induction and a conventional MRI machine using 1.5 T. Several papers have also been published using prototype LF MRI scanners, typically 1.5 T scanners with magnetic inductance reduced to 0.55 T. However, these devices were not approved for clinical use and were used only in research mode. Therefore, we excluded these studies. Based on our analysis, we believe that there is potential for LF MRI machines, especially as a complement to the already established scanners using 1.5 and 3 T.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p36
|
PMC11276230
|
sec[3]/p[1]
|
4. Discussion
| 2.4375 |
biomedical
|
Other
|
[
0.9951171875,
0.0014276504516601562,
0.0033512115478515625
] |
[
0.0797119140625,
0.916015625,
0.0032329559326171875,
0.001117706298828125
] |
We believe that a study to identify suitable applications for low-field scanners would be essential. Lower costs for low-field equipment, as well as lower operating costs would make MRI examinations more affordable for patients and could also reduce waiting times for examinations. Early diagnosis can be important for further prevention of disease progression, especially in oncology.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p37
|
PMC11276230
|
sec[3]/p[2]
|
4. Discussion
| 2.097656 |
biomedical
|
Other
|
[
0.9912109375,
0.0018291473388671875,
0.0070343017578125
] |
[
0.0158538818359375,
0.982421875,
0.0009188652038574219,
0.0007557868957519531
] |
With the increasing use of artificial intelligence in image processing, images from LF MRI machines could be sufficient for a growing number of diseases, and LF MRI machines could be used alone in hospitals without a 1.5 or 3 T scanner.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p38
|
PMC11276230
|
sec[3]/p[3]
|
4. Discussion
| 3.972656 |
biomedical
|
Study
|
[
0.9990234375,
0.0005011558532714844,
0.00031113624572753906
] |
[
0.95263671875,
0.0005574226379394531,
0.046630859375,
0.0002187490463256836
] |
All identified studies had an observational design without rigorous checking for the potential risk of bias, which could result in, for example, a higher likelihood of false negatives or failure to detect true differences in measurement results. The sample of patients in the identified studies was small (9 and 27) and not representative of the target population in terms of age, gender, heterogeneity of disease status, etc. Only one area was affected by the identified studies, namely brain imaging. In both identified studies, patients underwent repeated examinations using 0.55 T and 1.5 T MRI technologies within a short time interval. The results of the examinations were analysed by two raters (blinded and unblinded). The studies examined indicators of technical image quality (noise, contrast, etc.), lesion size, and ability to diagnose stroke. None of the identified studies investigated whether the use of a 0.55 T MRI device would lead to a change in patient health outcomes or clinical management compared with 1.5 T MRI scanners.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999995 |
PMC11276230_p39
|
PMC11276230
|
sec[3]/p[4]
|
4. Discussion
| 3.931641 |
biomedical
|
Other
|
[
0.99853515625,
0.00054168701171875,
0.000988006591796875
] |
[
0.349365234375,
0.35400390625,
0.295654296875,
0.001140594482421875
] |
LF MR devices generally have less influence on the tissue under examination. For comparable examinations, LF MR devices have a lower SAR (specific absorption rate) at the patient and less heating in the area under examination, reducing the risk of interaction with implants and reducing acoustic noise. On the other hand, LF MR devices will produce images with a poorer signal-to-noise ratio (SNR) compared to conventional devices at similar examination times, resulting in lower geometric resolution, longer examination times, smaller field of view (FOV) and less benefit from the use of gadolinium contrast agent .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p40
|
PMC11276230
|
sec[3]/p[5]
|
4. Discussion
| 3.890625 |
biomedical
|
Study
|
[
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[
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With new artificial intelligence-based image processing methods, the reconstructed methods can improve the signal-to-noise ratio, and the disadvantages of low magnetic fields can be suppressed. Also, artefacts caused by e.g., metal implants are lower in low magnetic field MRI systems compared to 1.5 T and 3 T. In general, lower magnetic induction leads to shorter T1 times and, conversely, longer T2 times, allowing shorter TR and longer spin echo acquisition sequences .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
PMC11276230_p41
|
PMC11276230
|
sec[3]/sec[0]/p[0]
|
4.1. Limitations
| 3.544922 |
biomedical
|
Review
|
[
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[
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The main limitation of this systematic review is the lack of evidence linking the results of imaging by different MRI technologies to the impact on clinically relevant outcomes, i.e., patient diagnosis, treatment, and clinical outcomes.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
PMC11276230_p42
|
PMC11276230
|
sec[3]/sec[0]/p[1]
|
4.1. Limitations
| 3.861328 |
biomedical
|
Review
|
[
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[
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In the context of a systematic review, 39 studies were analysed after screening titles and abstracts. Only two studies met the predefined criteria. Excluded studies were assessed as inappropriate in terms of publication type (e.g., review article) or study type (e.g., commentary). Additional excluded studies compared the assessed technology with an inappropriate comparator (e.g., Computed Tomography) or had an inappropriate study population or outcome . There were also studies excluded due to inappropriate technology . These were comparative studies on prototypes that were not included because these prototypes represented experimental devices, were yet to be on the market, and had different technical parameters from devices on the market.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
PMC11276230_p43
|
PMC11276230
|
sec[3]/sec[0]/p[2]
|
4.1. Limitations
| 1.93457 |
biomedical
|
Other
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[
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[
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Also, only one type of scanner (Siemens) passed the original criteria, i.e., a whole-body scanner with a low inductance lower than 1 T that is approved for clinical usage.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p44
|
PMC11276230
|
sec[3]/sec[0]/p[3]
|
4.1. Limitations
| 2.255859 |
biomedical
|
Other
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[
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The amount of literature on the diagnostic efficacy of MRI technologies may be limited in part due to the existing legislative framework for medical device regulation. Current, and especially previously applicable, regulations do not require device manufacturers to provide extensive clinical studies demonstrating clinical and diagnostic efficacy for the patient. For these reasons, manufacturers of MRI technologies are not “forced” to conduct similar studies that examine the impact of the technology on the clinical outcomes of patients.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
PMC11276230_p45
|
PMC11276230
|
sec[3]/sec[1]/p[0]
|
4.2. Perspectives
| 2.712891 |
biomedical
|
Other
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[
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[
0.00873565673828125,
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LF MRI imaging systems generally require less space for installation and are lighter in weight than the conventional 1.5 T and 3 T MRI systems commonly used in clinical practice, making the installation requirements of LF MRI systems more flexible. The scanners are lighter in weight, whereas high-field MRI systems have a minimum weight of 3 tonnes. In addition, high-field systems require more separate rooms (examination rooms, workrooms and technical rooms with powerful electronics). Due to their ease of installation, LF MRI systems can be used in operating rooms, interventional theatres and emergency departments .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999995 |
PMC11276230_p46
|
PMC11276230
|
sec[3]/sec[1]/p[1]
|
4.2. Perspectives
| 4.058594 |
biomedical
|
Study
|
[
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[
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According to international studies, LF MR systems can offer cost-saving opportunities due to lower production costs and reduced installation and operation requirements. According to a study by Vosshenrich et al. , the acquisition cost of LF MR systems is approximately 43% lower than that of 1.5 T systems, comparable in software and coil equipment. Cost reductions also occur in shipping, as the weight of the instrument is 25% less than for the 1.5 T and 3 T systems, which can cut the cost per carrier in half. Weight and size also affect on-site transportation, which can sometimes be much simpler (without a crane, without building reconstruction and with other modifications). In addition, according to the authors of this study, there is no need for refrigeration equipment due to the minimal amount of helium. Significant savings also result from lower requirements for ventilation, cooling, electromagnetic shielding and wiring. According to the authors, MRI devices allow for savings in installation and maintenance costs compared to higher-intensity MRI systems. Lower low-field equipment and operating costs could also lead to improved patient care in developing countries and better access to MRI scans.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p47
|
PMC11276230
|
sec[4]/p[0]
|
5. Conclusions
| 3.566406 |
biomedical
|
Other
|
[
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[
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Technical development has contributed significantly to the improvement of the image quality of LF MRI systems and their diagnostic efficacy. The low magnetic induction value means that in specific cases, the LF MRI system is preferable to standard clinical devices with 1.5 T and 3 T. However, it has some disadvantages . Therefore, low magnetic field induction devices cannot currently be seen as fully-fledged devices suitable for comprehensive examinations of a wide range of patients in many different areas, but are rather suitable as a complement to standard 1.5 T and 3 T magnetic induction devices, but this may change with further development, particularly in the field of SW .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
PMC11276230_p48
|
PMC11276230
|
sec[4]/p[1]
|
5. Conclusions
| 3.630859 |
biomedical
|
Review
|
[
0.9990234375,
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[
0.377685546875,
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] |
According to a literature search, there is limited peer-reviewed scientific evidence on the accuracy and diagnostic efficacy of LF MRI compared to 1.5 T devices. Well-designed, larger clinical trials are needed to draw valid conclusions regarding how effective and accurate the new 0.55 T MRI technology is compared to conventional 1.5 T MRI technology.
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p49
|
PMC11276230
|
sec[4]/p[2]
|
5. Conclusions
| 3.529297 |
biomedical
|
Other
|
[
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[
0.0618896484375,
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LF MRI systems can be used especially in specific examinations where low magnetic field induction seems to be advantageous, such as reduction of artefacts from metal implants or reduction of the influence of different susceptibility of the examined tissues, e.g., lung tissue . Due to the lower SAR, this technique is also suitable where it is necessary to limit possible interaction with medical devices or effects on metal implants .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
PMC11276230_p50
|
PMC11276230
|
sec[4]/p[3]
|
5. Conclusions
| 2.144531 |
biomedical
|
Other
|
[
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] |
[
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Given the anticipated further development, it can be expected that LF MRI systems will be a suitable complement to existing MRI imaging instrumentation, reducing the cost of MRI examinations and “lightening” the burden on standard clinical devices .
|
[
"Barbora Mašková",
"Martin Rožánek",
"Ondřej Gajdoš",
"Evgeniia Karnoub",
"Vojtěch Kamenský",
"Gleb Donin"
] |
https://doi.org/10.3390/diagnostics14141564
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p0
|
39056915
|
sec[0]/p[0]
|
1. Introduction
| 3.396484 |
other
|
Other
|
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[
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Learning from time-ordered data represents an important problem in machine learning and AI. One of the first approaches used in time series modeling was to predict future values of time series from previous ones, using (auto) regressive or moving average models . Later on, it was shown how learning from such data can benefit from the identification of latent states and their sequences, performed through hidden Markov models (HMMs) or Markov switch models . The usage and applicability of these tools was greatly enhanced by the introduction of computationally scalable and efficient strategies for solution (e.g., the Baum–Welch algorithm ) and inference of the most likely sequences of latent states (Viterbi paths) .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p1
|
39056915
|
sec[0]/p[1]
|
1. Introduction
| 2.453125 |
other
|
Other
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[
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Recently, deep learning methods became increasingly popular in time series analysis applications. Deep neural networks (DNNs) gained the ability to capture temporal information thanks to several advancements such as the use of recurrent connectivity , convolution in time , memory , or the attention layers in transformers models . Those factors have also significantly increased the capabilities of deep learning in learning from text and sequence data. Nevertheless, despite their success, explainability and computational cost scaling remain very challenging issues in DNN applications . This is particularly relevant for models that operate in the so-called overparametrized regime and on time series .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p2
|
39056915
|
sec[0]/p[2]
|
1. Introduction
| 3.564453 |
other
|
Review
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A mathematical framework of approximate entropic learning that was introduced very recently promises to provide robust, computationally scalable, and explainable ways of machine learning and AI in the so-called “small data” regime, when the underlying learning task is highly underdetermined due to a large problem dimension and relatively small data statistics size. Entropic learning methods have been successfully applied to various domain disciplines, demonstrating superior performance on a range of long-standing “small data learning” problems in weather/climate research (like the intra-seasonal El Nino prediction) , in material sciences (like detection of material inhomogeneities from magnetic imaging data) , in biomedicine (like learning from omics data , in processing of ultra-noisy CT images in the ultra-low radiation regime ), and in economics (like prediction of stock over- and under- performance based on short and non-stationary company data time series) .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999999 |
39056915_p3
|
39056915
|
sec[0]/p[3]
|
1. Introduction
| 1.633789 |
other
|
Other
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[
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In the following, we provide more details on the entropic learning and present a novel extension of this methodology that allows learning from short and noisy (time-)ordered data.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p4
|
39056915
|
sec[0]/sec[0]/p[0]
|
1.1. Denoising Time Series
| 3.351563 |
biomedical
|
Study
|
[
0.74609375,
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[
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One common task in time series analysis is the removal of noise. Let us consider, as an example, the application of denoising a signal obtained from a Markov process that alternates between different states. In each time point, a value is sampled from a state-dependent probability distribution. This is illustrated in Figure 1 A, where two normal distributions are used as probability distributions for each state, each possessing its own mean, but having the same variance.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p5
|
39056915
|
sec[0]/sec[0]/p[1]
|
1.1. Denoising Time Series
| 4.152344 |
biomedical
|
Study
|
[
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[
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Let us consider the identification of the state at a given time by using techniques that do not intrinsically possess a notion of order or time, for example, k-means clustering . Using this technique involves calculating mean values and the assignments of each point to clusters is given by inspecting the Euclidean distance. Note how the same answer would be obtained for any permutation of the input data. That is because k-means is invariant with respect to ordering of the data points and ignores the time information. The assignment can be performed on new data by calculating the optimal parameters from a portion of recording where labels are given, and applying them to a portion without labels. For situations with low levels of noise and with mean values of the state-dependent distributions that are sufficiently far apart , k-means clustering can correctly identify the states through the affiliation of each data point to each cluster. This is not surprising, since the data are inherently clustered, as each state is characterized by a specific distribution of the data points, and the distributions can be separated. However, lower signal-to-noise ratios or overlapping mean values can rapidly lead to degradation in performance, as the clusters cannot be easily separated anymore. As illustrated in Figure 1 A, in the bottom right panel, it is easy to understand why in this case, i.e., with large standard deviation, points belonging to the red state may be mistaken for points emitted in the blue state, by virtue of their mean being closer to 1 than to 2, and vice versa. Even incorporating the information about the labels, by using as assignment the labels of the training dataset, would not improve the performance on the test dataset of such a classifier.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p6
|
39056915
|
sec[0]/sec[0]/sec[0]/p[0]
|
1.1.1. FEMH1
| 4.265625 |
biomedical
|
Study
|
[
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[
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By including an additional term to the optimization problem solved while finding the k-means solution, it is possible to introduce a penalty that considers a notion of smoothness, such as the H 1 seminorm , when solving the problem. This method, which is called FEMH1 since it is based on the finite elements method , consists of finding the optimal parameters Γ ∗ and C ∗ that, given a data matrix X ∈ R D × T with D features and T data points, minimize the following functional: (1) L F E M H 1 = ∑ t = 1 T ∑ k = 1 K ∑ d = 1 D Γ k , t ( X d , t − C d , k ) 2 + ε 2 ∑ k = 1 K ∑ t = 1 T − 1 ( Γ k , t + 1 − Γ k , t ) 2 under the condition that Γ is a stochastic matrix, i.e.,: (2) ∀ t , k : 0 ≤ Γ k , t ≤ 1 , (3) ∀ t : ∑ k = 1 K Γ k , t = 1 , where C ∈ R D , K is a matrix collecting a set of D -dimensional points (one for each cluster), Γ ∈ K × T is a matrix expressing the affiliation probability of each data point to any of the K clusters, and ε is a parameter which controls the relative weight of each term of the problem (discretization vs. smoothness) . Problem (1) can be solved iteratively by finding the optimal values of C and Γ while keeping, respectively, Γ and C fixed. This formulation retains the simplicity of the k-means algorithm, together with its efficiency in terms of computational complexity, and is able to achieve impressive levels of denoising at very small signal-to-noise ratios, while the main computational cost of this algorithm is the quadratic programming (QP) problem introduced when solving for Γ , an efficient solver for this step has been formulated by leveraging the structure of the specific problem, and is described in .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p7
|
39056915
|
sec[0]/sec[0]/sec[1]/p[0]
|
1.1.2. Overlapping Means
| 3.632813 |
biomedical
|
Study
|
[
0.73193359375,
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[
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In the previous section, we discussed the inclusion of a notion of smoothness to bias the solution towards one that displays less pronounced regime switching. This, however, does not grant a good performance in case of overlapping means. Indeed, if the state-dependent distributions possess the same mean but a different variance, the technique above will not necessarily be able to correctly assign data points to the right cluster. This is illustrated in Figure 1 B, where the two state-dependent distributions are selected to be normal distributions, with the same mean and different standard deviation. Note how the second dimension is uniformly distributed, and a scatter plot of the first two dimensions (right panel) leads to a problem that is not easily separable, even including smoothness.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p8
|
39056915
|
sec[0]/sec[0]/sec[1]/p[1]
|
1.1.2. Overlapping Means
| 4.09375 |
biomedical
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Study
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[
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[
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A way to obviate to this issue can be the use of a more general set of distributions instead of centroids (which can be considered as a Delta distribution for each cluster), and of likelihood instead of Euclidean distances, to assign points, in a similar way to Gaussian mixture models (GMMs) . GMMs involve fitting multivariate Gaussian distributions to data, by using the expectation maximization algorithm. The result of using this method is the description of the data using a mixture of distributions with the highest likelihood. The advantage introduced by this approach is that it allows, e.g., to recognize clusters having overlapping means but different variance. The price, however, is that (i) the technique becomes a parametric method, and thus we must be able to confidently assume that the data are indeed classifiable using a mixture of Gaussian distributions , and (ii) the use of multivariate Gaussian distributions can translate to an elevated computational cost in the case of data with high dimensionality, which is often the case in practical applications and most notably in natural sciences.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p9
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39056915
|
sec[0]/sec[1]/sec[0]/p[0]
|
1.2.1. Small Data
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biomedical
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Study
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A disadvantage of neural networks is that, in order to learn robust functions, they tend to require a considerable amount of training data, which lead to coining the term “Big Data”, directly referring to the need for a large amount of training samples . It is to be noted that the needed amount of training data directly depends on the dimensionality of the problem at hand. The opposite of “Big Data” is “Small Data”, which instead refers to a situation where the number of dimensions (or features) is elevated, and/or the amount of data points is low . A concrete example is from the field of -omics, where technical advancements rendered possible to measure from a small population an extremely rich set of features, and often the dimensionality can exceed the number of instances . This situation is traditionally challenging, as in induces overfitting, where models can learn perfectly what they have seen during training, but are not able to generalize to novel data .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p10
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39056915
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sec[0]/sec[1]/sec[1]/p[0]
|
1.2.2. High Dimensionality
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biomedical
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Study
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In many cases, the dimensions that are actually relevant with respect to the learning task are often only a subset or a subspace of the original ones. Redundant or irrelevant measures can constitute a large part of the training data, which can contribute to the cost of the fitting without providing advantages; therefore, their exclusion constitutes a benefit. Common machine learning techniques do not include the possibility to identify and select the relevant dimensions. Traditionally, the subset or the subspace of relevant feature is selected before the training in a separate step in which other tools, such as principal component analysis (PCA) , tSNE , or UMAP , are used for preprocessing . It is important to notice, however, that those techniques (in their original formulation) are unsupervised, and thus are not “aware” of the learning problem that will subsequently receive and use their output. PCA, for example, will produce an approximation of the data by projection on a lower dimensional (linear) manifold, such that most of the variance of the original data is retained in the approximation. This is not necessarily the projection that (i) better separates the label, or (ii) better represents the data, given the linearity of the manifold. Similar arguments can be used with regards to unsupervised nonlinear dimensionality reduction methods used as preprocessing steps. This fact is illustrated in Figure 1 C, where the ideal nonlinear manifold would allow the simple separation of the two classes, but taking the first principal component would instead lead to inability to do so.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p11
|
39056915
|
sec[0]/sec[1]/sec[1]/p[1]
|
1.2.2. High Dimensionality
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biomedical
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Study
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Furthermore, in case of projection-based dimensionality reduction, it does not guarantee the simplification of the future data collection process, as all dimensions may be needed to perform the projection. Instead, the dimensionality reduction methods that return a subset of the features allow the use of further data, which only contain measurements in the relevant subset of features to be processed by the model. A variation that maximizes the separability between classes, linear discriminant analysis (LDA) , similarly does not take into account the entire learning problem and is based on a linear manifold, which may not, in general, be sufficient. Furthermore, LDA does not typically provide good results when the means of the clusters are overlapping. Moreover, both PCA and LDA can be negatively affected in terms of the performance in the conditions of small sample size with respect to the number of feature dimensions .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p12
|
39056915
|
sec[0]/sec[1]/sec[2]/p[0]
|
1.2.3. Entropic Learning
| 4.179688 |
biomedical
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Study
|
[
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[
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Entropic learning refers to a mathematical framework proposing a solution to the aforementioned problems, as it has shown the ability to successfully operate in the small data condition, outperforming state-of-the-art techniques in terms of both performance and training cost, and has been applied in various disciplines, including climate science , financial applications , medical imaging , natural sciences , and computer science (application to the reduction in weights in neural networks ). The central idea of the framework is to formulate the learning task as a single holistic mathematical problem that includes all of the standard pipeline for machine learning, including feature selection, discretization, and either classification or regression , thus removing the need for external dimensionality reduction. The classification variant (called eSPA+) uses as input a data matrix X ∈ R D × T , where D and T refer to the number of features and instances, respectively, and a label probability matrix Π ∈ M × T , where M is the number of possible labels. To fit the model, we seek the parameters S ∗ , Γ ∗ , W ∗ , Λ ∗ that minimize the following functional: (4) L eSPA + = 1 T ∑ d = 1 D W d ∑ t = 1 T ( X d , t − { S Γ } d , t ) 2 + ε E ∑ d = 1 D W d log ( W d ) − ε C L T ∑ m = 1 M ∑ t = 1 T Π m , t log ∑ k = 1 K Λ m , k Γ k , t , such that: (5) ∀ t , k : 0 ≤ Γ k , t ≤ 1 , (6) ∀ t : ∑ k = 1 K Γ k , t = 1 , (7) ∀ d : 0 ≤ W d ≤ 1 (8) ∑ d = 1 D W d = 1 , (9) ∀ m , k : 0 ≤ Λ m , k ≤ 1 (10) ∀ k : ∑ m = 1 M Λ m , k = 1
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p13
|
39056915
|
sec[0]/sec[1]/sec[2]/p[1]
|
1.2.3. Entropic Learning
| 4.164063 |
biomedical
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Study
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[
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[
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In Problem (4), each parameter can provide insight on the operation of the model and has a specific meaning, that will be described in the next paragraphs. Matrix Γ ∈ K , T , similarly to its role in Problem (1), is a stochastic matrix representing the probability of each data point to belong to each of the K clusters. The number of clusters K is an hyperparameter that can be learned from the data by using cross-validation. S ∈ R D × K describes the position of the centroid for each cluster, Λ ∈ M × K is a stochastic classification matrix that indicates, for each cluster, what is the probability of assuming each label, and W ∈ D is a probability vector indicating the contribution of each dimension. As with k-means, the space is implicitly discretized by a Voronoi tessellation, with the addition that each cell possesses a label probability distribution . The introduction of W , which is regularized using entropy (hence the name, Entropic learning), allows feature selection to be included in the solution of the problem. Thus, this formulation not only effectively allows combining discretization, dimensionality reduction and classification in a single problem, but also guarantees that each step is optimal with respect to the problem in its entirety. As with FEMH1, we can solve Problem (4) by iteratively solving the problem with respect to each single variable, considering the others fixed, until convergence is reached.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p14
|
39056915
|
sec[0]/sec[1]/sec[2]/p[2]
|
1.2.3. Entropic Learning
| 3.996094 |
biomedical
|
Study
|
[
0.962890625,
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[
0.96826171875,
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0.00012624263763427734
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Note that this is an entirely non-parametric method, i.e., we do not rely on any assumption of linearity as the optimal combination of discretization/dimensionality reduction/classification is learned from the data, “from the perspective of” the learning problem. This means, practically, that, for example, a dimension with a lot of variance but which is irrelevant to the learning problem will (rightfully) not be considered. The label probabilities for a data point are assigned through the use of Voronoi cells which can tessellate the feature space in any arbitrary possible way, effectively allowing nonlinear and non-dyadic relationships to be captured . The sensitivity to perturbations of this type of discretization can be precisely formulated in mathematical terms, through the definition of minimal adversarial distance .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p15
|
39056915
|
sec[0]/sec[1]/sec[2]/p[3]
|
1.2.3. Entropic Learning
| 3.53125 |
biomedical
|
Study
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[
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[
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This method proved to be able to operate in the small data regime , but it does not include a notion of time or ordering, and can suffer from the same limitation as FEMH1 with respect to overlapping means. In this work, we combine the two methodologies (FEMH1 with eSPA+), in order to expand the application to supervised classification problems to ordered data. This allows us to mutually mitigate the main weaknesses of the two methods, since the formulation of FEMH1 did not allow solving supervised problems, while eSPA+ does not allow to include time ordering information. At the same time, we endow each cluster with a probability distribution, so that the affiliation of new data points can be calculated using the likelihood instead of the Euclidean distance.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p16
|
39056915
|
sec[1]/sec[0]/p[0]
|
2.1. Mathematical Formulation of eSPA-Markov
| 3.896484 |
biomedical
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Study
|
[
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[
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As mentioned in Section 1 , the method we will describe, which we name eSPA-Markov, originates from the confluence of eSPA and FEMH1 . Let us define as input a data matrix X ∈ R D × T , where D is the number of dimensions, or features, and T is the size of the statistics, i.e., the number of sampled points. Since we are dealing with a supervised classification problem, we also accept as input a matrix of label probabilities Π ∈ M × T , where M is the number of possible labels. Note that Π is a matrix of probabilities, and as such it is assumed that each entry is a number between zero and one, and that each column of this matrix sums to one. Effectively, each column represents the discrete probability distribution over the possible M labels for a specific data point. This notation generalizes one-hot encoding, which is the special case where ∀ m , t : Π m , t ∈ { 0 , 1 } with m = 1 , 2 , … , M and t = 1 , 2 , … , T . In terms of our algorithm, there is no difference between having one-hot-encoded labels and probabilities.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p17
|
39056915
|
sec[1]/sec[0]/p[1]
|
2.1. Mathematical Formulation of eSPA-Markov
| 4.171875 |
biomedical
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Study
|
[
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As with eSPA, we would like to simultaneously find the optimal discretization of the input data, and assign to each of those cells a label probability distribution that is the best in term of Kullback–Leibler divergence between the reconstruction and the true labels. Furthermore, we also simultaneously select the most relevant features through the use of the vector W , which is regularized through its entropy. The functional to be minimized is the following: (11) L eSPA - Markov = ε L T ∑ d = 1 D ∑ k = 1 K ∑ t = 1 T W d Γ k , t L ( X d , t , θ d , k ) + ε E ∑ d = 1 D W d log ( W d ) − ε C L T ∑ m = 1 M ∑ t = 1 T Π m , t log ∑ k = 1 K Λ m , k Γ k , t + 1 T ∑ k 1 = 1 K ∑ k 2 = 1 K ∑ t = 1 T − 1 ( Γ k 1 , t + 1 − P k 1 , k 2 Γ k 2 , t ) 2 , which is subject to the following constraints: (5)–(10).
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p18
|
39056915
|
sec[1]/sec[0]/p[2]
|
2.1. Mathematical Formulation of eSPA-Markov
| 4.261719 |
biomedical
|
Study
|
[
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[
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In Equation (11), L represents a generic loss function, which can be, e.g., the Euclidean distance between the original data points and the centroid θ k for a given cluster k . Without a loss of generality, we will focus on the case where the loss is calculated using ℓ ( x , μ , σ ) , which is the negative 1 dimensional Gaussian log likelihood of a data point ( x ), and θ d , k are the parameters μ d , k , σ d , k of the centroid-dependent distributions. Doing so results in the following formulation: (12) L eSPA - Markov = ε L T ∑ d = 1 D ∑ k = 1 K ∑ t = 1 T W d Γ k , t ℓ ( X d , t , μ d , k , σ d , k ) + ε E ∑ d = 1 D W d log ( W d ) − ε C L T ∑ m = 1 M ∑ t = 1 T Π m , t log ∑ k = 1 K Λ m , k Γ k , t + 1 T ∑ k 1 = 1 K ∑ k 2 = 1 K ∑ t = 1 T − 1 ( Γ k 1 , t + 1 − P k 1 , k 2 Γ k 2 , t ) 2 , which is subject to the following constraints: (5)–(10). As previously mentioned, in Problem (12) ℓ ( x , μ , σ ) refers to the negative log likelihood: (13) ℓ ( x , μ , σ ) = 1 2 log ( 2 π σ 2 ) + ( x − μ ) 2 2 σ 2 , and P ∈ R K , K is a matrix that influences the transition between different clusters. It is possible to use for P a stochastic transition matrix expressing the transition probability between each state and each other. For increased computational simplicity, we solve Problem (12) after applying Jensen’s inequality: (14) L eSPA - Markov = ε L T ∑ d = 1 D ∑ k = 1 K ∑ t = 1 T W d Γ k , t ℓ ( X d , t , μ d , k , σ d , k ) + ε E ∑ d = 1 D W d log ( W d ) − ε C L T ∑ m = 1 M ∑ t = 1 T Π m , t ∑ k = 1 K log Λ m , k Γ k , t + 1 T ∑ k 1 = 1 K ∑ k 2 = 1 K ∑ t = 1 T − 1 ( Γ k 1 , t + 1 − P k 1 , k 2 Γ k 2 , t ) 2 which is subject to the following constraints: (5)–(10). We will now illustrate similarities and differences between this formulation and eSPA/FEMH1. The main framework is that of eSPA+, i.e., we can solve supervised learning problems, with the difference that we do not use matrix S ∈ R D × K to store the values of the centroids for each cluster, which is instead replaced by two new terms: μ ∈ R D × K and σ ∈ R D × K . The first is the counterpart of S in eSPA, which contains the position of the centroids for each cluster, and the second is a matrix of variances for each cluster and each dimension. Note that we propose reconstructing the data using combination of univariate Gaussian distributions, as we sum the log likelihood in each dimension independently. This is a rather parsimonious assumption as the Gaussian distribution is the least informative distribution that can be used, following the maximum entropy principle. Having mean and variances, instead of minimizing the squared distance between each data point and the discretized representation as performed in eSPA+, we instead minimize the sum of the negative log likelihood of each data point given the mean and variance for each cluster, scaled by the affiliation probability and the feature probability vector W .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999999 |
39056915_p19
|
39056915
|
sec[1]/sec[0]/p[3]
|
2.1. Mathematical Formulation of eSPA-Markov
| 1.719727 |
other
|
Other
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[
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[
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As with eSPA, we express the affiliation using the matrix Γ , but with the difference that each entry is allowed to be ∈ instead of being binary. This has the great advantage of allowing fuzzy clustering, despite coming with the cost of the absence of an analytical solution.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p20
|
39056915
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sec[1]/sec[0]/p[4]
|
2.1. Mathematical Formulation of eSPA-Markov
| 3.371094 |
biomedical
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Study
|
[
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[
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Another difference is the addition of a more general formulation of regularization through the ordering, which can be juxtaposed to the H 1 term, which is used in FEMH1 to bias the solution towards a solution that is sufficiently “smooth” . However, we introduce a transition penalization matrix P ∈ R K × K , which allows us to solve more general classes of problems. Indeed, in FEMH1, the assumption imposed is that the states are persistent, while the introduction of P allows different persistence levels. By choosing P to be an identity matrix of size K , we reduce this regularization term to that of FEMH1, which is what was used throughout this work.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p21
|
39056915
|
sec[1]/sec[0]/p[5]
|
2.1. Mathematical Formulation of eSPA-Markov
| 1.792969 |
other
|
Other
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[
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[
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Another difference is the placement of the coefficients that regulate the importance of each sub-problem, with the problem being a multicriteria optimization problem. In this work, the coefficient is in front of the likelihood term rather than in front of the H 1 term, as the former can assume values from a very large interval. Thus, this change in coefficient grants increased numerical stability to the optimization of the entire problem.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p22
|
39056915
|
sec[1]/sec[1]/p[0]
|
2.2. Solutions of the Individual Steps in the Optimization Problem
| 1.695313 |
biomedical
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Other
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[
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In the following section, we will discuss the solution of each individual step, as well as the solution of the entire minimization problem, together with the computation of prediction from unseen data.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p23
|
39056915
|
sec[1]/sec[1]/sec[0]/p[0]
|
2.2.1. Solution of μ and σ Steps
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other
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Other
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The procedure for finding the values of μ and σ that minimize the loss functional in Problem (14) can be treated together for simplicity. Both problems admit an analytical solution; namely, the optimal value for μ is found equivalently to that of S in eSPA, and the optimal value for σ is the standard deviation in each dimension, weighted by the cluster affiliations.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999999 |
39056915_p24
|
39056915
|
sec[1]/sec[1]/sec[1]/p[0]
|
2.2.2. Solution of the Γ Step
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other
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Other
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The solution to the problem of finding a value of Γ that minimizes the loss functional is very similar to that of the equivalent Γ problem in FEMH1 , featuring some adjustments in the linear term only. Therefore, it is possible to use the efficient SPG-QP solver to calculate the updated value of Γ .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p25
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39056915
|
sec[1]/sec[1]/sec[2]/p[0]
|
2.2.3. Solution of the Λ Step
| 2.910156 |
other
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Study
|
[
0.292724609375,
0.000751495361328125,
0.70654296875
] |
[
0.72216796875,
0.275390625,
0.0018110275268554688,
0.0005993843078613281
] |
The main difference between Problems (12) and (14) is the solution of the Λ step. Indeed, there exists no analytic solution for this step in the first case. Therefore, when solving Problem (12), it is necessary to use solvers based, e.g., on the interior point method. Instead, the solution of the Λ step in Problem (14) is equivalent to the solution of the Λ step in eSPA+. The optimal value Λ ∗ that minimizes the loss functional (14) under the constraints (9) and (10) can be computed using: (20) Λ m , k ∗ = Λ ^ m , k ∑ m = 1 M Λ ^ m , k . where Λ ^ m , k = ∑ t = 1 T Π m , t Γ k , t .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p26
|
39056915
|
sec[1]/sec[1]/sec[3]/p[0]
|
2.2.4. Solution of the W Step
| 3.642578 |
biomedical
|
Study
|
[
0.69189453125,
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0.307373046875
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[
0.884765625,
0.1141357421875,
0.0009975433349609375,
0.0003020763397216797
] |
The solution of the W problem, i.e., the value of W ∗ that minimizes the loss functional (14) for a given collection of the remaining parameters can be obtained analytically in an equivalent way as the computation of the optimal value of W in eSPA+, and can be computed using the softmax function: (21) W ∗ = exp − 1 T ε E b 1 D T exp − 1 T ε E b where (22) b d = ∑ t = 1 T ∑ k = 1 K Γ k , t ℓ ( X d , t , μ d , k , σ d , k ) .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p27
|
39056915
|
sec[1]/sec[1]/sec[4]/p[0]
|
2.2.5. Solution to the Entire Problem
| 3.888672 |
biomedical
|
Study
|
[
0.82763671875,
0.0006113052368164062,
0.1717529296875
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[
0.95556640625,
0.043792724609375,
0.0006785392761230469,
0.0001811981201171875
] |
The solution to the entire optimization problem of minimizing (12) or (14) can be found through iterative subspace algorithm, and is illustrated in Algorithm 1. Label predictions for a new dataset X t e s t , given values of W , μ , σ , Λ and hyperparameters ε E , ε L can be obtained by solving for Γ once, as illustrated in Lemma 2, using a random feasible initial value, to obtain the affiliations to the clusters. Note that, in this case, not having a corresponding label probability matrix Π requires one to calculate the value of Γ ∗ that minimizes Problem (14) under the constraints (5) and (6) while setting the value of ε C L to 0. Using the obtained Γ and the given matrix Λ , the label probabilities for each data point can be computed as: (23) Π ˜ = Λ Γ . Algorithm 1: eSPA-Markov fitting algorithm
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p28
|
39056915
|
sec[1]/sec[1]/sec[5]/p[0]
|
2.2.6. Direct One-Shot Learning
| 2.158203 |
other
|
Other
|
[
0.197998046875,
0.0008373260498046875,
0.80126953125
] |
[
0.2880859375,
0.7080078125,
0.0026569366455078125,
0.0009775161743164062
] |
The eSPA-Markov framework can be used also in a direct way to learn a model in a one-shot way (note: our definition of one-shot refers to learning the optimal parameters without iterative procedure, that can be applied to any other dataset originating from the same process, rather than the traditional definition employed in the field of large language model or computer vision), in the cases where it is possible to associate each centroid with a single label (and vice versa). Formal presentation of this procedure and the obtaining of assignments for any given test dataset is provided in the following theorems.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p29
|
39056915
|
sec[1]/sec[2]/p[0]
|
2.3. Experiments
| 1.493164 |
biomedical
|
Other
|
[
0.7734375,
0.0015707015991210938,
0.224853515625
] |
[
0.131103515625,
0.8671875,
0.0007328987121582031,
0.0009031295776367188
] |
All the experimental results were obtained using MATLAB , on a Dell PowerEdge R750 (Dell, Round Rock, TX, USA), with 2x Intel Xeon Platinum 8368 CPU (Intel, Santa Clara, CA, USA) (2.40 GHz), and 2048 GB of RAM memory.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p30
|
39056915
|
sec[1]/sec[3]/p[0]
|
2.4. Synthetic Data
| 4.011719 |
biomedical
|
Study
|
[
0.994140625,
0.00023186206817626953,
0.005756378173828125
] |
[
0.99853515625,
0.001399993896484375,
0.00016105175018310547,
0.000046372413635253906
] |
The synthetic dataset is generating by simulating a Markov chain with two possible states and a transition matrix of the following form: P = 1 − ε ε ε 1 − ε , where ε was chosen to be a small number (0.01). This enforces persistence, i.e., each state to be more significantly likely to be followed by itself rather than the other one. In order to ensure the presence of both labels in each cross-validation split, rather than using a realization of a Markov process, we generated steps with stochastically determined length, centered at an interval that guarantees the visiting of both states in each partition of the dataset.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p31
|
39056915
|
sec[1]/sec[3]/sec[0]/p[0]
|
2.4.1. Example 1
| 4 |
biomedical
|
Study
|
[
0.99462890625,
0.00025844573974609375,
0.0048980712890625
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[
0.99755859375,
0.0022716522216796875,
0.00022459030151367188,
0.00006437301635742188
] |
For each timestep, the system emits a measurement, sampled from a normal distribution with mean 0 and standard deviation being either σ 1 or σ 2 , dependent on the state of the Markov chain. Namely, in the first state, the standard deviation was set to 1, and in the second state was varied, in order to obtain different σ 1 / σ 2 ratios. The value of the ratio dictates the signal-to-noise ratio of the generated trace. A graphical representation of the projection on the first two dimensions of such a dataset is illustrated in the right panel of Figure 1 B.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p32
|
39056915
|
sec[1]/sec[3]/sec[1]/p[0]
|
2.4.2. Example 2
| 3.292969 |
biomedical
|
Study
|
[
0.9697265625,
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0.0296173095703125
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[
0.73583984375,
0.262939453125,
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0.0004298686981201172
] |
The measurement for each time step is collected from a bivariate normal distribution, which are generated using a covariance matrix of the form: C = ε 0 0 1 , where ε controls the thickness of the distribution.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p33
|
39056915
|
sec[1]/sec[3]/sec[1]/p[1]
|
2.4.2. Example 2
| 3.572266 |
biomedical
|
Study
|
[
0.955078125,
0.00043010711669921875,
0.04473876953125
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[
0.9677734375,
0.03125,
0.000583648681640625,
0.000156402587890625
] |
For the second state, the data was rotated with a rotation matrix with parameter α : R = cos ( α ) − sin ( α ) sin ( α ) cos ( α ) . In this scenario, α controls the angle between the two distributions, such that π / 2 refers to the case where the two distributions are superimposed with an angle of 90 degrees, i.e., they are orthogonal and simpler to separate, and in the π / 16 case instead, the two distributions will be largely overlapping. A graphical representation of such a dataset is illustrated in Figure 1 , in the right bottom panel.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p34
|
39056915
|
sec[1]/sec[3]/sec[2]/p[0]
|
2.4.3. Synthetic RNA Sequencing Inspired Toy Example
| 3.720703 |
biomedical
|
Other
|
[
0.9970703125,
0.0005254745483398438,
0.00218963623046875
] |
[
0.35888671875,
0.63720703125,
0.0025997161865234375,
0.0013427734375
] |
This example is based by the task of denoising DNA or RNA sequencing traces obtained using Nanopore technology . For simplicity, we generated an example reading using two bases (‘A’ and ‘B’), and with number of bases read at a given time (k-mer length) of 2. Each of their four possible combinations will correspond to a reading with a specific distribution of pore currents , and will persist in the pore for a dwell time that is selected from a combination-specific distribution. This example has a single dimension, and is used to illustrate the possibility to learn one-shot.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p35
|
39056915
|
sec[1]/sec[3]/sec[3]/p[0]
|
2.4.4. Extra Dimensions
| 3.257813 |
biomedical
|
Study
|
[
0.95947265625,
0.0004172325134277344,
0.040191650390625
] |
[
0.95947265625,
0.03973388671875,
0.0006165504455566406,
0.0002053976058959961
] |
Multivariate datasets of this kind were obtain in identical manner, with the exception that a number of additional “uninformative” dimensions were appended, with the same number of sampled points. Those extra D − 1 dimensions brought the dimensionality of the dataset to a total of D , and are sampled from the uniform distribution from the interval . Thus, both examples are scalable in terms of number of instances, dimensions and “difficulty”, which for the first example means how large the noise is and for the second one instead how overlapping the two distributions are.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p36
|
39056915
|
sec[1]/sec[4]/sec[0]/p[0]
|
Embedding
| 4.058594 |
biomedical
|
Study
|
[
0.97802734375,
0.0003218650817871094,
0.0216064453125
] |
[
0.99853515625,
0.0010061264038085938,
0.00021636486053466797,
0.00004094839096069336
] |
In order to provide time information to ML models that do not include order into account, we performed time embedding of the datasets with a variable window length . The length of the window was selected independently for each of those models as an hyperparameter using cross-validation from the following values: 10, 50, and 100. This is a version of Takens’ delayed embedding reconstruction that operates on multivariate data in the following way: (33) ϕ ( x ( : , t ) ) = [ x ( : , t ) , x ( : , t − 1 ) , … , x ( : , t − l ) ] , where l represents the length of the embedding time window. As a result, from a single data point x ( t ) ∈ R D , we obtain a new embedded representation of the data point ϕ ( x ( t ) ) ∈ R D × ( l + 1 ) . Only data points where the entire window was available were considered.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p37
|
39056915
|
sec[1]/sec[5]/p[0]
|
2.6. Machine Learning Methods
| 2.921875 |
biomedical
|
Study
|
[
0.8359375,
0.00046515464782714844,
0.1636962890625
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[
0.9130859375,
0.0858154296875,
0.0008864402770996094,
0.0002639293670654297
] |
For comparison, we used support vector machine (using the built-in MATLAB fitcsvm function) , random forest (using the built-in MATLAB treebagger function) , and deep learning. For deep learning, we used either a CNN network with a 1-D convolution layer, or a CNN-LSTM network the consisted of the same network with an addition of an LSTM layer and dropout . For example, 1, we also included the same CNN-LSTM network which was provided with the wavelet transform of the input data .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p38
|
39056915
|
sec[1]/sec[5]/sec[0]/p[0]
|
Cross-Validation
| 2.669922 |
biomedical
|
Study
|
[
0.8671875,
0.0006818771362304688,
0.1319580078125
] |
[
0.97607421875,
0.022796630859375,
0.0006961822509765625,
0.00019860267639160156
] |
In order to characterize the performance of each method on the problems at hand, we used cross-validation with triple splitting of the data. For every of the 20 cross-validation fold, we generated a dataset and split it in three equal parts, to be used as training, validation, and test. Note that the reported T in this work refers to the training data size, and not the total generated dataset size.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p39
|
39056915
|
sec[1]/sec[5]/sec[0]/p[1]
|
Cross-Validation
| 4.113281 |
biomedical
|
Study
|
[
0.98583984375,
0.0004737377166748047,
0.01373291015625
] |
[
0.99951171875,
0.0004172325134277344,
0.00023043155670166016,
0.000036716461181640625
] |
Hyperparameter selection was performed by exhaustively searching every possible hyperparameter combination for each method, with the grid reported in Table 1 , and training them using the training dataset. Quality of the prediction was evaluated using the area under the receiver operating curve (AUC), a metric that describes the discriminatory skill of a classifier. AUC values close to 0.5 denote chance level predictions, while instead 1 indicates perfect classification. In contrast to other common metrics (for example, accuracy), it enables robust performance assessments in situations of (strongly) imbalanced data . Then, the model with the best AUC when predicting the validation set was selected and its performance was evaluated on the test set. The training time refers to the training cost of the best model. The model labeled as “w-CNN-LSTM” refers to the same architecture and grid employed for the CNN-LSTM model, but with input provided as the wavelet transform of the data, using 12 voices per octave. eSPA-Markov was performed from 10 random initial points for each parameter combination. For the decision tree, the predictor selection “interaction-curvature” was only used for Example 1.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p40
|
39056915
|
sec[2]/p[0]
|
3. Results
| 3.568359 |
biomedical
|
Study
|
[
0.84619140625,
0.0005884170532226562,
0.1531982421875
] |
[
0.99755859375,
0.00218963623046875,
0.00036025047302246094,
0.00007236003875732422
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We will now describe the results of benchmarking the eSPA-Markov algorithm in comparison to the methods introduced in the previous section. In Figure 2 and Figure 3 , we present results obtained on the example number 1 (described in Section 2.4.1 ) for common machine learning and deep learning methods (respectively) and a fixed value of dimensionality ( D ) of 1. This condition therefore does not require the models to identify the relevant dimension within confounding ones, but reveals the ability to learn from the given time series. We trained all methods with datasets of increasing size in terms of available statistics, starting from an extremely limited amount of data (250 data points), to a moderate size to a more conspicuous amount of training samples .
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p41
|
39056915
|
sec[2]/p[1]
|
3. Results
| 4.125 |
biomedical
|
Study
|
[
0.99853515625,
0.00032973289489746094,
0.0013113021850585938
] |
[
0.99951171875,
0.0001379251480102539,
0.00036334991455078125,
0.000038504600524902344
] |
The goal of this comparison was not only to characterize the impact of limited amount of training data on the performance of the various algorithms, but also to investigate the effect of varying the signal-to-noise ratio of the data. Indeed, we repeated the comparisons for different values of σ -ratio, which is the ratio between the standard deviations of the distribution of the data in the two different states. An increase in the σ -ratio corresponds to decreasing levels of noise in the recording. This way, we can obtain discrimination curves for each method for the three conditions of data availability, which are plotted in the upper three panels. As expected, the performance for any method is reduced to random choice (AUC value close to 0.5) when the ratio is equal to 1 (i.e., there is no difference between the two states), as under those circumstances it is not possible to learn any distinction. It is possible to notice how, for each method, more training data leads to better performance in terms of the area under the ROC curve (AUC) on previously unseen test data. Note how the generalization ability of the investigated models, as illustrated with the difference in AUC between the training and testing sets, can increases with decreasing noise and data size. This is particularly noticeable for RF, while eSPA-Markov displays closer train and test scores. In the bottom three panels, instead, we report the computational cost for training the models, and illustrate the scaling of computational cost with respect to the level of noise and of the increase in the size of the data.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p42
|
39056915
|
sec[2]/p[2]
|
3. Results
| 3.564453 |
biomedical
|
Study
|
[
0.9599609375,
0.0004487037658691406,
0.039794921875
] |
[
0.99755859375,
0.00205230712890625,
0.00034999847412109375,
0.00006264448165893555
] |
In Figure 4 and Figure 5 , we report results obtained using datasets generated with the process described in example 1, the same as the previous figure, with the difference that in this case the number of dimensions used was 10. In order to successfully perform prediction of the labels associated with the data points, it is therefore necessary to identify the single relevant dimension in which there is a difference between the two classes while being provided with nine additional uninformative dimensions. Results are plotted in the same way as Figure 2 , including comparison of the AUC on the test dataset in the top row, the generalization ability in the middle row and the computational cost in the bottom row by varying the value of σ -ratio at three different levels of data size.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p43
|
39056915
|
sec[2]/p[3]
|
3. Results
| 2.800781 |
biomedical
|
Study
|
[
0.763671875,
0.0008368492126464844,
0.2352294921875
] |
[
0.97705078125,
0.022064208984375,
0.0009136199951171875,
0.00020825862884521484
] |
In Figure 6 and Figure 7 , we report the results on example 2 (described in Section 2.4.2 ), keeping a fixed amount of available statistics for training , but varying the dimensionality of the dataset. The leftmost plots represent datasets with dimension (D) equal to 5, the middle ones instead have dimension equal to 100 and on the right the dimensionality is instead of dimension 500. This comparison captures the performance and the computational cost of fitting the different algorithms for data that is increasingly “small” (using the definition provided in Section 1.2.1 ). For this example, we examined the performance by varying the angle between the two distributions ( α ). Note that in comparison, smaller values of α (on the right) represent a more challenging situation.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999998 |
39056915_p44
|
39056915
|
sec[2]/p[4]
|
3. Results
| 2.03125 |
biomedical
|
Other
|
[
0.8994140625,
0.0023326873779296875,
0.09808349609375
] |
[
0.174560546875,
0.82080078125,
0.0029144287109375,
0.0016317367553710938
] |
Figure 8 depicts the outcome of applying the direct one-shot learning methodology, on a toy example inspired by Oxford Nanopore sequencing.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p45
|
39056915
|
sec[2]/p[5]
|
3. Results
| 4.070313 |
biomedical
|
Study
|
[
0.99951171875,
0.00019288063049316406,
0.00031256675720214844
] |
[
0.974609375,
0.0235137939453125,
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0.0004191398620605469
] |
This example is of particular relevance, as this type of data represents a paradigm shift in sequencing technology, enabling the reading of long sequences in the form of noisy recording of current . Briefly, this molecular biology technique allows the sequencing of nucleic acid polymers to identify the order of the bases. To do so, individual molecules are moved across an impermeable membrane through a pore, while the current across the pore can be read. Within the pore, at any given time of the passage of the molecule, it is possible to find a certain (fixed) number of bases, which is called the length of the k-mer. For our toy example, we simulated an experiment as described above, with two possible bases (“A” and “B”) and a k-mer length of 2.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999999 |
39056915_p46
|
39056915
|
sec[2]/p[6]
|
3. Results
| 4.074219 |
biomedical
|
Study
|
[
0.9990234375,
0.00018513202667236328,
0.0007109642028808594
] |
[
0.9990234375,
0.0007967948913574219,
0.00016045570373535156,
0.000049233436584472656
] |
Each combination of bases will correspond to a unique distribution of currents that can be read by the device, which we simulated by introducing for each combination a specific mean and standard deviation. Moreover, as the passage though the pore is slower than the sampling rate of the instrument, each position along the macromolecule will correspond to several readings. It is also to be noted that each possible combination tends to exhibit a specific dwell time, i.e., the typical length of the sampling is dependent on the combination. This can be seen in Figure 8 , as, e.g., the combination “BA” (colored in green) typically has less persistent (shorter) reading times compared the combination “BB” (in blue).
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
39056915_p47
|
39056915
|
sec[2]/p[7]
|
3. Results
| 2.111328 |
biomedical
|
Other
|
[
0.716796875,
0.0015649795532226562,
0.281494140625
] |
[
0.093017578125,
0.9052734375,
0.00102996826171875,
0.000499725341796875
] |
As each pore in the machine is reading an independent signal, the data are generally a collection of single-dimensional vectors rather than a multivariate unified dataset. Therefore, in this case, there is no need to employ W , as it can be considered to be equal to 1 for the only dimension present.
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999997 |
39056915_p48
|
39056915
|
sec[2]/p[8]
|
3. Results
| 3.214844 |
biomedical
|
Study
|
[
0.92236328125,
0.0006213188171386719,
0.07720947265625
] |
[
0.962890625,
0.036102294921875,
0.00079345703125,
0.0002428293228149414
] |
By application of the direct one-shot learning methodology, we obtain near-perfect reconstruction, in virtue of being able to select the optimal value for the hyperparameter (in this case, only ε L , since the data has one dimension). Application of this model to test data, which were generated starting from a different sequence, also provides near-perfect reconstruction of the labels for each time instance (right panels).
|
[
"Davide Bassetti",
"Lukáš Pospíšil",
"Illia Horenko"
] |
https://doi.org/10.3390/e26070553
|
N/A
|
https://creativecommons.org/licenses/by/4.0/
|
en
| 0.999996 |
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