| { | |
| "paper_id": "W17-0207", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T04:20:24.988847Z" | |
| }, | |
| "title": "Aligning phonemes using finte-state methods", | |
| "authors": [ | |
| { | |
| "first": "Kimmo", | |
| "middle": [], | |
| "last": "Koskenniemi", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "University of Helsinki Helsinki", | |
| "location": { | |
| "country": "Finland" | |
| } | |
| }, | |
| "email": "[email protected]" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
| "identifiers": {}, | |
| "abstract": "The paper presents two finite-state methods which can be used for aligning pairs of cognate words or sets of different allomorphs of stems. Both methods use weighted finite-state machines for choosing the best alternative. Individual letter or phoneme correspondences can be weighted according to various principles, e.g. using distinctive features. The comparison of just two forms at a time is simple, so that method is easier to refine to include context conditions. Both methods are language independent and could be tuned for and applied to several types of languages for producing gold standard data. The algorithms were implemented using the HFST finite-state library from short Python programs. The paper demonstrates that the solving of some non-trivial problems has become easier and accessible for a wider range of scholars.", | |
| "pdf_parse": { | |
| "paper_id": "W17-0207", | |
| "_pdf_hash": "", | |
| "abstract": [ | |
| { | |
| "text": "The paper presents two finite-state methods which can be used for aligning pairs of cognate words or sets of different allomorphs of stems. Both methods use weighted finite-state machines for choosing the best alternative. Individual letter or phoneme correspondences can be weighted according to various principles, e.g. using distinctive features. The comparison of just two forms at a time is simple, so that method is easier to refine to include context conditions. Both methods are language independent and could be tuned for and applied to several types of languages for producing gold standard data. The algorithms were implemented using the HFST finite-state library from short Python programs. The paper demonstrates that the solving of some non-trivial problems has become easier and accessible for a wider range of scholars.", | |
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| "section": "Abstract", | |
| "sec_num": null | |
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| ], | |
| "body_text": [ | |
| { | |
| "text": "In this paper, finite-state automata (FSA) and finite-state transducers (FST) are used as the basic tools. In particular, the utility of weighted finitestate transducers (WFST) and automata (WFSA) is demonstrated.", | |
| "cite_spans": [], | |
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| "section": "Background", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "Finite-state toolboxes have been freely available for some time, e.g. OpenFST (Mohri et al., 2002) , Xerox XFST (Beesley and Karttunen, 2003) , HFST -Helsinki Finite-State Transducer Technology (Lind\u00e9n et al., 2011) , SFST (Schmid, 2005) and Foma (Hulden, 2009) . These implementations have been accessible as libraries for C or C++ programmers, some also as command line programs which can be pipelined (HFST), and some as scripting languages (XFST, SFST, Foma, HFST) . Combining independent programs using shell commands is easy and suitable for many kinds of tasks, but certain combinations of operations are difficult or impossible to achieve this way. Even the XFST and SFST scripting languages have their restrictions, especially for looping, testing and input/output. It seems that none of the tasks discussed in this paper could be conveniently solved using the XFST or SFST scripting language.", | |
| "cite_spans": [ | |
| { | |
| "start": 78, | |
| "end": 98, | |
| "text": "(Mohri et al., 2002)", | |
| "ref_id": "BIBREF12" | |
| }, | |
| { | |
| "start": 107, | |
| "end": 141, | |
| "text": "XFST (Beesley and Karttunen, 2003)", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 144, | |
| "end": 215, | |
| "text": "HFST -Helsinki Finite-State Transducer Technology (Lind\u00e9n et al., 2011)", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 223, | |
| "end": 237, | |
| "text": "(Schmid, 2005)", | |
| "ref_id": "BIBREF15" | |
| }, | |
| { | |
| "start": 242, | |
| "end": 261, | |
| "text": "Foma (Hulden, 2009)", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 444, | |
| "end": 468, | |
| "text": "(XFST, SFST, Foma, HFST)", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
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| "section": "Background", | |
| "sec_num": "1" | |
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| "text": "More recently, most finite-state packages have been also available through Python in one way or the other. The HFST Python embedding was used here for a few reasons: it is implemented for Python 3 which uses Unicode as its native code, one could use weighted transducers, and HFST contained the kinds of functions that were needed.", | |
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| "section": "Background", | |
| "sec_num": "1" | |
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| "text": "Automatic alignment of letters or phonemes is relevant in several areas, e.g. finding the pronunciation of unknown words or names in speech synthesis, see e.g. (Jiampojamarn et al., 2007) , phonetically based spelling correction, see e.g. (Toutanova and Moore, 2002) , in comparing cognate words in historical linguistics, see e.g. (Covington, 1998; Kondrak, 2000) , reconstructing proto-languages, e.g. (Bouchard-C\u00f4t\u00e9 et al., 2009) and in many other areas of linguistics. Character by character alignment can be approached as a machine learning problem, as in (Ciobanu and Dinu, 2014) or as a linguistic task as is done in this paper. The methods presented here make use of general properties of phonology. Still, more specific rules can be included where needed.", | |
| "cite_spans": [ | |
| { | |
| "start": 160, | |
| "end": 187, | |
| "text": "(Jiampojamarn et al., 2007)", | |
| "ref_id": "BIBREF6" | |
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| { | |
| "start": 239, | |
| "end": 266, | |
| "text": "(Toutanova and Moore, 2002)", | |
| "ref_id": "BIBREF17" | |
| }, | |
| { | |
| "start": 332, | |
| "end": 349, | |
| "text": "(Covington, 1998;", | |
| "ref_id": "BIBREF4" | |
| }, | |
| { | |
| "start": 350, | |
| "end": 364, | |
| "text": "Kondrak, 2000)", | |
| "ref_id": "BIBREF8" | |
| }, | |
| { | |
| "start": 404, | |
| "end": 432, | |
| "text": "(Bouchard-C\u00f4t\u00e9 et al., 2009)", | |
| "ref_id": "BIBREF2" | |
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| { | |
| "start": 561, | |
| "end": 585, | |
| "text": "(Ciobanu and Dinu, 2014)", | |
| "ref_id": "BIBREF3" | |
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| "section": "Previous work on alignment", | |
| "sec_num": "2" | |
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| "text": "Covington (1998) used a special six step measure for phoneme distances and (Nerbonne and Heeringa, 1997) used phonetic features and the plain Levenshtein distance between sequences of features in order to estimate differences between Dutch dialects. (Somers, 1999) used distinctive features in the comparison and his algorithm used the (manually marked) stressed vowels as the starting point whereas other approaches progressed from left to right. All these approaches were local in the sense that they measure each pair of phonemes separately and the sum of the measures was the measure of the whole alignment. Their methods appear to depend on this assumption and therefore exclude the inclusion of context dependent phenomena e.g. assimilation, metathesis, constraints of syllable structure etc.", | |
| "cite_spans": [ | |
| { | |
| "start": 75, | |
| "end": 104, | |
| "text": "(Nerbonne and Heeringa, 1997)", | |
| "ref_id": "BIBREF14" | |
| }, | |
| { | |
| "start": 250, | |
| "end": 264, | |
| "text": "(Somers, 1999)", | |
| "ref_id": "BIBREF16" | |
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| "section": "Previous work on alignment", | |
| "sec_num": "2" | |
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| "text": "The work presented here separates the definition of the measure from the algorithm for finding the best alignment. Measures are represented as WFSTs and they are built by producing weighted regular expressions using simple Python scripts. The algorithms used here utilize the efficient algorithms already available in the finite-state calculus for finding the best paths from weighted acyclic automata (Mohri, 2009) .", | |
| "cite_spans": [ | |
| { | |
| "start": 402, | |
| "end": 415, | |
| "text": "(Mohri, 2009)", | |
| "ref_id": "BIBREF13" | |
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| "section": "Previous work on alignment", | |
| "sec_num": "2" | |
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| "text": "Simple phoneme by phoneme (or letter by letter) alignment is needed when relating cognate words of related languages or e.g. relating the written words in old texts with their present day forms. The process of alignment consists here of making phonetically similar phonemes correspond to each other and adding zeroes \u00d8 where necessary (due to epenthesis or elision). E.g. Estonian leem and Finnish liemi would be aligned by adding one zero at the end of the Estonian form:", | |
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| "section": "Weighting the correspondences of phonemes", | |
| "sec_num": "3" | |
| }, | |
| { | |
| "text": "l e e m \u00d8 l i e m i", | |
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| "section": "Weighting the correspondences of phonemes", | |
| "sec_num": "3" | |
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| { | |
| "text": "In general, consonants may not correspond to vowels or vice versa, except for glides, approximants or semivowels which may correspond to certain vowels and certain consonants. In this paper, many-to-one, and one-to-many correspondences are simply expressed by using combinations of phoneme to phoneme correspondences, phoneme to zero and zero to phoneme correspondences.", | |
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| "section": "Weighting the correspondences of phonemes", | |
| "sec_num": "3" | |
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| "text": "Vowels can be described by using distinctive features such as the height of the tongue, frontness/backness and rounding/unrounding, see Figure 1. Using such features, one may compute distances between different vowels. Similarly, consonants can be characterized by their place of articulation, voicing and the manner of articulation, see Figure 2 . The measure used here is not intended to be an absolute or universal measure, it is just an ad hoc approximation suitable for Estonian and Finnish.", | |
| "cite_spans": [ | |
| { | |
| "start": 136, | |
| "end": 145, | |
| "text": "Figure 1.", | |
| "ref_id": null | |
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| "ref_spans": [ | |
| { | |
| "start": 338, | |
| "end": 346, | |
| "text": "Figure 2", | |
| "ref_id": "FIGREF0" | |
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| "eq_spans": [], | |
| "section": "Weighting the correspondences of phonemes", | |
| "sec_num": "3" | |
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| "text": "Figure 1: Description of some Finnish and Estonian orthographic vowels using distinctive features. IPA symbol for letters for which they are not the letter itself:\u00fc = y,\u00f6 = \u00f8,\u00f5 = 7,\u00e4 = ae, a = A The work described here permits different kinds of definitions for measuring the distances, including those used in (Covington, 1998; Kondrak, 2000; Nerbonne and Heeringa, 1997; Somers, 1999) . Any measure which can reasonably be expressed as a WFST can be used by the algorithm presented in Section 4.", | |
| "cite_spans": [ | |
| { | |
| "start": 311, | |
| "end": 328, | |
| "text": "(Covington, 1998;", | |
| "ref_id": "BIBREF4" | |
| }, | |
| { | |
| "start": 329, | |
| "end": 343, | |
| "text": "Kondrak, 2000;", | |
| "ref_id": "BIBREF8" | |
| }, | |
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| "start": 344, | |
| "end": 372, | |
| "text": "Nerbonne and Heeringa, 1997;", | |
| "ref_id": "BIBREF14" | |
| }, | |
| { | |
| "start": 373, | |
| "end": 386, | |
| "text": "Somers, 1999)", | |
| "ref_id": "BIBREF16" | |
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| "section": "Weighting the correspondences of phonemes", | |
| "sec_num": "3" | |
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| "text": "From the phoneme descriptions shown in Figure 1, one can compute simple distances between any two vowels or any two consonants. The formula chosen in this study was heuristic. Tongue height had three steps corresponding to values 1, 2, 3 and the distance was taken to be the difference of those values. The distance between front and back was taken to be 1 as was the distance between rounding and unrounding. The distance between any two vowels was defined to be the sum of these three numbers. 1 A similar formula was used for consonants where the positions of articulation was numbered from 1 to 5 and their difference was the distance, see Figure 2 . Different voicing counted as 1, and so did the manner of articulation. Again, the total distance was the sum of these three numbers.", | |
| "cite_spans": [ | |
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| "start": 496, | |
| "end": 497, | |
| "text": "1", | |
| "ref_id": null | |
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| "start": 39, | |
| "end": 45, | |
| "text": "Figure", | |
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| "start": 644, | |
| "end": 652, | |
| "text": "Figure 2", | |
| "ref_id": "FIGREF0" | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Weighting the correspondences of phonemes", | |
| "sec_num": "3" | |
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| "text": "A double loop through vowels and another through consonants produced a list of feasible combinations of phonemes and the computed measure for their difference. These triplets were then formatted as strings and glued together into a long regular expression, see some samples of it ... | u:u::0 | u:y::1 | u:\u00e4::4 | u:\u00f6::2 ... | k:g::1 | k:h::2 | k:j::2 | k:k::0 ...", | |
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| "section": "Weighting the correspondences of phonemes", | |
| "sec_num": "3" | |
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| "text": "Note that the weight is after a double colon according to the extended notation for weighted regular expressions used in HFST. Thus, in the above formula, u may correspond to u at null cost, and k may correspond to g at a cost of 1.", | |
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| "section": "Weighting the correspondences of phonemes", | |
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| "text": "Any phoneme could be deleted or inserted at a cost. A simple loop produced the additional correspondences and their weights: In Finnish and in Estonian, long vowels are represented as two successive vowels. The default correspondences and weights clearly allow shortening of long vowels (or double consonants), but there would be two ways to express it with equal weights: one where the first of the two corresponds to zero, and the other where the second component corresponds to zero. In order to avoid this ambiguity, there was yet another loop which produced the necessary pieces of expressions which had a slightly smaller weight than the deletion alone. Note that e.g. p:\u00d8 p will remain acceptable, but the expression below gives a lower weight for the combination where the latter component corresponds to zero. One can use the same technique for handling orthographic conventions. One language might use kk and the other ck for a geminate k, similarly ks instead of x and ts instead of z. One can make such correspondences to have a zero distance by listing them with an explicit zero weight, e.g.: One could use the same mechanism for giving some phoneme relations a lower weight. One could e.g. prefer assimilations over arbitrary combinations by imposing a lower weight for a variant if preceded or followed by phoneme which articulated in the same place. Local metathesis affecting two consecutive phonemes could also be expressed fairly neatly.", | |
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| "section": "Weighting the correspondences of phonemes", | |
| "sec_num": "3" | |
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| "text": "When all expressions are glued together, enclosed in brackets and followed by a Kleene star, the regular expression is ready to be compiled into a WFST. After compilation, the WFST which holds the distances as weights, can be stored as a file to be used later by the aligning algorithm.", | |
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| "section": "Weighting the correspondences of phonemes", | |
| "sec_num": "3" | |
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| "text": "Now, we are ready to write a small but general Python script which reads in the similarity WFST described in Section 3 and (1) reads in a pair of cognate words from the standard input and (2) converts them into FSTs W1 and W2, (3) adds explicit zero symbols freely to each, (4) compares the zero-filled expressions using the weighed distance transducer ALIGN and produces in this way all possible alignments and their total weights as a weighted transducer RES. Of these many possible alignments accepted by RES, (5) the best one is chosen and (6) printed, see Figure 3 .", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 561, | |
| "end": 569, | |
| "text": "Figure 3", | |
| "ref_id": "FIGREF4" | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Aligning pairs of words", | |
| "sec_num": "4" | |
| }, | |
| { | |
| "text": "import sys, hfst algfile = hfst.HfstInputStream(\"d.fst\") ALIGN = algfile.read() for line in sys.stdin: The algorithm in Figure 3 considers all possible ways to add zero symbols to the cognates. It even adds an indefinite number of zeros to each cognate word. For Estonian leem and Finnish liemi the adding of the zeros would result in strings covered by the following expressions.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 120, | |
| "end": 128, | |
| "text": "Figure 3", | |
| "ref_id": "FIGREF4" | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Aligning pairs of words", | |
| "sec_num": "4" | |
| }, | |
| { | |
| "text": "# (1) F1,F2 = line.strip().split(sep=\":\") # (1) W1 = hfst.fst(F1) # (2) W1.insert_freely((\"\u00d8\",\"\u00d8\")) # (3) W2 = hfst.fst(F2) # (2) W2.insert_freely((\"\u00d8\",\"\u00d8\")) # (3) W1.compose(ALIGN) # (4) W1.compose(W2) # (4) RES = W1.n_best(1).minimize() # (5) paths = # (6) res.extract_paths(output='text') # (6) print(paths.strip()) # (6)", | |
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| "section": "Aligning pairs of words", | |
| "sec_num": "4" | |
| }, | |
| { | |
| "text": "\u00d8* l \u00d8* e \u00d8* e \u00d8* m \u00d8* W2: \u00d8* l \u00d8* i \u00d8* e \u00d8* m \u00d8* i \u00d8*", | |
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| "section": "W1:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The key idea is in the composition of these two FSAs so that the distance metric transducer ALIGN is in the middle:", | |
| "cite_spans": [], | |
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| "section": "W1:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "W1 .o. ALIGN .o. W2", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
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| "section": "W1:", | |
| "sec_num": null | |
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| "text": "Transducers W1, W2 and the ALIGN are all epsilon-free, so the composition accepts only same length string pairs. Note that the distance metric ALIGN does not allow a zero to correspond to another zero, so the zero filled strings may only be at most twice so long as the longer cognate was. There would still be quite a few comparisons to do, if one would compare and evaluate them one pair at a time.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "W1:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The HFST function n best(1) finds the pair of strings which would have the least weight. This is one of the operations that are efficient for WF-STs. The operation produces a FST which accepts exactly the best string pair. Another function is needed for extracting the transition labels which constitute the strings themselves.", | |
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| "ref_spans": [], | |
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| "section": "W1:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The aligner was used among other things, for relating word forms of Modern Finnish and Finnish of a Bible translation of year 1642. With slight tuning of the WFST, the aligner worked as the primary tool for aligning further pairs of old and new words which were used for writing and testing the rules which related the two forms of Finnish. The old orthography was less phonemic than the modern one and there was more orthographic variation in the old texts. After the initial adjusting to the orthography of the old texts, only a little tuning was needed to modify the computation of the similarities until the formula appeared to be stable.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
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| "section": "W1:", | |
| "sec_num": null | |
| }, | |
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| "text": "As an informal check, the manually edited and checked set of 203 pairs of old and new word forms was cleaned from the added zeros and realigned using the aligner. Only one difference was observed in the result as compared with the original. 2", | |
| "cite_spans": [], | |
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| "section": "W1:", | |
| "sec_num": null | |
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| "text": "The aligner was developed for aligning pairs of cognate words given to it. In this task, the aligner can and perhaps must be quite general. When we are studying the relation between two languages, we ought not commit ourselves to certain sound changes (or sound laws) when we start by preparing the source data for analyzing the relation itself.", | |
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| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "One might speculate that the aligner could also be used as a predictor of the likely shapes of the missing half of a cognate pair. The WFST alone is, however, not useful for such because it generates too many candidates, not only those which would follow from the sound changes which govern the relation of the languages. The correct candidate would be buried under a heap of incorrect ones.", | |
| "cite_spans": [], | |
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| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Instead of proposing the missing halves of cognate pairs from scratch, one can get useful results if one has a word list of the other language. Preparing for the processing, one first converts the word list into a FSA, say words-et.fst.", | |
| "cite_spans": [], | |
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| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Then, one types in a known word from the first language. The script (1) converts it into a FSA, (2) shuffles it freely with zeros, (3) composes it with the distance WFST, (4) deletes all zeros from the result and then (5) composes it with a FSA containing the word list. From the result of this chain, (6) the best word pairs are retrieved and printed for the user. Using HFST command line tools, the chain of programs looks like: This is a pipeline of programs which expects the user to feed words of the first language. For each word typed in, the programs do the operations, and from the resulting WFST, the last program prints five best matches, e.g. for the Finnish word ajo ('driving', 'trip') it produces: > ajo ajo:aju 1 ajo:aje 2 ajo:aie 3 ajo:\u00e4iu 3 ajo:agu 3", | |
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| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "$ hfst-", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "The pipeline computes five best guesses as pairs of the Finnish and the Estonian words, and shows their weights. In this case, the first guess Estonian aju happens to be the correct one. In other cases, the correct one may not the best scored candidate, as for vierastus, the correct candidate v\u00f5\u00f5rastus is the third in the list. Some short words may have many similar words in the word list. For them, the desired candidate is often too far down in the list of best ranking candidates and will not be found this way.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Using the aligner is of course less precise than building a realistic model of sound changes as was done in (Koskenniemi, 2013a) where two-level rules were used for this purpose.", | |
| "cite_spans": [ | |
| { | |
| "start": 108, | |
| "end": 128, | |
| "text": "(Koskenniemi, 2013a)", | |
| "ref_id": "BIBREF9" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "6 Aligning a set of stems or other morphs", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Comparing several words is needed when relating more than two historically connected languages but also when relating e.g. different stems of a word in order to build lexical entries which can be used in morphological analysis. The reason for relating stems is usually to construct one common morphophonemic representation for all stems of a word.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "In a simplified version of the two-level morphological analysis, one does not postulate underlying forms which are plain sequences of phonemes. Instead, one uses alternations of phonemes (morphophonemes) when different phonemes alternate with each other, cf. (Koskenniemi, 2013b) . The problem of aligning three or more different words is similar to the one discussed above but somewhat different methods are needed.", | |
| "cite_spans": [ | |
| { | |
| "start": 259, | |
| "end": 279, | |
| "text": "(Koskenniemi, 2013b)", | |
| "ref_id": "BIBREF10" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Let us look at the Estonian word pagu ('an escape') which inflects in forms like pagu, paos, pakku. Traditional generative phonology would prefer an underlying stem like paku and derive the other forms from that using a sequence of rewriting rules. In contrast to this, the linguist following the methods of the simplified two-level morphology, would first locate the boundaries between the stem morphs and the suffix morphs, i.e. pagu+, pao+s and pakku+, then take the stems pagu, pao, and pakku, then insert a few zeros in order to make the stem morphs same length, i.e. pag\u00d8u, pa\u00d8\u00d8o, pakku. Thus, the linguist would arrive at the morphophonemic representation p a {g\u00d8k} {\u00d8\u00d8k} {uou} by merging the corresponding letters of each stem morph.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Let us see, how an algorithm could simulate the linguist when it starts from the point where the boundaries have already been located. The task of the algorithm is (1) to produce all alignments, including lots of nonsense alignments, (2) filter out infeasible alignments, and (3) to evaluate the feasible alignments and choose the best among them.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "In order to carry out the first task, the algorithm blindly inserts some (or no) zero symbols into each stem in order to make all stem candi-dates same length. Thus, some stems are expanded to a number of alternatives where the zeros are at all different places. Assuming that five letters suffice for our example word, the first stem needs one zero, the second stem needs two zeros, and the third stem does not need any. 3 The insertion of the zeros to the first stem pagu would produce the strings \u00d8pagu, p\u00d8agu, pa\u00d8gu, pag\u00d8u and pagu\u00d8. Only one of these five will turn out to be useful but the algorithm does not know yet which. It does not actually produce the set of strings with zeros, but instead, it produces an automaton which accepts all of them.", | |
| "cite_spans": [ | |
| { | |
| "start": 422, | |
| "end": 423, | |
| "text": "3", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "The feasibility of an alignment is evaluated using the phoneme (or letter) correspondences which are caused by the insertion of zeros. Aligning \u00d8pagu, pa\u00d8\u00d8o and pakku would imply correspondences \u00d8-p-p, p-a-a, a-\u00d8-k, g-\u00d8-k and u-ou. Such an alignment is infeasible, as it includes two forbidden correspondences: the second and the third phoneme correspondences p-a-a and a-\u00d8-k are both infeasible because they contain both a consonant and a vowel (the dashes of the correspondences will be omitted hereafter). Another alignment, e.g. pag\u00d8u, pa\u00d8\u00d8 and pakku would imply the correspondences ppp, aaa, g\u00d8k, \u00d8\u00d8k and uou which all seem phonologically feasible containing only identical or closely related sounds and zeros.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Each phoneme correspondence is evaluated separately and assigned a weight according to the similarity of the participating phonemes. The goodness of an alignment is computed as a sum of all weights for the phoneme correspondences in the alignment. In the same manner as when comparing two words, a correspondence consisting of identical phonemes e.g. ppp has a zero weight.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "Two different distance measures were used. For vowels, the number of distinct vowels participating the correspondence was used as the measure. If the zero was also a member of the correspondence, 0.4 was added. For consonants, the differences of their features was counted. If there were both voiced and unvoiced, then 1 was added, if there were different manners of articulation, then one less than the number of manners was added. The positions of articulation were numbered from 0 to 4 and they contributed so that 0.5 times the difference of values for the most back and most front position was added. One or more zeros in the correspondence added 2.6 to the total measure. Semivowels were included both as consonants and vowels. Their combinations with vowels was restricted to those that are actually feasible, e.g. j was allowed to combine with i but not with other vowels.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "All these measures are ad hoc. Readers are encouraged to experiment and improve the formulas of the measures. In particular, machine learning methods could be utilized for optimizing the parameters.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Other uses for the distance WFSTs", | |
| "sec_num": "5" | |
| }, | |
| { | |
| "text": "The goal for the aligning of several words or stems were specified in the preceding section. The logic of the algorithm which implements them is shown in Figure 4 as a Python function extracted from the full implementation. Variables containing binary FSAs or FSTs as their values are in capital letters. The Python function shuffle w zeros() takes a stem as a string and returns an automaton accepting strings of the required length (by using a few HFST functions) so that exactly the correct amount of zeros are inserted freely.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 154, | |
| "end": 162, | |
| "text": "Figure 4", | |
| "ref_id": "FIGREF5" | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "The first goal of the algorithm (after inserting the necessary zeros) is to produce all combinations of the first and the second stem (with zeros inserted). The function cross product() is a standard HFST function for the cross product of two FSAs. As a result, R is a transducer which maps any of the possible versions of the first stem into any of the versions of the second stem. Our example from Section 6, i.e. paku pao pakko would become mappings between two sets of strings:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "{\u00d8pagu, p\u00d8agu, pa\u00d8gu, pag\u00d8u, pagu\u00d8} and {\u00d8\u00d8pao, \u00d8p\u00d8ao, \u00d8pa\u00d8o, \u00d8pao\u00d8, p\u00d8\u00d8ao, p\u00d8a\u00d8o, p\u00d8ao\u00d8, pa\u00d8\u00d8o, pa\u00d8o\u00d8, pao\u00d8\u00d8}", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "The transducer R maps any of the stings in the first set into any of the second set. The combination of the fourth in the first set and the eighth in the second is a good candidate for the alignment, i.e. pak\u00d8u:pa\u00d8\u00d8o or equivalently as a sequence of corresponding character pairs (where identical pairs are abbreviated): p a g:\u00d8 \u00d8 u:o. At this stage of the algorithm, however, R accepts all 50 combinations.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "Two problems arise here: First, we cannot continue immediately, because for the next cross product, we need a FSA instead of a FST. A transducer can be encoded to become an automaton by a standard function fst to fsa() which substitutes all label pairs x:y with label pairs xy:xy so that the result becomes a FSA again.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "The other problem is, that there may be many unwanted correspondences in the result, letting consonants correspond to vowels or vice versa. Thus, a user-made function remove bad transitions() checks the encoded FSA for infeasible labels and removes the corresponding transitions. 4 Now the product of the first two stem expressions is again a FSA, and not too large. So we can proceed by applying the process to the next stem expression and so on. When all stems have been processed, we have a FSA representing all feasible combinations of the zero-padded stems, i.e. all feasible alignments. All alignments are feasible in the sense that they do not contain forbidden combinations of vowels and consonants.", | |
| "cite_spans": [ | |
| { | |
| "start": 280, | |
| "end": 281, | |
| "text": "4", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "Consider first stems laps, lapse and las and some of their feasible alignments, the morphophonemic representation, the weights for each correspondence (i.e. morphophoneme) and the sum of weights:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "laps\u00d8 lapse las\u00d8\u00d8 l a pps ss\u00d8 \u00d8e\u00d8 0 1 2 2.6 1.4 = 7.0 laps\u00d8 lapse la\u00d8s\u00d8 l a pp\u00d8 s \u00d8e\u00d8 0 1 2.6 0 1.4 = 5.0", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "The former is not entirely impossible. It involves a stem final deletion of e which is common to both alignments, and in addition the deletion of s and changing the p into s (which would be uncommon). Considering the weights, the second alignment is clearly better because there is no alternation of s, only a deletion of p.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "Other cases may be more difficult to resolve. Consider the stems litter, litri and litre where we would have at least two competing alignments, the latter of which is one inserted zero longer than the former:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "litter litri\u00d8 litre\u00d8 l i t trr eie r\u00d8\u00d8 0 1 0 2 2 2.6 = 7.6 litter\u00d8 lit\u00d8\u00d8ri lit\u00d8\u00d8re l i t t\u00d8\u00d8 e\u00d8\u00d8 r \u00d8ie 0 1 0 2.6 1.4 0 2.4 = 7.4", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "The linguist would probably choose the latter and reject the former. So does the formula for assigning weights to the morphophonemes. The example also shows that that the algorithm must not stop on the shortest feasible alignment.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "The algorithm has a function weightf() which computes a weight for each candidate combination of phonemes according to the principles explained in Section 6. It is used first in excluding completely impossible transitions when building the intermediate results. It is used again in another function set weights() which inserts appropriate weights into the transitions of the final result containing still all feasible alignments for the stems.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "Once we have a weighted FSA which represents all alignments, it is easy to choose the best alignment with an HFST function n best. Some sets of stems, such as t\u00f6\u00f6 t\u00f6 would have two equally good alignments, t\u00f6\u00f6 t\u00f6\u00d8 and t\u00f6\u00f6 t\u00d8\u00f6. Therefore, more than one of the top alignments are chosen first. Out of the equally good top candidates, the program selects the one in which the deletions are more to the right. Behind this choice is the observation that in suffixing languages, the deletions are more likely to occur near the affix morphemes. Using this criterion, t\u00f6\u00f6 t\u00f6\u00d8 is chosen over the other alternative.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "Anyway, the weighting is made in a transparent manner in the program, so it would be easy to experiment, modify and tune the weighting, if it turns out that other types of languages need different principles to resolve such ties.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Algorithm for aligning multiple stems", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "After the initial implementation of the algorithm it was tested against a language resource tyvebaas.pmf containing Estonian words with inflectional information and was freely available from the Institute of the Estonian Language (Eesti Keele Instituut). The file contained among other things, a base form, inflectional class, part of speech code and a list of all actual stem allomorphs of the lexeme. For this experiment the nouns were extracted, and furthermore, only those nouns which had more than one stem given. Out of these entries, only the stems were extracted and all other information was ignored. The original file contained entries like: ='aasima 28 V | at: 'aasi, an: aasi ='aasta 01 S | a0: 'aasta, a0r: 0 =aastak 02 S | a0: aastak, b0: aastaku, b0r:... 'aastane 10 A | a0: 'aastane, b0: 'aastase,...", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Aligning Estonian noun stems", | |
| "sec_num": "8" | |
| }, | |
| { | |
| "text": "The first and the last entries were not nouns and they were discarded. The second entry was a noun but only with one stem. It was discarded as well. The third entry was a noun and had more than one stem, and it was chosen and produced an entry for the purposes of this study. The selected 15 934 sets of noun stem sets entries were like the following examples (after some cleaning): 5", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Aligning Estonian noun stems", | |
| "sec_num": "8" | |
| }, | |
| { | |
| "text": "The whole test material was run through the aligner and the result studied using some sampling and some other checking. Some example alignments made by the algorithm are given in Figure 5 .", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 179, | |
| "end": 187, | |
| "text": "Figure 5", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "aastak aastaku aatom aatomi aatome abajas abaja", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "At least for the author, the alignments in Figure 5 appeared to be acceptable. The whole material was then checked by sampling and by looking at infrequent or untypical letter combinations in a frequency list of all letter combinations. In the whole material, three alignments were found where the author disagrees with the result of the algorithm, see Figure 6 . Figure 6 : The three questionable alignments found in the Estonian word list of nouns 9 Tasks for the future Distances between phonemes as described in Section 4 seems like a challenge for further research. In essence, the relation looks like a two-level rule relation with weights. No present compiler for two-level rules can directly assign weights to correspondences. It appears to be possible to include some form of weighting to the rule formalism and write a compiler. A two-level compiler dedicated for alignment tasks could express the language specific patterns of phoneme alternations. A clear case for such rules would be the proper handling of vowel lengthening and gemination. Furthermore, one guiding the insertions and deletions could be made more transparent and robust using rules.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 353, | |
| "end": 361, | |
| "text": "Figure 6", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 364, | |
| "end": 372, | |
| "text": "Figure 6", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "aastak aastaku aatom aatomi aatome abajas abaja", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Writing dedicated compilers for two-level rules has now become much easier. It would be a reasonable project to write a compiler which is oriented towards alignment. In this way, one could implement suitable context constraints for the target language(s) and integrate it into the process of alignment.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "aastak aastaku aatom aatomi aatome abajas abaja", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The algorithm with the weights made for Estonian stems, was tested also for the alignment of Finnish noun stems. The result appeared to be fully clean, but only model words for different inflectional classes were tested. The same weights were also tested for some cognate word sets for Uralic languages found in en.wictionary.org as far as the symbols were available. The alignments for those seemed to be OK. Extensive tests are needed to evaluate the performance on those areas.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "aastak aastaku aatom aatomi aatome abajas abaja", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "All programs made and the testing data used in this project is in the open source and has been made accessible to all 7 . Even without a nicer compiler, the modification of the weighting schemes is easy for anybody who has slight command of Python programming. In particular, researchers interested in statistical or machine learning methods are encouraged to apply their methods for finding optimal weightings for phoneme combinations or using the material as a gold standard for other types of solutions. Even linguists who have better command of Estonian than the author, are encouraged to report mistakes in the aligned material or critique on what the optimal alignment ought to be.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "aastak aastaku aatom aatomi aatome abajas abaja", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Using the Python programs with the finite state tools requires the availability of Python3, the HFST library and the SWIG interface for using the library from Python. 8", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "aastak aastaku aatom aatomi aatome abajas abaja", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The FIN-CLARIN language infrastructure project has developed and maintains the HFST software. The author is grateful for their technical support and assistance. Particular thanks are due to Erik Axelsson.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Credits", | |
| "sec_num": "10" | |
| }, | |
| { | |
| "text": "This is sometimes called Manhattan distance as opposed to the Euclidean distance which would be the square root of the sum of squares.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The manually aligned lep\u00e4\u00d8siv\u00e4t:lew\u00e4isi\u00d8\u00d8t was problematic because Old Finnish had a different morpheme for the third person past tense -it whereas the Modern Finnish has -iv\u00e4t. Thus, no 'correct' alignment actually exists. The pair to be aligned ought to be lep\u00e4isit:lew\u00e4isit.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "One may start with the shortest possible stems. If no results are produced (because one would have to match some consonant to a vowel), one may add one more zero and try again, and repeat this until the matching succeeds, and then still try with adding one more zero.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In principle, the cross product multiplies the size of the automaton fast if there would be several stems and several zeros involved.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The goal was just to test the algorithm, at this time not to produce a lexicon to be accompanied with endings and morphophonological rules. Those other tasks would seem quite feasible to do at a later stage with some cooperation with suitable parties.6 One could have used a more phonemic representation for the words by representing long vowels by a single phoneme, e.g. A instead of aa. Such a representation could have made the task a bit simpler and maybe the mistakes could have been avoided altogether.", | |
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| "sec_num": null | |
| }, | |
| { | |
| "text": "See https://github.com/koskenni/alignment for the programs and for the test data 8 See https://hfst.github.io/ for the documentation and instructions for downloading, installing and using the Python HFST", | |
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| "uris": null, | |
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| }, | |
| "FIGREF1": { | |
| "text": "... | o:\u00d8::3 | p:\u00d8::3 | r:\u00d8::3 | ... | \u00d8:o::3 | \u00d8:p::3 | \u00d8:r::3 | ...", | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null | |
| }, | |
| "FIGREF2": { | |
| "text": "... | o \u00d8:o::2 | p \u00d8:p::2 | r \u00d8:r::2 ... | o o:\u00d8::2 | p p:\u00d8::2 | r r:\u00d8::2 ...", | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null | |
| }, | |
| "FIGREF3": { | |
| "text": "k:c::0 k::0 | k:x s:\u00d8::0 | t:z s:\u00d8::0", | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null | |
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| "uris": null, | |
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| "num": null | |
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| "FIGREF5": { | |
| "text": "Function which produces the set of all feasible alignments and their weights as a weighted FSA", | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null | |
| } | |
| } | |
| } | |
| } |