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function out=fun_predicted_vector_2_label(vector,nmb_of_labels)
%
% predicted vector of length 25 to digit label 1, ..., 25
% vector=predicted_vector;
[~,dtsz]=size(vector);
digit=zeros(1,dtsz);
distance=zeros(1,dtsz);
nn=nmb_of_labels;
v=vector(1:nn,:);
I=eye(nn);
vv=zeros(nn,1);
for j=1:dtsz
for i=1:nn
[cc,~]=loss_function(v(:,j),I(:,i));
vv(i)=cc;
end
[aa,idx]=min(vv);
digit(j)=idx;
distance(j)=aa;
end
out.label=digit;
out.distance=distance;
%%%%%%%%%%
function [loss,dloss]=loss_function(predicted_x,true_y)
% cross_entropy loss
%
eps=1e-8;
[n, N]=size(true_y);
loss=sum(sum((true_y+eps).*log((true_y+eps)./(predicted_x+eps))))/N;
% ind_loss=sum((true_y+eps).*log((true_y+eps)./(predicted_x+eps)),1);
bb=-(true_y(1:end-1,:)+eps)./(predicted_x(1:end-1,:)+eps);
w=bb+ones(n-1,1)*(true_y(end,:)+eps)./(predicted_x(end,:)+eps);
dloss=w'/N;
end
%%%%%%%%%%
end
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