Hi idimou,
PRTools svc classifier uses one-against-all strategy when handling multi-class problems.
Yes, the svc output is probabilistic. The raw SVC output is scaled by a sigmoid into 0,1 interval. This output may be considered a classifier-conditional posterior, because the sigmoid is fitted to the classifier outputs. The slope of a sigmoid is optimized by a maximum likelihood estimator (on the same data, may result in some overfit of your data). The position of the sigmoid is fixed so that zero classifier output corresponds to probability of 0.5
To peek into the complete multi-class svc, you might use the PRSD Studio sdconvert command:
>> a=gendatm
Multi-Class Problem, 160 by 2 dataset with 8 classes: [20 20 20 20 20 20 20 20]
>> w=svc(a,'r',2)
Support Vector Classifier, 2 to 8 trained mapping --> stacked
>> p=sdconvert(w)
sequential pipeline 2x8 'Support Vector Classifier'
1 sdp_stack 2x8
% the stack contains 8 SVCs:
>> p{1}
stacked pipeline 2x8 ''
1 pipeline 2x1
2 pipeline 2x1
3 pipeline 2x1
4 pipeline 2x1
5 pipeline 2x1
6 pipeline 2x1
7 pipeline 2x1
8 pipeline 2x1
% to get the first SVC:
>> p2=p{1}{1}
sequential pipeline 2x1 'Feature Selection'
1 sdp_svc 2x1 Support Vector Classifier, 'rbf', par=2.0, 30 SVs
2 sdp_sigmoid 1x2 scale=0.18
3 sdp_fsel 2x1 Feature Selection
>> p{1}{3}
sequential pipeline 2x1 'Feature Selection'
1 sdp_svc 2x1 Support Vector Classifier, 'rbf', par=2.0, 38 SVs
2 sdp_sigmoid 1x2 scale=0.45
3 sdp_fsel 2x1 Feature Selection
% note different scale of the sigmoid
% to study raw outputs and sigmoid-scaled outputs on a test set:
>> b=gendatm(10)
Multi-Class Problem, 10 by 2 dataset with 6 classes: [1 1 2 1 2 3]
% executing only the svc step - these are raw outputs:
>> out=+b*p2(1)
out =
1.3081
-1.3444
-1.0221
-1.0194
-1.0206
-1.0573
-1.0616
-1.3247
-1.2862
-0.9536
% executing svc and sigmoid steps:
>> out=+b*p2(1:2)
out =
0.9992 0.0008
0.0006 0.9994
0.0036 0.9964
0.0037 0.9963
0.0037 0.9963
0.0030 0.9970
0.0029 0.9971
0.0007 0.9993
0.0009 0.9991
0.0053 0.9947
With Best Regards,
Pavel
