Why SVM is not giving expected result

I have training data composed from only one feature.

The feature have around 113K observation.

• 8K only of those observation have positive class.
• 105K of those observation have negative class.
• The 8K observation composed of a number below 1 (90%), and 10% above 1
• The 105K observation composed of a number above 1 (80%), and 20% below 1Hence, almost, any X value below than 1 show be predicted as positive class, and any X value above 1 should be predicted as negative class.

I used the following fitcsvm call:

svmStruct = fitcsvm(X,Y,'Standardize',true, 'Prior','uniform','KernelFunction','linear','KernelScale','auto','Verbose',1,'IterationLimit',1000000);

the fitcsvm give message at the end saying SVM optimization did not converge to the required tolerance., ... but why ... most of first class X values are below 1 and visa versa ... so it should be easy to find classification boundary. and when I run:

[label,score,cost]= predict(svmStruct, X) ;

it gives wrong prediction.

Below a portion of my X values is listed:

0.9911
    0.9836
    0.9341
    0.9751
    0.9880
    0.9977
    0.9853
    0.9861
    1.0143
    1.0086
    0.9594
    0.9787
    0.9927
    0.9839
    1.0024
    0.9931
    0.9930
    1.0275

The image below shows a gscatter diagram. Notice, the positive values are only around 8K, while negative around 105K. Since there is only 1 feature, I created an X with values from 1 to length of Y.

I also attached "features.txt" which contains the features column and "Y.txt" which contains the two groups.

Answer 1

[Ilya]

This is a difficult problem for SVM. SVM performs best when two classes are separable or have a modest overlap. This is not the case here. To make things even harder for SVM, less than 7000 points out of your 110k are unique.

Why not use a classifier such as decision tree or linear discriminant?