Dimensions Reduction in Matlab using PCA

Hi;

I have a matrix of 35 columns, and I'm trying to reduce the dimension using PCA.

I run PCA on my data:

   [coeff,score,latent,tsquared,explained,mu] = pca(data);

explained =

     99.9955
      0.0022
      0.0007
      0.0003
      0.0002
      0.0001
      0.0001
      0.0001

Then, by looking at explained vector I notice the value of the first is 99, so based on this I decided to take only the first compoenet. So I did the follwoing:

       k=1;
       X = bsxfun(@minus, data, mean(data)) * coeff(:, 1:k);

and Now, I used X for SVM training,

svmStruct = fitcsvm(X,Y,'Standardize',true, 'Prior','uniform','KernelFunction','linear','KernelScale','auto','Verbose',0,'IterationLimit', 1000000);

However, when I tried to do predict and calculate the miss-classification rate:

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

The result was disappointing. I notice, when I select only one component (k=1), I got all classification wrong,however, as I increase number of included component (k), result is improving, as you can see from below diagram, but this doesn't make since according to explained, I should be fine with the first eginvector only.

Did I do any mistake?

Below diagram shows classification error for each number of included eginvector.

Answer 1

[Tom Lane]

The first component explains most of the variation in the columns of DATA, but Y is not involved in that. Of course I don't understand your data. But it is certainly mathematically possible for Y to depend more strongly on a component that explains a lower amount of variance.

Also, for simplicity you may find it convenient to use the SCORE output from PCA instead of computing it yourself.