How to use svmtrain() with a custom kernel in Matlab?

svmtain() is a function in MATLAB for SVM learning. The help doc is here:

http://www.mathworks.com/help/bioinfo/ref/svmtrain.html

How can I use it with a custom kernel? In the help doc, it says:

------------------------------------------------------------------------------------

@kfun — Function handle to a kernel function. A kernel function must be of the form

function K = kfun(U, V)

The returned value, K, is a matrix of size M-by-N, where U and V have M and N rows respectively. ------------------------------------------------------------------------------------

It mentions nothing about what U and V are and what M and N mean. I just don't know how to use it in the right format. Can anyone tell me what U and V are and what M and N mean? For example, the training data are 5-dimensional vectors and the kernel function is the sum of the length of the vectors. How can I write the kernel function?

Thank you!

Answer 1

[Ilya]

By convention adopted for svmtrain, observations are in rows and predictors are in columns. The same convention would hold for kfun. This means U is of size M-by-P, and V is of size N-by-P, where P is the number of predictors (P=5 for you). Other functions such as pdist2 in the Statistics Tlbx follow the same convention. If you want your kernel function to be a simple dot product, you would do

kfun = @(U,V) U*V';

[Tom]

Thank you very much :-) I am a beginner. Can you explain more detailed? If P is the number of dimensions here, what do M and N mean? And what are U and V? From my understanding, a kernel function replaces the inner product of the data vectors. So U and V should be two data vectors, which should be of size 1-by-# of dimension. Why do they have M and N rows?

[Ilya]

U is M vectors, each of size 1-by-P, concatenated vertically, and V is, similarly, N such vectors. You could compute dot products between M and N observations by defining a function of two vectors and writing a nested loop. You would go over 1:M indices in the outer loop and over 1:N indices in the inner loop, and compute M*N dot products of two vectors. This could be slow. svmtrain tries to speed up by vectorizing this code. That's why svmtrain wants you to write a vectorized function capable of computing all dot products between M and N observations at once.

[Fatih Temiz]

I have the same issue. I could not even understand how to call the function. I have a code

xdata=meas(1:end,1:5);
group = species(1:end);

svmStruct = svmtrain(xdata,group,'kernel_function' ,'polynomial', 'ShowPlot',0)
result = svmclassify(svmStruct,newdata,'ShowPlot',0)

which runs perfectly. As far as I understand, I should replace 'polynomial' with @kfun as

svmStruct = svmtrain(xdata,group,'kernel_function' ,@kfun, 'ShowPlot',0)

However it does not run. I thought, the purpose is lack of the inputs. I tried this time

svmStruct = svmtrain(xdata,group,'kernel_function' ,@kfun(U,V), 'ShowPlot',0)

but it gives an error again. What is my mistake? Is it about the function? Or do I miss anything else?

[Defne Ozan]

For anyone else having similar problems, writing the kernel function in a separate file (instead of at the bottom of the same file) and then calling it with 'KernelFunction','kernel' worked for me.

[jyoti lele]

can you please give the code of 'kernel' you wrote