Matlab SVM custom kernel function

Question

In the Matlab SVM tutorial, it says

You can set your own kernel function, for example, kernel, by setting 'KernelFunction','kernel'. kernel must have the following form:

function G = kernel(U,V)

where:

U is an m-by-p matrix. V is an n-by-p matrix. G is an m-by-n Gram matrix of the rows of U and V.

When I followed the custom SVM kernel example, I set a break point in mysigmoid.m function. However, I found U and V were in fact 1-by-p vectors and G was a scalar.

Why does not MATLAB process the kernel by matrices?

My custom kernel function is

function G = mysigmoid(U,V)
% Sigmoid kernel function with slope gamma and intercept c
gamma = 0.5;
c = -1;
G = tanh(gamma*U*V' + c);
end

My Matlab script is

%% Train SVM Classifiers Using a Custom Kernel

rng(1); % For reproducibility
n = 100; % Number of points per quadrant

r1 = sqrt(rand(2*n,1)); % Random radius
t1 = [pi/2*rand(n,1); (pi/2*rand(n,1)+pi)]; % Random angles for Q1 and Q3
X1 = [r1.*cos(t1), r1.*sin(t1)]; % Polar-to-Cartesian conversion

r2 = sqrt(rand(2*n,1));
t2 = [pi/2*rand(n,1)+pi/2; (pi/2*rand(n,1)-pi/2)]; % Random angles for Q2 and Q4
X2 = [r2.*cos(t2), r2.*sin(t2)];

X = [X1; X2]; % Predictors
Y = ones(4*n,1);
Y(2*n + 1:end) = -1; % Labels

% Plot the data
figure(1);
gscatter(X(:,1),X(:,2),Y);
title('Scatter Diagram of Simulated Data');

SVMModel1 = fitcsvm(X,Y,'KernelFunction','mysigmoid','Standardize',true);

% Compute the scores over a grid
d = 0.02; % Step size of the grid
[x1Grid,x2Grid] = meshgrid(min(X(:,1)):d:max(X(:,1)),...
min(X(:,2)):d:max(X(:,2)));
xGrid = [x1Grid(:),x2Grid(:)]; % The grid
[~,scores1] = predict(SVMModel1,xGrid); % The scores

figure(2);
h(1:2) = gscatter(X(:,1),X(:,2),Y);
hold on;
h(3) = plot(X(SVMModel1.IsSupportVector,1),X(SVMModel1.IsSupportVector,2),...
'ko','MarkerSize',10);
% Support vectors
contour(x1Grid,x2Grid,reshape(scores1(:,2),size(x1Grid)),[0,0],'k');
% Decision boundary
title('Scatter Diagram with the Decision Boundary');
legend({'-1','1','Support Vectors'},'Location','Best');
hold off;

CVSVMModel1 = crossval(SVMModel1);
misclass1 = kfoldLoss(CVSVMModel1);
disp(misclass1);

ABC ABC · Accepted Answer · 2015-05-25T02:53:29

Kernels add dimensions to a feature. If you have, for example, one feature for sample x={a} it will expand it into something like x= {a_1... a_q}. As you are doing this for all of your data at once, you are going to have a M x P (M is the number of examples in your training set and P is the number of features). The second matrix it asks for is P x N, where N is the number of examples in the training/test set.

That said, your output should be M x N. Since it is instead 1, it means that you have U = 1XM and V=Nx1 where N=M. To have an output of M x N logic follows that you should simply transpose your inputs.

Matlab SVM custom kernel function

1 Answers