what is the algorithm for an RBF kernel matrix in Matlab?

问题

If I am given training data sets and unlabeled datasets, what is the RBF Kernel matrix algorithm for Matlab?

回答1:

This should be what you are looking for. It is taken from here

% With Fast Computation of the RBF kernel matrix
% To speed up the computation, we exploit a decomposition of the Euclidean distance (norm)
%
% Inputs:
%       ker:    'lin','poly','rbf','sam'
%       X:      data matrix with training samples in rows and features in columns
%       X2:     data matrix with test samples in rows and features in columns
%       sigma: width of the RBF kernel
%       b:     bias in the linear and polinomial kernel
%       d:     degree in the polynomial kernel
%
% Output:
%       K: kernel matrix
%
% Gustavo Camps-Valls
% 2006(c)
% Jordi (jordi@uv.es), 2007
% 2007-11: if/then -> switch, and fixed RBF kernel

function K = kernelmatrix(ker,X,X2,sigma)

switch ker
    case 'lin'
        if exist('X2','var')
            K = X' * X2;
        else
            K = X' * X;
        end

    case 'poly'
        if exist('X2','var')
            K = (X' * X2 + b).^d;
        else
            K = (X' * X + b).^d;
        end

    case 'rbf'

        n1sq = sum(X.^2,1);
        n1 = size(X,2);

        if isempty(X2);
            D = (ones(n1,1)*n1sq)' + ones(n1,1)*n1sq -2*X'*X;
        else
            n2sq = sum(X2.^2,1);
            n2 = size(X2,2);
            D = (ones(n2,1)*n1sq)' + ones(n1,1)*n2sq -2*X'*X2;
        end;
        K = exp(-D/(2*sigma^2));

    case 'sam'
        if exist('X2','var');
            D = X'*X2;
        else
            D = X'*X;
        end
        K = exp(-acos(D).^2/(2*sigma^2));

    otherwise
        error(['Unsupported kernel ' ker])
end

回答2:

To produce the grahm/kernel matrix (matrix of inner products) do:

function [ Kern ] = produce_kernel_matrix( X, t, beta )
%
X = X';
t = t';
X_T_2 = sum(X.^2,2) + sum(t.^2,2).' - (2*X)*t.'; % ||x||^2 + ||t||^2 - 2<x,t>
Kern =exp(-beta*X_T_2); %
end

then to do the interpolation do:

function [ mdl ] = learn_RBF_linear_algebra( X_training_data, Y_training_data, mdl )
%
Kern_matrix = produce_kernel_matrix_bsxfun(X_training_data, mdl.t, mdl.beta); % (N x K)
C = Kern_matrix \ Y_training_data';  % (K x D) = (N x K)' x (N x D)
mdl.c = C; % (K x D)
end

note beta is 1/2sigma

来源：https://stackoverflow.com/questions/17690132/what-is-the-algorithm-for-an-rbf-kernel-matrix-in-matlab

标签

algorithm

matlab

kernel