[英]what is the algorithm for an RBF kernel matrix in Matlab?
如果为我提供了训练数据集和未标记的数据集,那么Matlab的RBF内核矩阵算法是什么?
This should be what you are looking for. 这应该是您想要的。 It is taken from here 从这里取
% 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
To produce the grahm/kernel matrix (matrix of inner products) do: 要生成grahm /内核矩阵(内部乘积矩阵),请执行以下操作:
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: 然后做插值:
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
注意beta是1/2sigma
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