matlab 实现 kernel SVD 高斯核

建议先看HOSVD的实现：/article/11131649.html

1、计算矩阵的秩

输入一个张量：

A(: , : ,1)=[1,0,0;1,0,0;0,0,0];

A(: , : ,2)=[0,0,0;0,1,0;0,0,0];

A(: , : ,3)=[0,0,0;0,0,0;0,0,1]；

A=tensor(A);

2、将张量A沿mode-n展开

A1=tenmat(A,1);

A2=tenmat(A,2);

A3=tenmat(A,3);

3、计算每个展开张量的标准差

rows = reshape(A1.data,3*9,1);

std(rows);

mean(rows);

ans =

0.1481

4、计算高斯核矩阵

K1 = KGaussian(A1, A1, 1/0.1418);

K2 = KGaussian(A2, A2, 1/0.1418);

K3 = KGaussian(A3, A3, 1/0.1418);

5、对k进行svd：

[U1,V1,W1]=svd(K1);

[U2,V2,W2]=svd(K2);

[U3,V3,W3]=svd(K3);

6、计算核心张量

S = ttm(A,{U1’,U2’,U3’})

7、计算近似张量

B=ttm(S,{U1,U2,U3})

结果：

B is a tensor of size 3 x 3 x 3

B(:,:,1) =

0.9438 0.0023 0.0015

1.3129 0.0033 0.0020

0.0148 0.0001 0.0016

B(:,:,2) =

0.0023 0.5834 0.0100

0.0033 0.8115 0.0136

0.0001 0.0094 0.0169

B(:,:,3) =

0.0015 0.0100 0.0170

0.0020 0.0136 0.0025

0.0016 0.0169 1.0002

附录：

function K = KGaussian(A, tilde_A, gamma)

% for building kernel data matrix, reduced or full, with Gaussian kernel.

%

% Inputs

% A: full data set.

% tilde_A: can be full or reduced set.

% gamma: width parameter, kernel value = exp{-gamma |A_i-tilde_A_j|_2^2}.

%

% Outputs

% K: kernel data, full or reduced.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

r1 = size(A,1); r2=size(tilde_A,1); K=zeros(r1,r2);

for i = 1: r1

for j = 1: r2

dis=A(i,:)-tilde_A(j,:);

K(i,j) = exp( -( gamma * ( dis * dis’ ) ) );

end

end