【文件属性】：
文件名称：基于核函数的特征提取
文件大小：2KB
文件格式：ZIP
更新时间：2018-05-06 02:35:40
KPCA
function data_out = kernelpca_tutorial(data_in,num_dim)
%
% This function does principal component analysis (non-linear) on the given
% data set using the Kernel trick
%
% Data_Out = kernelpca_tutorial(Data_in,Num_Dim)
%
% Data_in - Input data (d (dimensions) X N (# of points)
% Num_Dim - Dimensions of output data. (Num_Dim <= d)
% Data_Out - Output data. (Num_Dim (dimensions) X N (# of points))
%
% Ambarish Jash
% ambarish.jash@colorado.edu
%
%% Checking to ensure output dimensions are lesser than input dimension.
if num_dim > size(data_in,1)
fprintf('\nDimensions of output data has to be lesser than the dimensions of input data\n');
fprintf('Closing program\n');
return
end
%% Using the Gaussian Kernel to construct the Kernel K
% K(x,y) = -exp((x-y)^2/(sigma)^2)
% K is a symmetric Kernel
K = zeros(size(data_in,2),size(data_in,2));
for row = 1:size(data_in,2)
for col = 1:row
temp = sum(((data_in(:,row) - data_in(:,col)).^2));
K(row,col) = exp(-temp); % sigma = 1
end
end
K = K + K';
% Dividing the diagonal element by 2 since it has been added to itself
for row = 1:size(data_in,2)
K(row,row) = K(row,row)/2;
end
% We know that for PCA the data has to be centered. Even if the input data
% set 'X' lets say in centered, there is no gurantee the data when mapped
% in the feature space [phi(x)] is also centered. Since we actually never
% work in the feature space we cannot center the data. To include this
% correction a pseudo centering is done using the Kernel.
one_mat = ones(size(K));
K_center = K - one_mat*K - K*one_mat + one_mat*K*one_mat;
clear K
【文件预览】：
kernelpca_tutorial.m
license.txt