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详细说明： 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_di m > 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 ...展开收缩
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