lpp.zip_LPP_MATLAB_局部保持投影

function [mappedX, mapping] = lpp(X, no_dims, k, sigma, eig_impl) %LPP Perform linearity preserving projection % % [mappedX, mapping] = lpp(X, no_dims, k, sigma, eig_impl) % % Perform the Linearity Preserving Projection on dataset X to reduce it to % dimensionality no_dims. The number of neighbors that is used by LPP is % specified by k (default = 12). The variable sigma determines the % bandwidth of the Gaussian kernel (default = 1). % % % This file is part of the Matlab Toolbox for Dimensionality Reduction. % The toolbox can be obtained from http://homepage.tudelft.nl/19j49 % You are free to use, change, or redistribute this code in any way you % want for non-commercial purposes. However, it is appreciated if you % maintain the name of the original author. % % (C) Laurens van der Maaten, Delft University of Technology if size(X, 2) > size(X, 1) error('Number of samples should be higher than number of dimensions.'); end if ~exist('no_dims', 'var') no_dims =4; end if ~exist('k', 'var') k = 12; end if ~exist('sigma', 'var') sigma = 1; end if ~exist('eig_impl', 'var') eig_impl = 'Matlab'; end % Construct neighborhood graph disp('Constructing neighborhood graph...'); if size(X, 1) < 4000 G = L2_distance(X', X'); % Compute neighbourhood graph [tmp, ind] = sort(G); for i=1:size(G, 1) G(i, ind((2 + k):end, i)) = 0; end G = sparse(double(G)); G = max(G, G'); % Make sure distance matrix is symmetric else G = find_nn(X, k); end G = G .^ 2; G = G ./ max(max(G)); % Compute weights (W = G) disp('Computing weight matrices...'); % Compute Gaussian kernel (heat kernel-based weights) G(G ~= 0) = exp(-G(G ~= 0)/ (2 )) ; % G(G ~= 0) =1; % Construct diagonal weight matrix D = diag(sum(G, 2)); % Compute Laplacian L = D - G; L(isnan(L)) = 0; D(isnan(D)) = 0; L(isinf(L)) = 0; D(isinf(D)) = 0; % Compute XDX and XLX and make sure these are symmetric disp('Computing low-dimensional embedding...'); DP = X' * D * X; LP = X' * L * X; DP = (DP + DP') / 2; LP = (LP + LP') / 2; % Perform eigenanalysis of generalized eigenproblem (as in LEM) if size(X, 1) > 200 && no_dims < (size(X, 1) / 2) if strcmp(eig_impl, 'JDQR') options.Disp = 0; options.LSolver = 'bicgstab'; [eigvector, eigvalue] = jdqz(LP, DP, no_dims, 'SA', options); else options.disp = 0; options.issym = 1; options.isreal = 1; [eigvector, eigvalue] = eigs(LP, DP, no_dims, 'SA', options); end else [eigvector, eigvalue] = eig(LP, DP); end % Sort eigenvalues in descending order and get smallest eigenvectors [eigvalue, ind] = sort(diag(eigvalue), 'ascend'); eigvector = eigvector(:,ind(1:no_dims)); % Compute final linear basis and map data mappedX = X * eigvector; mapping.M = eigvector; mapping.mean = mean(X, 1);