LPP局部保持映射Locality Preserving Projections

局部保持映射(LPP)是由何晓飞提出的一种用于降维的流型学习算法，它是一种线性的算法。

function [eigvector eigvalue Y] = LPP（X W options）
% LPP: Locality Preserving Projections
%
%       [eigvector eigvalue] = LPP（X W options）
% 
%             Input:
%               X       - Data matrix. Each row vector of fea is a data point.
%               W       - Affinity matrix. You can either call “constructW“
%                         to construct the W or construct it by yourself.
%               options - Struct value in Matlab. The fields in options
%                         that can be set:
%                            ReducedDim   -  The dimensionality of the
%                                            reduced subspace. If 0
%                                            all the dimensions will be
%                                            kept. Default is 0.
%                            PCARatio     -  The percentage of principal
%                                            component kept in the PCA
%                                            step. The percentage is
%                                            calculated based on the
%                                            eigenvalue. Default is 1
%                                            （100% all the non-zero
%                                            eigenvalues will be kept.
%             Output:
%               eigvector - Each column is an embedding function for a new
%                           data point （row vector） x  y = x*eigvector
%                           will be the embedding result of x.
%               eigvalue  - The eigvalue of LPP eigen-problem. sorted from
%                           smallest to largest. 
% 
% 
%       [eigvector eigvalue Y] = LPP（X W options）   
%               
%               Y:  The embedding results Each row vector is a data point.
%                   Y = X*eigvector
%
%
%    Examples:
%
%       fea = rand（5070）;
%       options = [];
%       options.Metric = ‘Euclidean‘;
%       options.NeighborMode = ‘KNN‘;
%       options.k = 5;
%       options.WeightMode = ‘HeatKernel‘;
%       options.t = 1;
%       W = constructW（feaoptions）;
%       options.PCARatio = 0.99
%       [eigvector eigvalue Y] = LPP（fea W options）;
%       
%       
%       fea = rand（5070）;
%       gnd = [ones（101）;ones（151）*2;ones（101）*3;ones（151）*4];
%       options = [];
%       options.Metric = ‘Euclidean‘;
%       options.NeighborMode = ‘Supervised‘;
%       options.gnd = gnd;
%       options.bLDA = 1;
%       W = constructW（feaoptions）;      
%       options.PCARatio = 1;
%       [eigvector eigvalue Y] = LPP（fea W options）;
% 
% 
% Note: After applying some simple algebra the smallest eigenvalue problem:
%    X^T*L*X = \lemda X^T*D*X
%      is equivalent to the largest eigenvalue problem:
%    X^T*W*X = \beta X^T*D*X
%  where L=D-W;  \lemda= 1 - \beta.
% Thus the smallest eigenvalue problem can be transformed to a largest 
% eigenvalue problem. Such tr

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     文件       5487  2014-07-14 16:25  LPP.m

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