核PCA ECA 分析谱聚类

function [eigvector, elapse, itn, Y] = SR(options, Responses, data) % SR: Spectral Regression % % [eigvector, elapse, itn, Y] = SR(options, Responses, data) % % Input: % data - data matrix. Each row vector of data is a % sample vector. % Responses - response vectors. Each column is a response vector % % options - Struct value in Matlab. The fields in options % that can be set: % % ReguAlpha - The regularization parameter. % Default value is 0.1. % % ReguType - 'Ridge': Tikhonov regularization % L2-norm regularizer % 'Lasso': L1-norm regularizer % 'RidgeLasso': Combine Ridge and Lasso % 'Custom': User provided % regularization matrix % Default: 'Ridge' % % 'Lasso' and 'RidgeLasso' will produce % sparse solution [See Ref 8] % % regularizerR - (nFea x nFea) regularization % matrix which should be provided % if ReguType is 'Custom'. nFea is % the feature number of data % matrix % % % % Output: % eigvector - Each column is an embedding function, for a new % sample vector (row vector) x, y = x*eigvector % will be the embedding result of x. % % If 'Lasso' or 'RidgeLasso' regularization is % used, the output eigvector will be a cell, % please see 'lars.m' for the result format. % % elapse - Time spent on different steps % % % % Examples: % % See SR_caller.m % %Reference: % % 1. Deng Cai, Xiaofei He, Jiawei Han, "Semi-Supervised Regression using % Spectral Techniques", Department of Computer Science % Technical Report No. 2749, University of Illinois at Urbana-Champaign % (UIUCDCS-R-2007-2749), July 2006. % % 2. Deng Cai, Xiaofei He, Jiawei Han, "Spectral Regression for % Dimensionality Reduction", Department of Computer Science % Technical Report No. 2856, University of Illinois at Urbana-Champaign % (UIUCDCS-R-2007-2856), May 2007. % % 3. Deng Cai, Xiaofei He, Jiawei Han, "SRDA: An Efficient Algorithm for % Large Scale Discriminant Analysis", Department of Computer Science % Technical Report No. 2857, University of Illinois at Urbana-Champaign % (UIUCDCS-R-2007-2857), May 2007. % % 4. Deng Cai, Xiaofei He, and Jiawei Han. "Isometric Projection", Proc. % 22nd Conference on Artifical Intelligence (AAAI'07), Vancouver, Canada, % July 2007. % % 5. Deng Cai, Xiaofei He, Jiawei Han, "Efficient Kernel Discriminant % Analysis via Spectral Regression", Department of Computer Science % Technical Report No. 2888, University of Illinois at Urbana-Champaign % (UIUCDCS-R-2007-2888), August 2007. % % 6. Deng Cai, Xiaofei He, Jiawei Han, "Spectral Regression: A Unified % Subspace Learning Framework for Content-Based Image Retrieval", ACM % Multimedia 2007, Augsburg, Germany, Sep. 2007. % % 7. Deng Cai, Xiaofei He, Jiawei Han, "Spectral Regression for Efficient % Regularized Subspace Learning", IEEE International Conference on % Computer Vision (ICCV), Rio de Janeiro, Brazil, Oct. 2007. % % 8. Deng Cai, Xiaofei He, Jiawei Han, "Spectral Regression: A Unified % Approach for Sparse Subspace Learning", Proc. 2007 Int. Conf. on Data % Mining (ICDM'07), Omaha, NE, Oct. 2007. % % 9. Deng Cai, Xiaofei He, Jiawei Han, "Efficient Kernel Discriminant % Analysis via Spectral Regression", Proc. 2007 Int. Conf. on Data % Mining (ICDM'07), Omaha, NE, Oct. 2007. % % 10. Deng Cai, Xiaofei He, Wei Vivian Zhang, Jiawei Han, "Regularized % Locality Preserving Indexing via Spectral Regression", Proc. 2007 ACM % Int. Conf. on Information and Knowledge Management (CIKM'07), Lisboa, % Portugal, Nov. 2007. % % % version 2.0 --Aug/2007 % version 1.0 --May/2006 % % Written by Deng Cai (dengcai2 AT cs.uiuc.edu) % if ~exist('data','var') global data; end if ~exist('Responses','var') global Responses; end AppendConstant = 0; if isfield(options,'AppendConstant') AppendConstant = options.AppendConstant; end [nSmp,nFea] = size(data); KernelWay = 0; if nFea > nSmp KernelWay = 1; end nScale = min(nSmp,nFea); if nScale < 3500 if isfield(options,'LSQR') & options.LSQR options.LSQR = 0; end end nRepeat = 20; if isfield(options,'nRepeat') nRepeat = options.nRepeat; end if ~isfield(options,'ReguAlpha') options.ReguAlpha = 0.1; end LassoCardi = 0; if isfield(options,'LassoCardi') LassoCardi = max(options.LassoCardi)+10; end tmp_T = cputime; if isfield(options,'RemoveMean') & options.RemoveMean sampleMean = mean(data); data = (data - repmat(sampleMean,nSmp,1)); AppendConstant = 0; end if AppendConstant data = [data ones(size(data,1),1)]; [nSmp,nFea] = size(data); end if strcmpi(options.ReguType,'Lasso') if nFea >= nSmp error('Please use RidgeLasso!'); end options.ReguAlpha = 0; options.ReguType = 'RidgeLasso'; end nVector = size(Responses,2); itn = 0; switch lower(options.ReguType) case {lower('Ridge')} if isfield(options,'LSQR') & options.LSQR [eigvector, istop, itn] = lsqr2(data, Responses, options.ReguAlpha, nRepeat); else if KernelWay ddata = data*data'; ddata = full(ddata); ddata = single(ddata); for i=1:size(ddata,1) ddata(i,i) = ddata(i,i) + options.ReguAlpha; end ddata = max(ddata,ddata'); R = chol(ddata); eigvector = R\(R'\Responses); eigvector = double(eigvector); eigvector = data'*eigvector; else ddata = data'*data; ddata = full(ddata); ddata = single(ddata); for i=1:size(ddata,1) ddata(i,i) = ddata(i,i) + options.ReguAlpha; end ddata = max(ddata,ddata'); B = data'*Responses; R = chol(ddata); eigvector = R\(R'\B); eigvector = double(eigvector); end end eigvector = eigvector./repmat(max(1e-10,sum(eigvector.^2,1).^.5),size(eigvector,1),1); case {lower('RidgeLasso')} if isfield(options, 'ResponseStart') iStart = options.ResponseStart; else iStart = 1; end if isfield(options, 'ResponseEnd') iEnd = options.ResponseEnd; else iEnd = nVector; end if isfield(options, 'ResponseRange') ResponseRange = options.ResponseRange; else ResponseRange = iStart:iEnd; end eigvector = {}; if nFea < 5000 global Gram; Gram = data'*data; Gram = max(Gram,Gram'); if options.ReguAlpha > 0 for i=1:size(Gram,1) Gram(i,i) = Gram(i,i) + options.ReguAlpha;