├── LICENSE ├── README.md ├── adjustedVariance.m ├── computeTradeOffCurve.m ├── invPow.m ├── optimizeVariance.m └── sparsePCA.m /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. By contrast, 15 | the GNU General Public License is intended to guarantee your freedom to 16 | share and change all versions of a program--to make sure it remains free 17 | software for all its users. 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Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Sparse PCA via Nonlinear IPM 2 | 3 | 4 | This archive contains a Matlab implementation of Sparse PCA 5 | using the *inverse power method for nonlinear eigenproblems (NIPM)*, 6 | introduced in the paper [1]. To compute multiple principal components, 7 | the deflation scheme described in [2] is used. 8 | 9 | 10 | 11 | 12 | 13 | ## Usage 14 | 15 | #### Computing a set of sparse loading vectors: 16 | 17 | [F, adj_var, cum_var] = sparsePCA(X, card, num_comp, num_runs, verbosity); 18 | 19 | #### Input variables 20 | 21 | X data matrix (num x dim) 22 | card desired number of non-sparse components (cardinality) of output 23 | for each principal component; card can be either a vector of size 24 | num_comp x 1, or a scalar (in this case all components will have 25 | the same cardinality) 26 | num_comp number of principal components 27 | num_runs number of additional runs of inverse power method with random 28 | initialization (default: 0) 29 | verbosity determines how much information is displayed (0-2, default: 1) 30 | 31 | #### Output variables 32 | 33 | F the sparse loading vectors 34 | adj_var the contributions to the adjusted variance of each component 35 | cum_var the cumulative adjusted variance 36 | 37 | 38 | #### Computing all loading vectors with cardinalities in a given range: 39 | 40 | [cards, vars, F] = computeTradeOffCurve(X, card_min, card_max, num_runs, verbosity); 41 | 42 | #### Input variables 43 | 44 | X data matrix (num x dim) 45 | card_min desired number of non-sparse components of output (cardinality) 46 | card_max if specified, all vectors with cardinality values in intervall 47 | [card_min,card_max] are computed (default: card_max=card_min) 48 | num_runs number of additional runs of inverse power method with random 49 | initialization (default: 0) 50 | verbosity determines frequency of console output (values 0-2, default: 1) 51 | 52 | #### Output variables 53 | 54 | cards the cardinalities (number of nonzeros) of the returned vectors 55 | vars the corresponding variances 56 | F the sparse loading vectors 57 | 58 | 59 | ## References 60 | 61 | [1] M. Hein and T. Bühler. 62 | *An Inverse Power Method for Nonlinear Eigenproblems with Applications 63 | in 1-Spectral Clustering and Sparse PCA*. 64 | Advances in Neural Information Processing Systems 23 (NIPS 2010). 65 | Extended version available at http://arxiv.org/abs/1012.0774. 66 | 67 | [2] T. Bühler. 68 | *A flexible framework for solving constrained ratio problems 69 | in machine learning*. Ph.D. Thesis, Saarland University, 2015. 70 | http://dx.doi.org/10.22028/D291-26604. 71 | 72 | 73 | ## License 74 | 75 | This program is free software: you can redistribute it and/or modify 76 | it under the terms of the GNU General Public License as published by 77 | the Free Software Foundation, either version 3 of the License, or 78 | (at your option) any later version. 79 | 80 | This program is distributed in the hope that it will be useful, 81 | but WITHOUT ANY WARRANTY; without even the implied warranty of 82 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 83 | GNU General Public License for more details. 84 | 85 | You should have received a copy of the GNU General Public License 86 | along with this program. If not, see . 87 | 88 | If you use this code for your publication, please include a reference 89 | to the paper "An inverse power method for nonlinear eigenproblems with 90 | applications in 1-spectral clustering and sparse PCA". 91 | 92 | 93 | ## Contact 94 | 95 | Copyright 2010-2015 Thomas Bühler and Matthias Hein (tb/hein@cs.uni-saarland.de). 96 | Machine Learning Group, Saarland University, Germany (http://www.ml.uni-saarland.de) 97 | -------------------------------------------------------------------------------- /adjustedVariance.m: -------------------------------------------------------------------------------- 1 | % Computes the (cumulative) adjusted variance via QR decomposition 2 | % 3 | % This program is free software: you can redistribute it and/or modify 4 | % it under the terms of the GNU General Public License as published by 5 | % the Free Software Foundation, either version 3 of the License, or 6 | % (at your option) any later version. 7 | % 8 | % Copyright 2010-15 Thomas Buehler and Matthias Hein 9 | % Machine Learning Group, Saarland University, Germany 10 | % http://www.ml.uni-saarland.de 11 | function [adj_var, cum_var]= adjustedVariance(Z, X) 12 | 13 | X = X - mean(X,1); 14 | factor = 1 / (size(X,1)-1); 15 | if (size(Z,2)==1) 16 | adj_var = factor * (norm(X * Z))^2; 17 | cum_var = adj_var; 18 | else 19 | U = X * Z; 20 | [Q, R] = qr(U); 21 | adj_var = factor * diag(R).^2; 22 | cum_var = cumsum(adj_var); 23 | end 24 | end 25 | -------------------------------------------------------------------------------- /computeTradeOffCurve.m: -------------------------------------------------------------------------------- 1 | % Computes the sparse PCA components using the nonlinear inverse power 2 | % method (NIPM), as described in the paper 3 | % 4 | % M. Hein and T. Buehler 5 | % An Inverse Power Method for Nonlinear Eigenproblems with Applications 6 | % in 1-Spectral Clustering and Sparse PCA 7 | % In Advances in Neural Information Processing Systems 23 (NIPS 2010) 8 | % Available online at http://arxiv.org/abs/1012.0774 9 | % 10 | % Usage: 11 | % [cards, vars, Z] = computeTradeOffCurve(X, card_min, card_max, num_runs, verbosity); 12 | % 13 | % X data matrix (num x dim) 14 | % card_min desired number of non-sparse components of output (cardinality) 15 | % card_max if specified, all vectors with cardinality values in intervall 16 | % [card_min,card_max] are computed (default: card_max=card_min) 17 | % num_runs number of runs of inverse power method with random 18 | % initialization (default: 0) 19 | % verbosity determines frequency of console output (values 0-2, default: 1) 20 | % 21 | % cards the cardinalities (number of nonzero components) of the 22 | % returned vectors 23 | % vars the corresponding variances 24 | % Z the sparse principal components 25 | % 26 | % This program is free software: you can redistribute it and/or modify 27 | % it under the terms of the GNU General Public License as published by 28 | % the Free Software Foundation, either version 3 of the License, or 29 | % (at your option) any later version. 30 | % 31 | % Copyright 2010-15 Thomas Buehler and Matthias Hein 32 | % Machine Learning Group, Saarland University, Germany 33 | % http://www.ml.uni-saarland.de 34 | function [cards, vars, Z]= computeTradeOffCurve(X, card_min, card_max, num_runs, verbosity) 35 | 36 | if (nargin<5), verbosity=1; end 37 | if (nargin<4), num_runs=0; end 38 | if (nargin<3), card_max=card_min; end 39 | 40 | assert(card_min>0,'Wrong usage. Cardinality has to positive.'); 41 | assert(card_max>=card_min,'Wrong usage. card_max cannot be smaller than card_min.'); 42 | assert(num_runs>=0,'Wrong usage. num_runs cannot be negative.'); 43 | assert(card_max<=size(X,2),'Wrong usage. Cardinality can not be larger than dim.'); 44 | 45 | [num,dim]=size(X); 46 | gam_left=0; 47 | gam_right=1; 48 | 49 | % compute startvector 50 | norm_a_i=zeros(dim,1); 51 | for i=1:dim, norm_a_i(i)=norm(X(:,i)); end 52 | [rho_max,i_max]=max(norm_a_i); 53 | start1=zeros(dim,1); 54 | start1(i_max)=1; 55 | 56 | % output 57 | results.cards=zeros(card_max-card_min+1,1); 58 | results.gammas=zeros(card_max-card_min+1,1); 59 | results.vars=zeros(card_max-card_min+1,1); 60 | results.Z=zeros(dim,card_max-card_min+1); 61 | results.lambdas=zeros(card_max-card_min+1,1); 62 | results.found_cards=zeros(card_max-card_min+1,1); 63 | 64 | card0=round((card_max+card_min)/2); 65 | 66 | % searches for a vector with cardinality card0 via binary search (and 67 | % stores the solutions for other cardinalities it finds along the way) 68 | results = binSearch(results, X, card0, gam_left, gam_right, ... 69 | num_runs, start1, card_min, card_max, verbosity); 70 | 71 | % repeat this until all gaps are filled 72 | ix1=find(results.found_cards==0,1); 73 | while(~isempty(ix1)) 74 | card_min_temp=card_min-1+ix1; 75 | if(card_min_temp>card_min) 76 | gam_right=results.gammas(card_min_temp-card_min); 77 | else 78 | gam_right= 1; 79 | end 80 | 81 | ix2=find(results.found_cards(ix1:end)>0,1); 82 | if(~isempty(ix2)) 83 | if results.found_cards(ix2)1) 98 | fprintf('card_min_temp= %d card_max_temp= %d gam_left=%.5g gam_right=%.5g\n',card_min_temp,card_max_temp,gam_left,gam_right); 99 | end 100 | 101 | results = binSearch(results, X, card0, gam_left, gam_right, num_runs, ... 102 | start1, card_min, card_max, verbosity); 103 | 104 | ix1=find(results.found_cards==0,1); 105 | end 106 | 107 | results = postProcess(results,X,card_min,card_max,num_runs,verbosity); 108 | 109 | cards=results.cards; 110 | vars=results.vars; 111 | Z=results.Z; 112 | 113 | end 114 | 115 | 116 | % perform sparse PCA with current value of gamma 117 | function [z, var_new, card_new, lambda_new] = performOneRun(X, gam, maxit, start) 118 | [z,lambda_new] = invPow(X,gam,maxit,start); 119 | ind_z=abs(z)>0; 120 | card_new = sum(ind_z); 121 | [z,var_new] = optimizeVariance(X,ind_z); 122 | end 123 | 124 | 125 | % perform sparse PCA with current value of gamma - one run initialized with 126 | % start1 and num_runs random initalizations 127 | function [Z, vars, cards, lambdas, best_card] = performMultipleRuns(X, gam, maxit, start1, num_runs) 128 | [num,dim]=size(X); 129 | [Z, vars, cards, lambdas] = performOneRun(X,gam,maxit,start1); 130 | 131 | % keep track of the cardinality corresponding to smallest lambda 132 | best_lambda = lambdas; 133 | best_card = cards; 134 | 135 | for l=1:num_runs 136 | start = randn(dim,1); 137 | [z, var_new, card_new, lambda_new] = performOneRun(X,gam,maxit,start); 138 | 139 | %find the best variance 140 | already_seen = false; 141 | for i = 1:length(cards) 142 | if cards(i) == card_new 143 | already_seen = true; 144 | if var_new > vars(i) 145 | vars(i) = var_new; 146 | Z(:,i) = z; 147 | lambdas(i) = lambda_new; 148 | end 149 | end 150 | end 151 | 152 | % append if cardinality has not been seen before 153 | if ~already_seen 154 | Z = [Z z]; 155 | vars = [vars var_new]; 156 | cards = [cards card_new]; 157 | lambdas = [lambdas lambda_new]; 158 | end 159 | 160 | % keep track of the cardinality corresponding to smallest lambda 161 | if lambda_new < best_lambda 162 | best_lambda = lambda_new; 163 | best_card = card_new; 164 | end 165 | end 166 | end 167 | 168 | 169 | % searches for a vector with cardinality card0 via binary search (and 170 | % stores the solutions for other cardinalities it finds along the way) 171 | function results = binSearch(results, X, card0, gam_left, gam_right, num_runs, ... 172 | start1, card_min_global, card_max_global, verbosity) 173 | 174 | maxit=100; 175 | epsilon=1E-6; 176 | isFound=false; 177 | splitpoint=0.5; 178 | gam=splitpoint*gam_left+(1-splitpoint)*gam_right; 179 | 180 | while (~isFound && gam_right-gam_left>epsilon) 181 | [Z_tmp, vars_tmp, cards_tmp, lambdas_tmp, best_card] = performMultipleRuns(X,gam, maxit,start1,num_runs); 182 | 183 | % consider the cardinality corresponding to smallest lambda 184 | if card0 == best_card 185 | isFound = true; 186 | else 187 | % update gamma boundaries 188 | if (best_card > card0) 189 | gam_left = gam; 190 | elseif (best_card < card0) 191 | gam_right = gam; 192 | end 193 | end 194 | 195 | % discard all values which are outside the cardinality range 196 | ind = find(cards_tmp >= card_min_global & cards_tmp <= card_max_global); 197 | 198 | if(verbosity>1) 199 | ind2 =find(cards_tmp < card_min_global | cards_tmp > card_max_global); 200 | if(~isempty(ind2)) 201 | for l=1:length(ind2) 202 | fprintf('Skipping solution with cardinality %d\n',cards_tmp(ind2(l))); 203 | end 204 | end 205 | end 206 | 207 | cards_tmp = cards_tmp(ind); 208 | vars_tmp = vars_tmp(ind); 209 | Z_tmp = Z_tmp(:,ind); 210 | lambdas_tmp = lambdas_tmp(ind); 211 | 212 | % store best results 213 | for l=1:length(cards_tmp) 214 | cur_card = cards_tmp(l); 215 | cur_var = vars_tmp(l); 216 | 217 | if cur_card == best_card 218 | results.found_cards(best_card-card_min_global+1) = best_card; 219 | end 220 | 221 | if results.vars(cur_card-card_min_global+1) < cur_var 222 | 223 | if verbosity>1 224 | if (results.cards(cur_card-card_min_global+1)==0) 225 | fprintf('Found solution with cardinality %d\n',cur_card); 226 | else 227 | fprintf('Improved solution with cardinality %d\n',cur_card); 228 | end 229 | end 230 | results.cards(cur_card-card_min_global+1) = cur_card; 231 | results.vars(cur_card-card_min_global+1) = cur_var; 232 | results.Z(:,cur_card-card_min_global+1) = Z_tmp(:,l); 233 | results.gammas(cur_card-card_min_global+1,:) = gam; 234 | results.lambdas(cur_card-card_min_global+1) = lambdas_tmp(l); 235 | end 236 | end 237 | gam=splitpoint*gam_left+(1-splitpoint)*gam_right; 238 | 239 | if(verbosity>1) 240 | fprintf('gam_left= %.3g gam=%.3g gam_right= %.3g gam_right-gam_left =%.3g best_card=%d card0=%d\n', ... 241 | gam_left,gam,gam_right,gam_right-gam_left,best_card,card0); 242 | end 243 | end 244 | 245 | % if no vector with cardinality card0 could be found, set entry to inf 246 | if(~isFound) 247 | % (might have been found as suboptimal solution) 248 | if results.cards(card0-card_min_global+1)==0 249 | results.cards(card0-card_min_global+1)=Inf; 250 | results.vars(card0-card_min_global+1)=Inf; 251 | end 252 | if verbosity>1 253 | fprintf('Skipping solution with cardinality %d\n',card0); 254 | end 255 | results.found_cards(card0-card_min_global+1)=inf; 256 | end 257 | end 258 | 259 | % fill gaps and make sure the variance is monotonically increasing 260 | function results=postProcess(results,X,card_min,card_max,num_runs,verbosity) 261 | 262 | dim=size(X,2); 263 | isChanging=true; 264 | vars_old=results.vars; 265 | while(isChanging) 266 | % check if variance is monotonically increasing 267 | cur_var=results.vars(1); 268 | curz=results.Z(:,1); 269 | % special treatment of first entry 270 | if(results.cards(1)==inf) 271 | % greedily add the components with highest variance 272 | norm_a_i=zeros(dim,1); 273 | for i=1:dim, norm_a_i(i)=norm(X(:,i)); end 274 | [norm_sorted,sort_ind]=sort(norm_a_i,'descend'); 275 | pattern=zeros(dim,1); 276 | pattern(sort_ind(1:card_min))=1; 277 | [z, new_var2]=optimizeVariance(X,logical(pattern)); 278 | 279 | results.vars(1)=new_var2; 280 | results.Z(:,1)=z; 281 | results.cards(1)=sum(pattern); 282 | assert(results.cards(1)==card_min) 283 | 284 | % check if we find something better via invpow 285 | gam_left=0; 286 | gam_right=1; 287 | 288 | results = binSearch(results, X, card_min, gam_left, gam_right, ... 289 | num_runs, z, card_min, card_max, verbosity); 290 | end 291 | for k=2:length(results.vars) 292 | new_var=results.vars(k); 293 | if(new_var increasse in variance guaranteed 296 | norm_a_i=zeros(dim,1); 297 | pattern = abs(curz)>0; 298 | ind=find(pattern==0); 299 | temp=X*curz;temp=temp/norm(temp); 300 | for i=1:length(ind), 301 | norm_a_i(ind(i))=(X(:,ind(i))'*temp)^2; 302 | end 303 | [rho_max,i_max]=max(norm_a_i); 304 | pattern(i_max)=1; 305 | [z, new_var2]=optimizeVariance(X,pattern); 306 | 307 | results.vars(k)=new_var2; 308 | results.Z(:,k)=z; 309 | results.cards(k)=sum(pattern); 310 | 311 | % check if we find something better via invpow 312 | card0=card_min-1+k; 313 | gam_left=0; 314 | gam_right=1; 315 | 316 | results = binSearch(results, X, card0, gam_left, gam_right, ... 317 | num_runs, z, card_min, card_max, verbosity); 318 | end 319 | cur_var=results.vars(k); 320 | curz=results.Z(:,k); 321 | end 322 | 323 | for k=1:length(results.vars) 324 | assert(results.vars(k)1 332 | fprintf('isChanging=%d normdiff=%.15g\n',isChanging,norm(results.vars-vars_old,inf)); 333 | end 334 | vars_old=results.vars; 335 | end 336 | 337 | if verbosity>1 338 | isDecreasing=false; 339 | cur_var=results.vars(1); 340 | for k=2:length(results.vars) 341 | new_var=results.vars(k); 342 | if new_var< cur_var 343 | isDecreasing=true; 344 | end 345 | cur_var=new_var; 346 | end 347 | fprintf('isChanging=%d isDecreasing=%d \n',isChanging,isDecreasing); 348 | end 349 | end 350 | -------------------------------------------------------------------------------- /invPow.m: -------------------------------------------------------------------------------- 1 | % Performs one run of the inverse power method for sparse PCA as 2 | % described in the paper 3 | % 4 | % M. Hein and T. Buehler 5 | % An Inverse Power Method for Nonlinear Eigenproblems with Applications in 1-Spectral Clustering and Sparse PCA 6 | % In Advances in Neural Information Processing Systems 23 (NIPS 2010) 7 | % Available online at http://arxiv.org/abs/1012.0774 8 | % 9 | % Usage: 10 | % [z,lambda,var]= invPow(X,gamma,maxit,z) 11 | % 12 | % This program is free software: you can redistribute it and/or modify 13 | % it under the terms of the GNU General Public License as published by 14 | % the Free Software Foundation, either version 3 of the License, or 15 | % (at your option) any later version. 16 | % 17 | % Copyright 2010-15 Thomas Buehler and Matthias Hein 18 | % Machine Learning Group, Saarland University, Germany 19 | % http://www.ml.uni-saarland.de 20 | function [z,lambda,var]= invPow(X,gamma,maxit,z) 21 | debug=false; 22 | tol=1E-5; 23 | [num,dim]=size(X); 24 | 25 | Xz=X * z; 26 | denom=norm(Xz); 27 | z=z/denom; 28 | sigmaZ= (X'*Xz)/denom; 29 | 30 | diff_lambda=inf; 31 | 32 | k=0; 33 | 34 | lambda_old=(1-gamma)*norm(z,2)+gamma*sum(abs(z)); 35 | while (k<=maxit && diff_lambda>tol) 36 | k=k+1; 37 | 38 | mu=sigmaZ*lambda_old; 39 | 40 | ix = find(abs(mu)>gamma); 41 | z_new = zeros(dim,1); 42 | z_new(ix)= mu(ix)-gamma*sign(mu(ix)); 43 | 44 | if(debug) 45 | primalobj= (1-gamma)*norm(z_new) + gamma*norm(z_new,1) - mu'*z_new; 46 | end 47 | 48 | Xz=X*z_new; 49 | denom = norm(Xz,2); 50 | z=z_new/denom; 51 | sigmaZ= (X'*Xz)/denom; 52 | 53 | lambda=(1-gamma)*norm(z,2)+gamma*sum(abs(z)); 54 | diff_lambda=(lambda_old-lambda)/lambda_old; 55 | assert(diff_lambda>=0 || abs(diff_lambda)<1E-15); 56 | lambda_old=lambda; 57 | end 58 | 59 | var=(norm(X*z)/norm(z))^2; 60 | end -------------------------------------------------------------------------------- /optimizeVariance.m: -------------------------------------------------------------------------------- 1 | % Finds the optimal variance for a given sparsity pattern ind 2 | % 3 | % This program is free software: you can redistribute it and/or modify 4 | % it under the terms of the GNU General Public License as published by 5 | % the Free Software Foundation, either version 3 of the License, or 6 | % (at your option) any later version. 7 | % 8 | % Copyright 2010-15 Thomas Buehler and Matthias Hein 9 | % Machine Learning Group, Saarland University, Germany 10 | % http://www.ml.uni-saarland.de 11 | function [z, var]=optimizeVariance(X,ind) 12 | tol = 1E-8; 13 | 14 | num_comp=sum(ind); 15 | if (num_comp==1) 16 | z=double(ind); 17 | var = (norm(X(:,ind)))^2; 18 | else 19 | X2=X(:,ind); 20 | z_temp = randn(num_comp,1); 21 | 22 | diff = inf; 23 | while diff > tol 24 | y = X2 * z_temp; 25 | z_temp_new = X2'* y; 26 | z_temp_new= z_temp_new / norm(z_temp_new); 27 | 28 | diff = norm(z_temp-z_temp_new); 29 | z_temp=z_temp_new; 30 | end 31 | var = (norm(X2 * z_temp))^2; 32 | 33 | z=zeros(size(X,2),1); 34 | z(ind)=z_temp; 35 | end 36 | end -------------------------------------------------------------------------------- /sparsePCA.m: -------------------------------------------------------------------------------- 1 | function [F,adj_var,cum_var] = sparsePCA(X, card, num_comp, num_runs, verbosity) 2 | % Computes multiple sparse PCA components. Each component is computed 3 | % using the nonlinear inverse power method described in the below paper, 4 | % then deflation is performed. 5 | % 6 | % M. Hein and T. Buehler 7 | % An Inverse Power Method for Nonlinear Eigenproblems with Applications 8 | % in 1-Spectral Clustering and Sparse PCA 9 | % In Advances in Neural Information Processing Systems 23 (NIPS 2010) 10 | % Available online at http://arxiv.org/abs/1012.0774 11 | % 12 | % Usage: 13 | % F = sparsePCA(X, card, num_comp, num_runs, verbosity); 14 | % 15 | % X data matrix (num x dim) 16 | % card desired number of non-sparse components of output (cardinality) 17 | % for each principal component; card can be either a vector of 18 | % length num_comp x 1, or a scalar (all components have same 19 | % cardinality) 20 | % num_comp number of principal components 21 | % num_runs number of additional runs of inverse power method with random 22 | % initialization (default: 0) 23 | % verbosity determines how much information is displayed (0-2, default: 1) 24 | % 25 | % F the loading vectors 26 | % adj_var the contributions to the adjusted variance of each component 27 | % cum_var the cumulative adjusted variance 28 | % 29 | % This program is free software: you can redistribute it and/or modify 30 | % it under the terms of the GNU General Public License as published by 31 | % the Free Software Foundation, either version 3 of the License, or 32 | % (at your option) any later version. 33 | % 34 | % Copyright 2010-15 Thomas Buehler and Matthias Hein 35 | % Machine Learning Group, Saarland University, Germany 36 | % http://www.ml.uni-saarland.de 37 | 38 | proj_pc=true; 39 | if (nargin<5), verbosity=1; end 40 | if (nargin<4), num_runs=0; end 41 | 42 | for l=1:length(card) 43 | assert(card(l)>0,'Wrong usage. Cardinality has to positive.'); 44 | assert(card(l)<=size(X,2),'Wrong usage. Cardinality can not be larger than dim.'); 45 | end 46 | assert(num_runs>=0,'Wrong usage. num_runs cannot be negative.'); 47 | 48 | if (length(card)==1) 49 | card = card * ones(num_comp,1); 50 | else 51 | assert(size(card,1)==num_comp && size(card,2)==1 ,'Wrong usage. card has wrong dimension.'); 52 | end 53 | 54 | X_cur=X; 55 | dim=size(X_cur,2); 56 | F=zeros(dim,num_comp); 57 | 58 | %main loop 59 | for l=1:num_comp 60 | [all_cards, all_vars, F_temp]= computeTradeOffCurve(X_cur,card(l),card(l),num_runs,verbosity); 61 | assert(size(F_temp,1) == dim) 62 | assert(size(F,1) == dim) 63 | assert(size(F,2) == num_comp) 64 | 65 | f=F_temp(:,end); 66 | F(:,l)=f; 67 | 68 | if verbosity>0 69 | fprintf('Finished computing principal component number %d. #nonzeros=%d\n',l,card(l)); 70 | end 71 | 72 | % perform deflation with respect to principal components 73 | if(proj_pc) 74 | z=X_cur*f; 75 | znorm=z/norm(z); 76 | 77 | % perform deflation 78 | X_cur= X_cur - znorm*(znorm'*X_cur); 79 | else % perform deflation with respect to loading vectors 80 | if l>1 81 | q= f- Q*(Q'*f); 82 | else 83 | q=f; 84 | end 85 | 86 | Q(:,l)=q/norm(q); %orthonormal basis for space spanned by previous f 87 | 88 | % perform deflation (orthogonal projection deflation) 89 | X_cur=X_cur-(X_cur*q)*q'; 90 | end 91 | end 92 | [adj_var, cum_var]= adjustedVariance(F,X); 93 | 94 | end 95 | 96 | --------------------------------------------------------------------------------