[26fa5c]: inst / nmf_bpas.m  Maximize  Restore  History

Download this file

712 lines (654 with data), 28.6 kB

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
## Copyright (c) 2012 by Jingu Kim and Haesun Park <jingu@cc.gatech.edu>
##
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program. If not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{W}, @var{H}, @var{iter}, @var{HIS}] = } nmf_bpas (@var{A}, @var{k})
## Nonnegative Matrix Factorization by Alternating Nonnegativity Constrained Least Squares
## using Block Principal Pivoting/Active Set method.
##
## This function solves one the following problems: given @var{A} and @var{k}, find @var{W} and @var{H} such that
## (1) minimize 1/2 * || @var{A}-@var{W}@var{H} ||_F^2
## (2) minimize 1/2 * ( || @var{A}-@var{W}@var{H} ||_F^2 + alpha * || @var{W} ||_F^2 + beta * || @var{H} ||_F^2 )
## (3) minimize 1/2 * ( || @var{A}-@var{W}@var{H} ||_F^2 + alpha * || @var{W} ||_F^2 + beta * (sum_(i=1)^n || @var{H}(:,i) ||_1^2 ) )
## where @var{W}>=0 and @var{H}>=0 elementwise.
## The input arguments are @var{A} : Input data matrix (m x n) and @var{k} : Target low-rank.
##
##
## @strong{Optional Inputs}
## @table @samp
## @item Type : Default is 'regularized', which is recommended for quick application testing unless 'sparse' or 'plain' is explicitly needed. If sparsity is needed for 'W' factor, then apply this function for the transpose of 'A' with formulation (3). Then, exchange 'W' and 'H' and obtain the transpose of them. Imposing sparsity for both factors is not recommended and thus not included in this software.
## @table @asis
## @item 'plain' to use formulation (1)
## @item 'regularized' to use formulation (2)
## @item 'sparse' to use formulation (3)
## @end table
##
## @item NNLSSolver : Default is 'bp', which is in general faster.
## @table @asis
## item 'bp' to use the algorithm in [1]
## item 'as' to use the algorithm in [2]
## @end table
##
## @item Alpha : Parameter alpha in the formulation (2) or (3). Default is the average of all elements in A. No good justfication for this default value, and you might want to try other values.
## @item Beta : Parameter beta in the formulation (2) or (3).
## Default is the average of all elements in A. No good justfication for this default value, and you might want to try other values.
## @item MaxIter : Maximum number of iterations. Default is 100.
## @item MinIter : Minimum number of iterations. Default is 20.
## @item MaxTime : Maximum amount of time in seconds. Default is 100,000.
## @item Winit : (m x k) initial value for W.
## @item Hinit : (k x n) initial value for H.
## @item Tol : Stopping tolerance. Default is 1e-3. If you want to obtain a more accurate solution, decrease TOL and increase MAX_ITER at the same time.
## @item Verbose :
## @table @asis
## @item 0 (default) - No debugging information is collected.@*
## @item 1 (debugging purpose) - History of computation is returned by 'HIS' variable.
## @item 2 (debugging purpose) - History of computation is additionally printed on screen.
## @end table
## @end table
##
## @strong{Outputs}
## @table @samp
## @item W : Obtained basis matrix (m x k)
## @item H : Obtained coefficients matrix (k x n)
## @item iter : Number of iterations
## @item HIS : (debugging purpose) History of computation
## @end table
##
## Usage Examples:
## @example
## nmf(A,10)
## nmf(A,20,'verbose',2)
## nmf(A,30,'verbose',2,'nnls_solver','as')
## nmf(A,5,'verbose',2,'type','sparse')
## nmf(A,60,'verbose',1,'type','plain','w_init',rand(m,k))
## nmf(A,70,'verbose',2,'type','sparse','nnls_solver','bp','alpha',1.1,'beta',1.3)
## @end example
##
## References:
## [1] For using this software, please cite:@*
## Jingu Kim and Haesun Park, Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons,@*
## In Proceedings of the 2008 Eighth IEEE International Conference on Data Mining (ICDM'08), 353-362, 2008@*
## [2] If you use 'nnls_solver'='as' (see below), please cite:@*
## Hyunsoo Kim and Haesun Park, Nonnegative Matrix Factorization Based @*
## on Alternating Nonnegativity Constrained Least Squares and Active Set Method, @*
## SIAM Journal on Matrix Analysis and Applications, 2008, 30, 713-730
##
## Check original code at @url{http://www.cc.gatech.edu/~jingu}
##
## @seealso{nmf_pg}
## @end deftypefn
## 2012 - Modified and adapted to Octave 3.6.1 by
## Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
# TODO
# - Format code.
# - Vectorize loops.
function [W, H, iter, HIS] = nmf_bpas (A, k , varargin)
page_screen_output (0, "local");
[m,n] = size(A);
ST_RULE = 1;
# --- Parse arguments --- #
parser = inputParser ();
parser.FunctionName = "nmf_bpas";
parser = addParamValue (parser,'Winit', rand(m,k), @ismatrix);
parser = addParamValue (parser,'Hinit', rand(k,n), @ismatrix);
parser = addParamValue (parser,'Tol', 1e-3, @(x)x>0);
parser = addParamValue (parser,'Alpha', mean (A(:)), @(x)x>=0);
parser = addParamValue (parser,'Beta', mean (A(:)), @(x)x>=0);
parser = addParamValue (parser,'MaxIter', 100, @(x)x>0);
parser = addParamValue (parser,'MaxTime', 1e3, @(x)x>0);
parser = addParamValue (parser,'Verbose', false);
val_type = @(x,c) ischar (x) && any (strcmpi (x,c));
parser = addParamValue (parser,'Type', 'regularized', ...
@(x)val_type (x,{'regularized', 'sparse','plain'}));
parser = addParamValue (parser,'NNLSSolver', 'bp', ...
@(x)val_type (x,{'bp', 'as'}));
parser = parse(parser,varargin{:});
% Default configuration
par.m = m;
par.n = n;
par.type = parser.Results.Type;
par.nnls_solver = parser.Results.NNLSSolver;
par.alpha = parser.Results.Alpha;
par.beta = parser.Results.Beta;
par.max_iter = parser.Results.MaxIter;
par.min_iter = 20;
par.max_time = parser.Results.MaxTime;
par.tol = parser.Results.Tol;
par.verbose = parser.Results.Verbose;
W = parser.Results.Winit;
H = parser.Results.Hinit;
# TODO check if can be removed
argAlpha = par.alpha;
argBeta = par.beta;
clear parser val_type
### PARSING TYPE
# TODO add callbacks here to use during main loop. See [1]
% for regularized/sparse case
salphaI = sqrt (par.alpha) * eye (k);
zerokm = zeros (k,m);
if strcmpi (par.type, 'regularized')
sbetaI = sqrt (par.beta) * eye (k);
zerokn = zeros (k,n);
elseif strcmpi (par.type, 'sparse')
sbetaE = sqrt (par.beta) * ones (1,k);
betaI = par.beta * ones (k,k);
zero1n = zeros (1,n);
end
###
# Verbosity
display(par);
### Done till here Sun Mar 25 19:00:26 2012
HIS = 0;
if par.verbose % collect information for analysis/debugging
[gradW,gradH] = getGradient(A,W,H,par.type,par.alpha,par.beta);
initGrNormW = norm(gradW,'fro');
initGrNormH = norm(gradH,'fro');
initNorm = norm(A,'fro');
numSC = 3;
initSCs = zeros(numSC,1);
for j=1:numSC
initSCs(j) = getInitCriterion(j,A,W,H,par.type,par.alpha,par.beta,gradW,gradH);
end
%---(1)------(2)--------(3)--------(4)--------(5)---------(6)----------(7)------(8)-----(9)-------(10)--------------(11)-------
% iter # | elapsed | totalTime | subIterW | subIterH | rel. obj.(%) | NM_GRAD | GRAD | DELTA | W density (%) | H density (%)
%------------------------------------------------------------------------------------------------------------------------------
HIS = zeros(1,11);
HIS(1,[1:5])=0;
ver.initGrNormW = initGrNormW;
ver.initGrNormH = initGrNormH;
ver.initNorm = initNorm; HIS(1,6) = ver.initNorm;
ver.SC1 = initSCs(1); HIS(1,7) = ver.SC1;
ver.SC2 = initSCs(2); HIS(1,8) = ver.SC2;
ver.SC3 = initSCs(3); HIS(1,9) = ver.SC3;
ver.W_density = length(find(W>0))/(m*k); HIS(1,10) = ver.W_density;
ver.H_density = length(find(H>0))/(n*k); HIS(1,11) = ver.H_density;
if par.verbose == 2
disp (ver);
end
tPrev = cputime;
end
tStart = cputime;
tTotal = 0;
initSC = getInitCriterion(ST_RULE,A,W,H,par.type,par.alpha,par.beta);
SCconv = 0;
SC_COUNT = 3;
#TODO: [1] Replace with callbacks avoid switching each time
for iter=1:par.max_iter
switch par.type
case 'plain'
[H,gradHX,subIterH] = nnlsm(W,A,H,par.nnls_solver);
[W,gradW,subIterW] = nnlsm(H',A',W',par.nnls_solver);, W=W';, gradW=gradW';
gradH = (W'*W)*H - W'*A;
case 'regularized'
[H,gradHX,subIterH] = nnlsm([W;sbetaI],[A;zerokn],H,par.nnls_solver);
[W,gradW,subIterW] = nnlsm([H';salphaI],[A';zerokm],W',par.nnls_solver);, W=W';, gradW=gradW';
gradH = (W'*W)*H - W'*A + par.beta*H;
case 'sparse'
[H,gradHX,subIterH] = nnlsm([W;sbetaE],[A;zero1n],H,par.nnls_solver);
[W,gradW,subIterW] = nnlsm([H';salphaI],[A';zerokm],W',par.nnls_solver);, W=W';, gradW=gradW';
gradH = (W'*W)*H - W'*A + betaI*H;
end
if par.verbose % collect information for analysis/debugging
elapsed = cputime-tPrev;
tTotal = tTotal + elapsed;
ver = [];
idx = iter+1;
%---(1)------(2)--------(3)--------(4)--------(5)---------(6)----------(7)------(8)-----(9)-------(10)--------------(11)-------
% iter # | elapsed | totalTime | subIterW | subIterH | rel. obj.(%) | NM_GRAD | GRAD | DELTA | W density (%) | H density (%)
%------------------------------------------------------------------------------------------------------------------------------
ver.iter = iter; HIS(idx,1)=iter;
ver.elapsed = elapsed; HIS(idx,2)=elapsed;
ver.tTotal = tTotal; HIS(idx,3)=tTotal;
ver.subIterW = subIterW; HIS(idx,4)=subIterW;
ver.subIterH = subIterH; HIS(idx,5)=subIterH;
ver.relError = norm(A-W*H,'fro')/initNorm; HIS(idx,6)=ver.relError;
ver.SC1 = getStopCriterion(1,A,W,H,par.type,par.alpha,par.beta,gradW,gradH)/initSCs(1); HIS(idx,7)=ver.SC1;
ver.SC2 = getStopCriterion(2,A,W,H,par.type,par.alpha,par.beta,gradW,gradH)/initSCs(2); HIS(idx,8)=ver.SC2;
ver.SC3 = getStopCriterion(3,A,W,H,par.type,par.alpha,par.beta,gradW,gradH)/initSCs(3); HIS(idx,9)=ver.SC3;
ver.W_density = length(find(W>0))/(m*k); HIS(idx,10)=ver.W_density;
ver.H_density = length(find(H>0))/(n*k); HIS(idx,11)=ver.H_density;
if par.verbose == 2, display(ver);, end
tPrev = cputime;
end
if (iter > par.min_iter)
SC = getStopCriterion(ST_RULE,A,W,H,par.type,par.alpha,par.beta,gradW,gradH);
if (par.verbose && (tTotal > par.max_time)) || (~par.verbose && ((cputime-tStart)>par.max_time))
break;
elseif (SC/initSC <= par.tol)
SCconv = SCconv + 1;
if (SCconv >= SC_COUNT)
break;
end
else
SCconv = 0;
end
end
end
[m,n]=size(A);
norm2=sqrt(sum(W.^2,1));
toNormalize = norm2>0;
W(:,toNormalize) = W(:,toNormalize)./repmat(norm2(toNormalize),m,1);
H(toNormalize,:) = H(toNormalize,:).*repmat(norm2(toNormalize)',1,n);
final.iterations = iter;
if par.verbose
final.elapsed_total = tTotal;
else
final.elapsed_total = cputime-tStart;
end
final.relative_error = norm(A-W*H,'fro')/norm(A,'fro');
final.W_density = length(find(W>0))/(m*k);
final.H_density = length(find(H>0))/(n*k);
display(final);
endfunction
%------------------------------------------------------------------------------------------------------------------------
% Utility Functions
%-------------------------------------------------------------------------------
function retVal = getInitCriterion(stopRule,A,W,H,type,alpha,beta,gradW,gradH)
% STOPPING_RULE : 1 - Normalized proj. gradient
% 2 - Proj. gradient
% 3 - Delta by H. Kim
% 0 - None (want to stop by MAX_ITER or MAX_TIME)
if nargin~=9
[gradW,gradH] = getGradient(A,W,H,type,alpha,beta);
end
[m,k]=size(W);, [k,n]=size(H);, numAll=(m*k)+(k*n);
switch stopRule
case 1
retVal = norm([gradW; gradH'],'fro')/numAll;
case 2
retVal = norm([gradW; gradH'],'fro');
case 3
retVal = getStopCriterion(3,A,W,H,type,alpha,beta,gradW,gradH);
case 0
retVal = 1;
end
endfunction
%-------------------------------------------------------------------------------
function retVal = getStopCriterion(stopRule,A,W,H,type,alpha,beta,gradW,gradH)
% STOPPING_RULE : 1 - Normalized proj. gradient
% 2 - Proj. gradient
% 3 - Delta by H. Kim
% 0 - None (want to stop by MAX_ITER or MAX_TIME)
if nargin~=9
[gradW,gradH] = getGradient(A,W,H,type,alpha,beta);
end
switch stopRule
case 1
pGradW = gradW(gradW<0|W>0);
pGradH = gradH(gradH<0|H>0);
pGrad = [gradW(gradW<0|W>0); gradH(gradH<0|H>0)];
pGradNorm = norm(pGrad);
retVal = pGradNorm/length(pGrad);
case 2
pGradW = gradW(gradW<0|W>0);
pGradH = gradH(gradH<0|H>0);
pGrad = [gradW(gradW<0|W>0); gradH(gradH<0|H>0)];
retVal = norm(pGrad);
case 3
resmat=min(H,gradH); resvec=resmat(:);
resmat=min(W,gradW); resvec=[resvec; resmat(:)];
deltao=norm(resvec,1); %L1-norm
num_notconv=length(find(abs(resvec)>0));
retVal=deltao/num_notconv;
case 0
retVal = 1e100;
end
endfunction
%-------------------------------------------------------------------------------
function [gradW,gradH] = getGradient(A,W,H,type,alpha,beta)
switch type
case 'plain'
gradW = W*(H*H') - A*H';
gradH = (W'*W)*H - W'*A;
case 'regularized'
gradW = W*(H*H') - A*H' + alpha*W;
gradH = (W'*W)*H - W'*A + beta*H;
case 'sparse'
k=size(W,2);
betaI = beta*ones(k,k);
gradW = W*(H*H') - A*H' + alpha*W;
gradH = (W'*W)*H - W'*A + betaI*H;
end
endfunction
%------------------------------------------------------------------------------------------------------------------------
function [X,grad,iter] = nnlsm(A,B,init,solver)
switch solver
case 'bp'
[X,grad,iter] = nnlsm_blockpivot(A,B,0,init);
case 'as'
[X,grad,iter] = nnlsm_activeset(A,B,1,0,init);
end
endfunction
%------------------------------------------------------------------------------------------------------------------------
function [ X,Y,iter,success ] = nnlsm_activeset( A, B, overwrite, isInputProd, init)
% Nonnegativity Constrained Least Squares with Multiple Righthand Sides
% using Active Set method
%
% This software solves the following problem: given A and B, find X such that
% minimize || AX-B ||_F^2 where X>=0 elementwise.
%
% Reference:
% Charles L. Lawson and Richard J. Hanson, Solving Least Squares Problems,
% Society for Industrial and Applied Mathematics, 1995
% M. H. Van Benthem and M. R. Keenan,
% Fast Algorithm for the Solution of Large-scale Non-negativity-constrained Least Squares Problems,
% J. Chemometrics 2004; 18: 441-450
%
% Written by Jingu Kim (jingu@cc.gatech.edu)
% School of Computational Science and Engineering,
% Georgia Institute of Technology
%
% Last updated Feb-20-2010
%
% <Inputs>
% A : input matrix (m x n) (by default), or A'*A (n x n) if isInputProd==1
% B : input matrix (m x k) (by default), or A'*B (n x k) if isInputProd==1
% overwrite : (optional, default:0) if turned on, unconstrained least squares solution is computed in the beginning
% isInputProd : (optional, default:0) if turned on, use (A'*A,A'*B) as input instead of (A,B)
% init : (optional) initial value for X
% <Outputs>
% X : the solution (n x k)
% Y : A'*A*X - A'*B where X is the solution (n x k)
% iter : number of iterations
% success : 1 for success, 0 for failure.
% Failure could only happen on a numericall very ill-conditioned problem.
if nargin<3, overwrite=0;, end
if nargin<4, isInputProd=0;, end
if isInputProd
AtA=A;,AtB=B;
else
AtA=A'*A;, AtB=A'*B;
end
[n,k]=size(AtB);
MAX_ITER = n*5;
% set initial feasible solution
if overwrite
[X,iter] = solveNormalEqComb(AtA,AtB);
PassSet = (X > 0);
NotOptSet = any(X<0);
else
if nargin<5
X = zeros(n,k);
PassSet = false(n,k);
NotOptSet = true(1,k);
else
X = init;
PassSet = (X > 0);
NotOptSet = any(X<0);
end
iter = 0;
end
Y = zeros(n,k);
Y(:,~NotOptSet)=AtA*X(:,~NotOptSet) - AtB(:,~NotOptSet);
NotOptCols = find(NotOptSet);
bigIter = 0;, success=1;
while(~isempty(NotOptCols))
bigIter = bigIter+1;
if ((MAX_ITER >0) && (bigIter > MAX_ITER)) % set max_iter for ill-conditioned (numerically unstable) case
success = 0;, bigIter, break
end
% find unconstrained LS solution for the passive set
Z = zeros(n,length(NotOptCols));
[ Z,subiter ] = solveNormalEqComb(AtA,AtB(:,NotOptCols),PassSet(:,NotOptCols));
iter = iter + subiter;
%Z(abs(Z)<1e-12) = 0; % One can uncomment this line for numerical stability.
InfeaSubSet = Z < 0;
InfeaSubCols = find(any(InfeaSubSet));
FeaSubCols = find(all(~InfeaSubSet));
if ~isempty(InfeaSubCols) % for infeasible cols
ZInfea = Z(:,InfeaSubCols);
InfeaCols = NotOptCols(InfeaSubCols);
Alpha = zeros(n,length(InfeaSubCols));, Alpha(:,:) = Inf;
InfeaSubSet(:,InfeaSubCols);
[i,j] = find(InfeaSubSet(:,InfeaSubCols));
InfeaSubIx = sub2ind(size(Alpha),i,j);
if length(InfeaCols) == 1
InfeaIx = sub2ind([n,k],i,InfeaCols * ones(length(j),1));
else
InfeaIx = sub2ind([n,k],i,InfeaCols(j)');
end
Alpha(InfeaSubIx) = X(InfeaIx)./(X(InfeaIx)-ZInfea(InfeaSubIx));
[minVal,minIx] = min(Alpha);
Alpha(:,:) = repmat(minVal,n,1);
X(:,InfeaCols) = X(:,InfeaCols)+Alpha.*(ZInfea-X(:,InfeaCols));
IxToActive = sub2ind([n,k],minIx,InfeaCols);
X(IxToActive) = 0;
PassSet(IxToActive) = false;
end
if ~isempty(FeaSubCols) % for feasible cols
FeaCols = NotOptCols(FeaSubCols);
X(:,FeaCols) = Z(:,FeaSubCols);
Y(:,FeaCols) = AtA * X(:,FeaCols) - AtB(:,FeaCols);
%Y( abs(Y)<1e-12 ) = 0; % One can uncomment this line for numerical stability.
NotOptSubSet = (Y(:,FeaCols) < 0) & ~PassSet(:,FeaCols);
NewOptCols = FeaCols(all(~NotOptSubSet));
UpdateNotOptCols = FeaCols(any(NotOptSubSet));
if ~isempty(UpdateNotOptCols)
[minVal,minIx] = min(Y(:,UpdateNotOptCols).*~PassSet(:,UpdateNotOptCols));
PassSet(sub2ind([n,k],minIx,UpdateNotOptCols)) = true;
end
NotOptSet(NewOptCols) = false;
NotOptCols = find(NotOptSet);
end
end
endfunction
%------------------------------------------------------------------------------------------------------------------------
function [ X,Y,iter,success ] = nnlsm_blockpivot( A, B, isInputProd, init )
% Nonnegativity Constrained Least Squares with Multiple Righthand Sides
% using Block Principal Pivoting method
%
% This software solves the following problem: given A and B, find X such that
% minimize || AX-B ||_F^2 where X>=0 elementwise.
%
% Reference:
% Jingu Kim and Haesun Park, Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons,
% In Proceedings of the 2008 Eighth IEEE International Conference on Data Mining (ICDM'08), 353-362, 2008
%
% Written by Jingu Kim (jingu@cc.gatech.edu)
% Copyright 2008-2009 by Jingu Kim and Haesun Park,
% School of Computational Science and Engineering,
% Georgia Institute of Technology
%
% Check updated code at http://www.cc.gatech.edu/~jingu
% Please send bug reports, comments, or questions to Jingu Kim.
% This code comes with no guarantee or warranty of any kind. Note that this algorithm assumes that the
% input matrix A has full column rank.
%
% Last modified Feb-20-2009
%
% <Inputs>
% A : input matrix (m x n) (by default), or A'*A (n x n) if isInputProd==1
% B : input matrix (m x k) (by default), or A'*B (n x k) if isInputProd==1
% isInputProd : (optional, default:0) if turned on, use (A'*A,A'*B) as input instead of (A,B)
% init : (optional) initial value for X
% <Outputs>
% X : the solution (n x k)
% Y : A'*A*X - A'*B where X is the solution (n x k)
% iter : number of iterations
% success : 1 for success, 0 for failure.
% Failure could only happen on a numericall very ill-conditioned problem.
if nargin<3, isInputProd=0;, end
if isInputProd
AtA = A;, AtB = B;
else
AtA = A'*A;, AtB = A'*B;
end
[n,k]=size(AtB);
MAX_ITER = n*5;
% set initial feasible solution
X = zeros(n,k);
if nargin<4
Y = - AtB;
PassiveSet = false(n,k);
iter = 0;
else
PassiveSet = (init > 0);
[ X,iter ] = solveNormalEqComb(AtA,AtB,PassiveSet);
Y = AtA * X - AtB;
end
% parameters
pbar = 3;
P = zeros(1,k);, P(:) = pbar;
Ninf = zeros(1,k);, Ninf(:) = n+1;
iter = 0;
NonOptSet = (Y < 0) & ~PassiveSet;
InfeaSet = (X < 0) & PassiveSet;
NotGood = sum(NonOptSet)+sum(InfeaSet);
NotOptCols = NotGood > 0;
bigIter = 0;, success=1;
while(~isempty(find(NotOptCols)))
bigIter = bigIter+1;
if ((MAX_ITER >0) && (bigIter > MAX_ITER)) % set max_iter for ill-conditioned (numerically unstable) case
success = 0;, break
end
Cols1 = NotOptCols & (NotGood < Ninf);
Cols2 = NotOptCols & (NotGood >= Ninf) & (P >= 1);
Cols3Ix = find(NotOptCols & ~Cols1 & ~Cols2);
if ~isempty(find(Cols1))
P(Cols1) = pbar;,Ninf(Cols1) = NotGood(Cols1);
PassiveSet(NonOptSet & repmat(Cols1,n,1)) = true;
PassiveSet(InfeaSet & repmat(Cols1,n,1)) = false;
end
if ~isempty(find(Cols2))
P(Cols2) = P(Cols2)-1;
PassiveSet(NonOptSet & repmat(Cols2,n,1)) = true;
PassiveSet(InfeaSet & repmat(Cols2,n,1)) = false;
end
if ~isempty(Cols3Ix)
for i=1:length(Cols3Ix)
Ix = Cols3Ix(i);
toChange = max(find( NonOptSet(:,Ix)|InfeaSet(:,Ix) ));
if PassiveSet(toChange,Ix)
PassiveSet(toChange,Ix)=false;
else
PassiveSet(toChange,Ix)=true;
end
end
end
NotOptMask = repmat(NotOptCols,n,1);
[ X(:,NotOptCols),subiter ] = solveNormalEqComb(AtA,AtB(:,NotOptCols),PassiveSet(:,NotOptCols));
iter = iter + subiter;
X(abs(X)<1e-12) = 0; % for numerical stability
Y(:,NotOptCols) = AtA * X(:,NotOptCols) - AtB(:,NotOptCols);
Y(abs(Y)<1e-12) = 0; % for numerical stability
% check optimality
NonOptSet = NotOptMask & (Y < 0) & ~PassiveSet;
InfeaSet = NotOptMask & (X < 0) & PassiveSet;
NotGood = sum(NonOptSet)+sum(InfeaSet);
NotOptCols = NotGood > 0;
end
endfunction
%------------------------------------------------------------------------------------------------------------------------
function [ Z,iter ] = solveNormalEqComb( AtA,AtB,PassSet )
% Solve normal equations using combinatorial grouping.
% Although this function was originally adopted from the code of
% "M. H. Van Benthem and M. R. Keenan, J. Chemometrics 2004; 18: 441-450",
% important modifications were made to fix bugs.
%
% Modified by Jingu Kim (jingu@cc.gatech.edu)
% School of Computational Science and Engineering,
% Georgia Institute of Technology
%
% Last updated Aug-12-2009
iter = 0;
if (nargin ==2) || isempty(PassSet) || all(PassSet(:))
Z = AtA\AtB;
iter = iter + 1;
else
Z = zeros(size(AtB));
[n,k1] = size(PassSet);
## Fixed on Aug-12-2009
if k1==1
Z(PassSet)=AtA(PassSet,PassSet)\AtB(PassSet);
else
## Fixed on Aug-12-2009
% The following bug was identified by investigating a bug report by Hanseung Lee.
[sortedPassSet,sortIx] = sortrows(PassSet');
breaks = any(diff(sortedPassSet)');
breakIx = [0 find(breaks) k1];
% codedPassSet = 2.^(n-1:-1:0)*PassSet;
% [sortedPassSet,sortIx] = sort(codedPassSet);
% breaks = diff(sortedPassSet);
% breakIx = [0 find(breaks) k1];
for k=1:length(breakIx)-1
cols = sortIx(breakIx(k)+1:breakIx(k+1));
vars = PassSet(:,sortIx(breakIx(k)+1));
Z(vars,cols) = AtA(vars,vars)\AtB(vars,cols);
iter = iter + 1;
end
end
end
endfunction
%!shared m, n, k, A
%! m = 30;
%! n = 20;
%! k = 10;
%! A = rand(m,n);
%!test
%! [W,H,iter,HIS]=nmf_bpas(A,k);
%!test
%! [W,H,iter,HIS]=nmf_bpas(A,k,'verbose',2);
%!test
%! [W,H,iter,HIS]=nmf_bpas(A,k,'verbose',1,'nnls_solver','as');
%!test
%! [W,H,iter,HIS]=nmf_bpas(A,k,'verbose',1,'type','sparse');
%!test
%! [W,H,iter,HIS]=nmf_bpas(A,k,'verbose',1,'type','sparse','nnls_solver','bp','alpha',1.1,'beta',1.3);
%!test
%! [W,H,iter,HIS]=nmf_bpas(A,k,'verbose',2,'type','plain','w_init',rand(m,k));
%!demo
%! m = 300;
%! n = 200;
%! k = 10;
%!
%! W_org = rand(m,k);, W_org(rand(m,k)>0.5)=0;
%! H_org = rand(k,n);, H_org(rand(k,n)>0.5)=0;
%!
%! % normalize W, since 'nmf' normalizes W before return
%! norm2=sqrt(sum(W_org.^2,1));
%! toNormalize = norm2>0;
%! W_org(:,toNormalize) = W_org(:,toNormalize)./repmat(norm2(toNormalize),m,1);
%!
%! A = W_org * H_org;
%!
%! [W,H,iter,HIS]=nmf_bpas (A,k,'type','plain','tol',1e-4);
%!
%! % -------------------- column reordering before computing difference
%! reorder = zeros(k,1);
%! selected = zeros(k,1);
%! for i=1:k
%! for j=1:k
%! if ~selected(j), break, end
%! end
%! minIx = j;
%!
%! for j=minIx+1:k
%! if ~selected(j)
%! d1 = norm(W(:,i)-W_org(:,minIx));
%! d2 = norm(W(:,i)-W_org(:,j));
%! if (d2<d1)
%! minIx = j;
%! end
%! end
%! end
%! reorder(i) = minIx;
%! selected(minIx) = 1;
%! end
%!
%! W_org = W_org(:,reorder);
%! H_org = H_org(reorder,:);
%! % ---------------------------------------------------------------------
%!
%! recovery_error_W = norm(W_org-W)/norm(W_org)
%! recovery_error_H = norm(H_org-H)/norm(H_org)

Get latest updates about Open Source Projects, Conferences and News.

Sign up for the SourceForge newsletter:





No, thanks