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
|
#' @include registry-algorithms.R
NULL
#' Fast Combinatorial Nonnegative Least-Square
#'
#' This function solves the following nonnegative least square linear problem
#' using normal equations and the fast combinatorial strategy from \cite{VanBenthem2004}:
#'
#' \deqn{
#' \begin{array}{l}
#' \min \|Y - X K\|_F\\
#' \mbox{s.t. } K>=0
#' \end{array}
#' }{min ||Y - X K||_F, s.t. K>=0}
#'
#' where \eqn{Y} and \eqn{X} are two real matrices of dimension \eqn{n \times p}{n x p}
#' and \eqn{n \times r}{n x r} respectively,
#' and \eqn{\|.\|_F}{|.|_F} is the Frobenius norm.
#'
#' The algorithm is very fast compared to other approaches, as it is optimised
#' for handling multiple right-hand sides.
#'
#' @details
#' Within the \code{NMF} package, this algorithm is used internally by the
#' SNMF/R(L) algorithm from \cite{KimH2007} to solve general Nonnegative
#' Matrix Factorization (NMF) problems, using alternating nonnegative
#' constrained least-squares.
#' That is by iteratively and alternatively estimate each matrix factor.
#'
#' The algorithm is an active/passive set method, which rearrange the
#' right-hand side to reduce the number of pseudo-inverse calculations.
#' It uses the unconstrained solution \eqn{K_u} obtained from the
#' unconstrained least squares problem,
#' i.e. \eqn{\min \|Y - X K\|_F^2}{min ||Y - X K||_F^2} , so as to determine
#' the initial passive sets.
#'
#' The function \code{fcnnls} is provided separately so that it can be
#' used to solve other types of nonnegative least squares problem.
#' For faster computation, when multiple nonnegative least square fits
#' are needed, it is recommended to directly use the function \code{\link{.fcnnls}}.
#'
#' The code of this function is a port from the original MATLAB code
#' provided by \cite{KimH2007}.
#'
#' @inheritParams .fcnnls
#' @param ... extra arguments passed to the internal function \code{.fcnnls}.
#' Currently not used.
#' @return A list containing the following components:
#'
#' \item{x}{ the estimated optimal matrix \eqn{K}.} \item{fitted}{ the fitted
#' matrix \eqn{X K}.} \item{residuals}{ the residual matrix \eqn{Y - X K}.}
#' \item{deviance}{ the residual sum of squares between the fitted matrix
#' \eqn{X K} and the target matrix \eqn{Y}. That is the sum of the square
#' residuals.} \item{passive}{ a \eqn{r x p} logical matrix containing the
#' passive set, that is the set of entries in \eqn{K} that are not null (i.e.
#' strictly positive).} \item{pseudo}{ a logical that is \code{TRUE} if the
#' computation was performed using the pseudoinverse. See argument
#' \code{pseudo}.}
#'
#' @seealso \code{\link{nmf}}
#' @references
#'
#' Original MATLAB code from Van Benthem and Keenan, slightly modified by H.
#' Kim:\cr \url{http://www.cc.gatech.edu/~hpark/software/fcnnls.m}
#'
#' @author
#' Original MATLAB code : Van Benthem and Keenan
#'
#' Adaption of MATLAB code for SNMF/R(L): H. Kim
#'
#' Adaptation to the NMF package framework: Renaud Gaujoux
#'
#' @keywords optimize multivariate regression
#' @export
#' @inline
#' @examples
#'
#' ## Define a random nonnegative matrix matrix
#' n <- 200; p <- 20; r <- 3
#' V <- rmatrix(n, p)
#'
#' ## Compute the optimal matrix K for a given X matrix
#' X <- rmatrix(n, r)
#' res <- fcnnls(X, V)
#'
#' ## Compute the same thing using the Moore-Penrose generalized pseudoinverse
#' res <- fcnnls(X, V, pseudo=TRUE)
#'
#' ## It also works in the case of single vectors
#' y <- runif(n)
#' res <- fcnnls(X, y)
#' # or
#' res <- fcnnls(X[,1], y)
#'
#'
setGeneric('fcnnls', function(x, y, ...) standardGeneric('fcnnls') )
#' This method wraps a call to the internal function \code{.fcnnls}, and
#' formats the results in a similar way as other lest-squares methods such
#' as \code{\link{lm}}.
#'
#' @param verbose toggle verbosity (default is \code{FALSE}).
#'
setMethod('fcnnls', signature(x='matrix', y='matrix'),
function(x, y, verbose=FALSE, pseudo=TRUE, ...){
# load corpcor if necessary
if( isTRUE(pseudo) ){
library(corpcor)
}
# call the internal function
res <- .fcnnls(x, y, verbose=verbose, pseudo=pseudo, ...)
# process the result
f <- x %*% res$coef
resid <- y - f
# set dimnames
if( is.null(rownames(res$coef)) ) rownames(res$coef) <- colnames(x)
# wrap up the result
out <- list(x=res$coef, fitted=f, residuals=resid, deviance=norm(resid, 'F')^2, passive=res$Pset, pseudo=pseudo)
class(out) <- 'fcnnls'
out
}
)
#' Shortcut for \code{fcnnls(as.matrix(x), y, ...)}.
setMethod('fcnnls', signature(x='numeric', y='matrix'),
function(x, y, ...){
fcnnls(as.matrix(x), y, ...)
}
)
#' Shortcut for \code{fcnnls(x, as.matrix(y), ...)}.
setMethod('fcnnls', signature(x='ANY', y='numeric'),
function(x, y, ...){
fcnnls(x, as.matrix(y), ...)
}
)
#' @export
print.fcnnls <- function(x, ...){
cat("<object of class 'fcnnls': Fast Combinatorial Nonnegative Least Squares>\n")
cat("Dimensions:", nrow(x$x)," x ", ncol(x$x), "\n")
cat("Residual sum of squares:", x$deviance,"\n")
cat("Active constraints:", length(x$passive)-sum(x$passive),"/", length(x$passive), "\n")
cat("Inverse method:",
if( isTRUE(x$pseudo) ) 'pseudoinverse (corpcor)'
else if( is.function(x$pseudo) ) str_fun(x$pseudo)
else 'QR (solve)', "\n")
invisible(x)
}
###% M. H. Van Benthem and M. R. Keenan, J. Chemometrics 2004; 18: 441-450
###%
###% Given A and C this algorithm solves for the optimal
###% K in a least squares sense, using that
###% A = C*K
###% in the problem
###% min ||A-C*K||, s.t. K>=0, for given A and C.
###%
###%
###% @param C the matrix of coefficients
###% @param A the target matrix of observations
###%
###% @return [K, Pset]
###%
#' Internal Routine for Fast Combinatorial Nonnegative Least-Squares
#'
#' @description
#' This is the workhorse function for the higher-level function
#' \code{\link{fcnnls}}, which implements the fast nonnegative least-square
#' algorithm for multiple right-hand-sides from \cite{VanBenthem2004} to solve
#' the following problem:
#'
#' \deqn{
#' \begin{array}{l}
#' \min \|Y - X K\|_F\\
#' \mbox{s.t. } K>=0
#' \end{array}
#' }{min ||Y - X K||_F, s.t. K>=0}
#'
#' where \eqn{Y} and \eqn{X} are two real matrices of dimension \eqn{n \times p}{n x p}
#' and \eqn{n \times r}{n x r} respectively,
#' and \eqn{\|.\|_F}{|.|_F} is the Frobenius norm.
#'
#' The algorithm is very fast compared to other approaches, as it is optimised
#' for handling multiple right-hand sides.
#'
#' @param x the coefficient matrix
#' @param y the target matrix to be approximated by \eqn{X K}.
#' @param verbose logical that indicates if log messages should be shown.
#' @param pseudo By default (\code{pseudo=FALSE}) the algorithm uses Gaussian
#' elimination to solve the successive internal linear problems, using the
#' \code{\link{solve}} function. If \code{pseudo=TRUE} the algorithm uses
#' Moore-Penrose generalized \code{\link[corpcor]{pseudoinverse}} from the
#' \code{corpcor} package instead of \link{solve}.
#' @param eps threshold for considering entries as nonnegative.
#' This is an experimental parameter, and it is recommended to
#' leave it at 0.
#'
#' @return A list with the following elements:
#'
#' \item{coef}{the fitted coefficient matrix.}
#' \item{Pset}{the set of passive constraints, as a logical matrix of
#' the same size as \code{K} that indicates which element is positive.}
#'
#' @export
.fcnnls <- function(x, y, verbose=FALSE, pseudo=FALSE, eps=0){
# check arguments
if( any(dim(y) == 0L) ){
stop("Empty target matrix 'y' [", paste(dim(y), collapse=' x '), "]")
}
if( any(dim(x) == 0L) ){
stop("Empty regression variable matrix 'x' [", paste(dim(x), collapse=' x '), "]")
}
# map arguments
C <- x
A <- y
# NNLS using normal equations and the fast combinatorial strategy
#
# I/O: [K, Pset] = fcnnls(C, A);
# K = fcnnls(C, A);
#
# C is the nObs x lVar coefficient matrix
# A is the nObs x pRHS matrix of observations
# K is the lVar x pRHS solution matrix
# Pset is the lVar x pRHS passive set logical array
#
# M. H. Van Benthem and M. R. Keenan
# Sandia National Laboratories
#
# Pset: set of passive sets, one for each column
# Fset: set of column indices for solutions that have not yet converged
# Hset: set of column indices for currently infeasible solutions
# Jset: working set of column indices for currently optimal solutions
#
# Check the input arguments for consistency and initializeerror(nargchk(2,2,nargin))
nObs = nrow(C); lVar = ncol(C);
if ( nrow(A)!= nObs ) stop('C and A have imcompatible sizes')
pRHS = ncol(A);
W = matrix(0, lVar, pRHS);
iter=0; maxiter=3*lVar;
# Precompute parts of pseudoinverse
#CtC = t(C)%*%C; CtA = t(C)%*%A;
CtC = crossprod(C); CtA = crossprod(C,A);
# Obtain the initial feasible solution and corresponding passive set
K = .cssls(CtC, CtA, pseudo=pseudo);
Pset = K > 0;
K[!Pset] = 0;
D = K;
# which columns of Pset do not have all entries TRUE?
Fset = which( colSums(Pset) != lVar );
#V+# Active set algorithm for NNLS main loop
oitr=0; # HKim
while ( length(Fset)>0 ) {
oitr=oitr+1; if ( verbose && oitr > 5 ) cat(sprintf("%d ",oitr));# HKim
#Vc# Solve for the passive variables (uses subroutine below)
K[,Fset] = .cssls(CtC, CtA[,Fset, drop=FALSE], Pset[,Fset, drop=FALSE], pseudo=pseudo);
# Find any infeasible solutions
# subset Fset on the columns that have at least one negative entry
Hset = Fset[ colSums(K[,Fset, drop=FALSE] < eps) > 0 ];
#V+# Make infeasible solutions feasible (standard NNLS inner loop)
if ( length(Hset)>0 ){
nHset = length(Hset);
alpha = matrix(0, lVar, nHset);
while ( nHset>0 && (iter < maxiter) ){
iter = iter + 1;
alpha[,1:nHset] = Inf;
#Vc# Find indices of negative variables in passive set
ij = which( Pset[,Hset, drop=FALSE] & (K[,Hset, drop=FALSE] < eps) , arr.ind=TRUE);
i = ij[,1]; j = ij[,2]
if ( length(i)==0 ) break;
hIdx = (j - 1) * lVar + i; # convert array indices to indexes relative to a lVar x nHset matrix
negIdx = (Hset[j] - 1) * lVar + i; # convert array indices to index relative to the matrix K (i.e. same row index but col index is stored in Hset)
alpha[hIdx] = D[negIdx] / (D[negIdx] - K[negIdx]);
alpha.inf <- alpha[,1:nHset, drop=FALSE]
minIdx = max.col(-t(alpha.inf)) # get the indce of the min of each row
alphaMin = alpha.inf[minIdx + (0:(nHset-1) * lVar)]
alpha[,1:nHset] = matrix(alphaMin, lVar, nHset, byrow=TRUE);
D[,Hset] = D[,Hset, drop=FALSE] - alpha[,1:nHset, drop=FALSE] * (D[,Hset, drop=FALSE]-K[,Hset, drop=FALSE]);
idx2zero = (Hset - 1) * lVar + minIdx; # convert array indices to index relative to the matrix D
D[idx2zero] = 0;
Pset[idx2zero] = FALSE;
K[, Hset] = .cssls(CtC, CtA[,Hset, drop=FALSE], Pset[,Hset, drop=FALSE], pseudo=pseudo);
# which column of K have at least one negative entry?
Hset = which( colSums(K < eps) > 0 );
nHset = length(Hset);
}
}
#V-#
#Vc# Make sure the solution has converged
#if iter == maxiter, error('Maximum number iterations exceeded'), end
# Check solutions for optimality
W[,Fset] = CtA[,Fset, drop=FALSE] - CtC %*% K[,Fset, drop=FALSE];
# which columns have all entries non-positive
Jset = which( colSums( (ifelse(!(Pset[,Fset, drop=FALSE]),1,0) * W[,Fset, drop=FALSE]) > eps ) == 0 );
Fset = setdiff(Fset, Fset[Jset]);
if ( length(Fset) > 0 ){
#Vc# For non-optimal solutions, add the appropriate variable to Pset
# get indice of the maximum in each column
mxidx = max.col( t(ifelse(!Pset[,Fset, drop=FALSE],1,0) * W[,Fset, drop=FALSE]) )
Pset[ (Fset - 1) * lVar + mxidx ] = TRUE;
D[,Fset] = K[,Fset, drop=FALSE];
}
}
#V-#
# return K and Pset
list(coef=K, Pset=Pset)
}
# ****************************** Subroutine****************************
#library(corpcor)
.cssls <- function(CtC, CtA, Pset=NULL, pseudo=FALSE){
# use provided function
if( is.function(pseudo) ){
pseudoinverse <- pseudo
pseudo <- TRUE
}
# Solve the set of equations CtA = CtC*K for the variables in set Pset
# using the fast combinatorial approach
K = matrix(0, nrow(CtA), ncol(CtA));
if ( is.null(Pset) || length(Pset)==0 || all(Pset) ){
K <- (if( !pseudo ) solve(CtC) else pseudoinverse(CtC)) %*% CtA;
# K = pseudoinverse(CtC) %*% CtA;
#K=pinv(CtC)*CtA;
}else{
lVar = nrow(Pset); pRHS = ncol(Pset);
codedPset = as.numeric(2.^(seq(lVar-1,0,-1)) %*% Pset);
sortedPset = sort(codedPset)
sortedEset = order(codedPset)
breaks = diff(sortedPset);
breakIdx = c(0, which(breaks > 0 ), pRHS);
for( k in seq(1,length(breakIdx)-1) ){
cols2solve = sortedEset[ seq(breakIdx[k]+1, breakIdx[k+1])];
vars = Pset[,sortedEset[breakIdx[k]+1]];
K[vars,cols2solve] <- (if( !pseudo ) solve(CtC[vars,vars, drop=FALSE]) else pseudoinverse(CtC[vars,vars, drop=FALSE])) %*% CtA[vars,cols2solve, drop=FALSE];
#K[vars,cols2solve] <- pseudoinverse(CtC[vars,vars, drop=FALSE])) %*% CtA[vars,cols2solve, drop=FALSE];
#TODO: check if this is the right way or needs to be reversed
#K(vars,cols2solve) = pinv(CtC(vars,vars))*CtA(vars,cols2solve);
}
}
# return K
K
}
###%
###% SNMF/R
###%
###% Author: Hyunsoo Kim and Haesun Park, Georgia Insitute of Technology
###%
###% Reference:
###%
###% Sparse Non-negative Matrix Factorizations via Alternating
###% Non-negativity-constrained Least Squares for Microarray Data Analysis
###% Hyunsoo Kim and Haesun Park, Bioinformatics, 2007, to appear.
###%
###% This software requires fcnnls.m, which can be obtained from
###% M. H. Van Benthem and M. R. Keenan, J. Chemometrics 2004; 18: 441-450
###%
###% NMF: min_{W,H} (1/2) || A - WH ||_F^2 s.t. W>=0, H>=0
###% SNMF/R: NMF with additional sparsity constraints on H
###%
###% min_{W,H} (1/2) (|| A - WH ||_F^2 + eta ||W||_F^2
###% + beta (sum_(j=1)^n ||H(:,j)||_1^2))
###% s.t. W>=0, H>=0
###%
###% A: m x n data matrix (m: features, n: data points)
###% W: m x k basis matrix
###% H: k x n coefficient matrix
###%
###% function [W,H,i]=nmfsh_comb(A,k,param,verbose,bi_conv,eps_conv)
###%
###% input parameters:
###% A: m x n data matrix (m: features, n: data points)
###% k: desired positive integer k
###% param=[eta beta]:
###% eta (for supressing ||W||_F)
###% if eta < 0, software uses maxmum value in A as eta.
###% beta (for sparsity control)
###% Larger beta generates higher sparseness on H.
###% Too large beta is not recommended.
###% verbos: verbose = 0 for silence mode, otherwise print output
###% eps_conv: KKT convergence test (default eps_conv = 1e-4)
###% bi_conv=[wminchange iconv] biclustering convergence test
###% wminchange: the minimal allowance of the change of
###% row-clusters (default wminchange=0)
###% iconv: decide convergence if row-clusters (within wminchange)
###% and column-clusters have not changed for iconv convergence
###% checks. (default iconv=10)
###%
###% output:
###% W: m x k basis matrix
###% H: k x n coefficient matrix
###% i: the number of iterations
###%
###% sample usage:
###% [W,H]=nmfsh_comb(amlall,3,[-1 0.01],1);
###% [W,H]=nmfsh_comb(amlall,3,[-1 0.01],1,[3 10]);
###% -- in the convergence check, the change of row-clusters to
###% at most three rows is allowed.
###%
###%
#function [W,H,i]
nmf_snmf <- function(A, x, maxIter= nmf.getOption('maxIter') %||% 20000L, eta=-1, beta=0.01, bi_conv=c(0, 10), eps_conv=1e-4, version=c('R', 'L'), verbose=FALSE){
#nmfsh_comb <- function(A, k, param, verbose=FALSE, bi_conv=c(0, 10), eps_conv=1e-4, version=c('R', 'L')){
# depending on the version:
# in version L: A is transposed while W and H are swapped and transposed
version <- match.arg(version)
if( version == 'L' ) A <- t(A)
#if( missing(param) ) param <- c(-1, 0.01)
m = nrow(A); n = ncol(A); erravg1 = numeric();
#eta=param[1]; beta=param[2];
maxA=max(A); if ( eta<0 ) eta=maxA;
eta2=eta^2;
# bi_conv
if( length(bi_conv) != 2 )
stop("SNMF/", version, "::Invalid argument 'bi_conv' - value should be a 2-length numeric vector")
wminchange=bi_conv[1]; iconv=bi_conv[2];
## VALIDITY of parameters
# eps_conv
if( eps_conv <= 0 )
stop("SNMF/", version, "::Invalid argument 'eps_conv' - value should be positive")
# wminchange
if( wminchange < 0 )
stop("SNMF/", version, "::Invalid argument 'bi_conv' - bi_conv[1] (i.e 'wminchange') should be non-negative")
# iconv
if( iconv < 0 )
stop("SNMF/", version, "::Invalid argument 'bi_conv' - bi_conv[2] (i.e 'iconv') should be non-negative")
# beta
if( beta <=0 )
stop("SNMF/", version, "::Invalid argument 'beta' - value should be positive")
##
# initialize random W if no starting point is given
if( isNumber(x) ){
# rank is given by x
k <- x
message('# NOTE: Initialise W internally (runif)')
W <- matrix(runif(m*k), m,k);
x <- NULL
} else if( is.nmf(x) ){
# rank is the number of basis components in x
k <- nbasis(x)
# seed the method (depends on the version to run)
start <- if( version == 'R' ) basis(x) else t(coef(x))
# check compatibility of the starting point with the target matrix
if( any(dim(start) != c(m,k)) )
stop("SNMF/", version, " - Invalid initialization - incompatible dimensions [expected: ", paste(c(m,k), collapse=' x '),", got: ", paste(dim(start), collapse=' x '), " ]")
# use the supplied starting point
W <- start
}else{
stop("SNMF/", version, ' - Invalid argument `x`: must be a single numeric or an NMF model [', class(x), ']')
}
if ( verbose )
cat(sprintf("--\nAlgorithm: SNMF/%s\nParameters: k=%d eta=%.4e beta (for sparse H)=%.4e wminchange=%d iconv=%d\n",
version, k,eta,beta,wminchange,iconv));
idxWold=rep(0, m); idxHold=rep(0, n); inc=0;
# check validity of seed
if( any(NAs <- is.na(W)) )
stop("SNMF/", version, "::Invalid initialization - NAs found in the ", if(version=='R') 'basis (W)' else 'coefficient (H)' , " matrix [", sum(NAs), " NAs / ", length(NAs), " entries]")
# normalize columns of W
W= apply(W, 2, function(x) x / sqrt(sum(x^2)) );
I_k=diag(eta, k); betavec=rep(sqrt(beta), k); nrestart=0;
i <- 0L
while( i < maxIter){
i <- i + 1L
# min_h ||[[W; 1 ... 1]*H - [A; 0 ... 0]||, s.t. H>=0, for given A and W.
res = .fcnnls(rbind(W, betavec), rbind(A, rep(0, n)));
H = res[[1]]
if ( any(rowSums(H)==0) ){
if( verbose ) cat(sprintf("iter%d: 0 row in H eta=%.4e restart!\n",i,eta));
nrestart=nrestart+1;
if ( nrestart >= 10 ){
warning("NMF::snmf - Too many restarts due to too big 'beta' value [Computation stopped after the 9th restart]");
break;
}
# re-initialize random W
idxWold=rep(0, m); idxHold=rep(0, n); inc=0;
erravg1 <- numeric();# re-initialize base average error
W=matrix(runif(m*k), m,k);
W= apply(W, 2, function(x) x / sqrt(sum(x^2)) ); # normalize columns of W
next;
}
# min_w ||[H'; I_k]*W' - [A'; 0]||, s.t. W>=0, for given A and H.
res = .fcnnls(rbind(t(H), I_k), rbind(t(A), matrix(0, k,m)));
Wt = res[[1]]
W= t(Wt);
# track the error (not computed unless tracking option is enabled in x)
if( !is.null(x) )
x <- trackError(x, .snmf.objective(A, W, H, eta, beta), niter=i)
# test convergence every 5 iterations OR if the base average error has not been computed yet
if ( (i %% 5==0) || (length(erravg1)==0) ){
# indice of maximum for each row of W
idxW = max.col(W)
# indice of maximum for each column of H
idxH = max.col(t(H))
changedW=sum(idxW != idxWold); changedH=sum(idxH != idxHold);
if ( (changedW<=wminchange) && (changedH==0) ) inc=inc+1
else inc=0
resmat=pmin(H, crossprod(W) %*% H - t(W) %*% A + matrix(beta, k , k) %*% H); resvec=as.numeric(resmat);
resmat=pmin(W, W %*% tcrossprod(H) - A %*% t(H) + eta2 * W); resvec=c(resvec, as.numeric(resmat));
conv=sum(abs(resvec)); #L1-norm
convnum=sum(abs(resvec)>0);
erravg=conv/convnum;
# compute base average error if necessary
if ( length(erravg1)==0 )
erravg1=erravg;
if ( verbose && (i %% 1000==0) ){ # prints number of changing elements
if( i==1000 ) cat("Track:\tIter\tInc\tchW\tchH\t---\terravg1\terravg\terravg/erravg1\n")
cat(sprintf("\t%d\t%d\t%d\t%d\t---\terravg1: %.4e\terravg: %.4e\terravg/erravg1: %.4e\n",
i,inc,changedW,changedH,erravg1,erravg,erravg/erravg1));
}
#print(list(inc=inc, iconv=iconv, erravg=erravg, eps_conv=eps_conv, erravg1=erravg1))
if ( (inc>=iconv) && (erravg<=eps_conv*erravg1) ) break;
idxWold=idxW; idxHold=idxH;
}
}
if( verbose ) cat("--\n")
# force to compute last error if not already done
if( !is.null(x) )
x <- trackError(x, .snmf.objective(A, W, H, eta, beta), niter=i, force=TRUE)
# transpose and reswap the roles
if( !is.null(x) ){
if( version == 'L' ){
.basis(x) <- t(H)
.coef(x) <- t(W)
}
else{
.basis(x) <- W
.coef(x) <- H
}
# set number of iterations performed
niter(x) <- i
return(x)
}else{
res <- list(W=W, H=H)
if( version == 'L' ){
res$W <- t(H)
res$H <- t(W)
}
return(invisible(res))
}
}
###% Computes the objective value for the SNMF algorithm
.snmf.objective <- function(target, w, h, eta, beta){
1/2 * ( sum( (target - (w %*% h))^2 )
+ eta * sum(w^2)
+ beta * sum( colSums( h )^2 )
)
}
snmf.objective <- function(x, y, eta=-1, beta=0.01){
.snmf.objective(y, .basis(x), .coef(x), eta, beta)
}
###% Wrapper function to use the SNMF/R algorithm with the NMF package.
###%
.snmf <- function(target, seed, maxIter=20000L, eta=-1, beta=0.01, bi_conv=c(0, 10), eps_conv=1e-4, ...){
# retrieve the version of SNMF algorithm from its name:
# it is defined by the last letter in the method's name (in upper case)
name <- algorithm(seed)
version <- toupper(substr(name, nchar(name), nchar(name)))
# perform factorization using Kim and Park's algorithm
ca <- match.call()
ca[[1L]] <- as.name('nmf_snmf')
# target
ca[['A']] <- ca[['target']]
ca[['target']] <- NULL
# seed
ca[['x']] <- ca[['seed']]
ca[['seed']] <- NULL
# version
ca[['version']] <- version
# verbose
ca[['verbose']] <- verbose(seed)
e <- parent.frame()
sol <- eval(ca, envir=e)
# nmf_snmf(target, seed, ..., version = version, verbose = verbose(seed))
# return solution
return(sol)
}
#' NMF Algorithm - Sparse NMF via Alternating NNLS
#'
#' NMF algorithms proposed by \cite{KimH2007} that enforces sparsity
#' constraint on the basis matrix (algorithm \sQuote{SNMF/L}) or the
#' mixture coefficient matrix (algorithm \sQuote{SNMF/R}).
#'
#' The algorithm \sQuote{SNMF/R} solves the following NMF optimization problem on
#' a given target matrix \eqn{A} of dimension \eqn{n \times p}{n x p}:
#' \deqn{
#' \begin{array}{ll}
#' & \min_{W,H} \frac{1}{2} \left(|| A - WH ||_F^2 + \eta ||W||_F^2
#' + \beta (\sum_{j=1}^p ||H_{.j}||_1^2)\right)\\
#' s.t. & W\geq 0, H\geq 0
#' \end{array}
#' }{
#' min_{W,H} 1/2 (|| A - WH ||_F^2 + eta ||W||_F^2
#' + beta (sum_j ||H[,j]||_1^2))
#'
#' s.t. W>=0, H>=0
#' }
#'
#' The algorithm \sQuote{SNMF/L} solves a similar problem on the transposed target matrix \eqn{A},
#' where \eqn{H} and \eqn{W} swap roles, i.e. with sparsity constraints applied to \code{W}.
#'
#' @param maxIter maximum number of iterations.
#' @param eta parameter to suppress/bound the L2-norm of \code{W} and in
#' \code{H} in \sQuote{SNMF/R} and \sQuote{SNMF/L} respectively.
#'
#' If \code{eta < 0}, then it is set to the maximum value in the target matrix is used.
#' @param beta regularisation parameter for sparsity control, which
#' balances the trade-off between the accuracy of the approximation and the
#' sparseness of \code{H} and \code{W} in \sQuote{SNMF/R} and \sQuote{SNMF/L} respectively.
#'
#' Larger beta generates higher sparseness on \code{H} (resp. \code{W}).
#' Too large beta is not recommended.
#' @param bi_conv parameter of the biclustering convergence test.
#' It must be a size 2 numeric vector \code{bi_conv=c(wminchange, iconv)},
#' with:
#' \describe{
#' \item{\code{wminchange}:}{the minimal allowance of change in row-clusters.}
#' \item{\code{iconv}:}{ decide convergence if row-clusters
#' (within the allowance of \code{wminchange})
#' and column-clusters have not changed for \code{iconv} convergence checks.}
#' }
#'
#' Convergence checks are performed every 5 iterations.
#' @param eps_conv threshold for the KKT convergence test.
#' @param ... extra argument not used.
#'
#' @rdname SNMF-nmf
#' @aliases SNMF/R-nmf
nmfAlgorithm.SNMF_R <- setNMFMethod('snmf/r', .snmf, objective=snmf.objective)
#' @aliases SNMF/L-nmf
#' @rdname SNMF-nmf
nmfAlgorithm.SNMF_L <- setNMFMethod('snmf/l', .snmf, objective=snmf.objective)
|