Sparse NMF Methods

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Last updated: 2019-11-05

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Summary

1. L1 penalty in NNLM::nnmf either put no/littlle thresholding or thresholds all entries to zero.

2. nsNMF and snmf in NMF package give sparse estimate of loadings and factors.

Data

set.seed(123)
n = 99
p = 300
k= 4
mfac = 2 # controls PVE of dense factor
L = matrix(0, nrow=n, ncol=k)
F = matrix(0, nrow=p, ncol=k)

L[1:(n/3),1] = 1
L[((n/3)+1):(2*n/3),2] = 1
L[((2*n/3)+1):n,3] = 1
L[,4] = 1+mfac*runif(n)

F[1:(p/3),1] = 1+10*runif(p/3)
F[((p/3)+1):(2*p/3),2] = 1+10*runif(p/3)
F[((2*p/3)+1):p,3] = 1+10*runif(p/3)
F[,4]= 1+mfac*runif(p)

lambda = L %*% t(F)
X = matrix(rpois(n=length(lambda),lambda),nrow=n)
image(X)

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NNLM-nnmf

library(NNLM)



fit_scd_L1.1 = NNLM::nnmf(A = X, k = 4, loss = "mse", method = "scd", max.iter = 10000, alpha=c(0,0,1))

for(i in 1:k){
    plot(fit_scd_L1.1$W[,i],main=paste0("L1 penalty = 1: estimated loadings ",i))
}

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fit_scd_L1.10 = NNLM::nnmf(A = X, k = 4, loss = "mse", method = "scd", max.iter = 10000, alpha=c(0,0,10))

for(i in 1:k){
    plot(fit_scd_L1.10$W[,i],main=paste0("L1 penalty = 10: estimated loadings ",i))
}

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fit_scd_L1.11 = NNLM::nnmf(A = X, k = 4, loss = "mse", method = "scd", max.iter = 10000, alpha=c(0,0,11))

for(i in 1:k){
    plot(fit_scd_L1.11$W[,i],main=paste0("L1 penalty = 11: estimated loadings ",i))
}

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fit_scd_L1.100 = NNLM::nnmf(A = X, k = 4, loss = "mse", method = "scd", max.iter = 10000, alpha=c(0,0,100))

for(i in 1:k){
    plot(fit_scd_L1.100$W[,i],main=paste0("L1 penalty = 100: estimated loadings ",i))
}

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NMF-nmf

Non-smooth NMF

Non-smooth NMF. Uses a modified version of Lee and Seung’s multiplicative updates for Kullback-Leibler divergence to fit a extension of the standard NMF model. It is meant to give sparser results.

Reference: Pascual-Montano2006

library(NMF)

Loading required package: pkgmaker

Loading required package: registry

Attaching package: 'pkgmaker'

The following object is masked from 'package:base':

    isFALSE

Loading required package: rngtools

Loading required package: cluster

NMF - BioConductor layer [OK] | Shared memory capabilities [NO: bigmemory] | Cores 7/8

  To enable shared memory capabilities, try: install.extras('
NMF
')

fit_nsNMF = nmf(X,4,method = 'nsNMF')

for(i in 1:k){
    plot(fit_nsNMF@fit@W[,i],main=paste0("nsNMF: estimated loadings ",i))
}

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for(i in 1:k){
    plot(fit_nsNMF@fit@H[i,],main=paste0("nsNMF: estimated factors ",i))
}

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Sparse NMF

Alternating Least Square (ALS) approach. It is meant to be very fast com- pared to other approaches.

Reference: KimH2007

Sparse Loading:

fit_snmfl = nmf(X,4,method = 'snmf/l',beta=1)

Warning in nmf_snmf(beta = 1, A = y, x = x, version = "L", verbose
= FALSE): NMF::snmf - Too many restarts due to too big 'beta' value
[Computation stopped after the 9th restart]

for(i in 1:k){
    plot(fit_snmfl@fit@W[,i],main=paste0("snmfl: estimated loadings ",i))
}

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Sparse Factors:

fit_snmfr = nmf(X,4,method = 'snmf/r',beta=1)

Warning in nmf_snmf(beta = 1, A = y, x = x, version = "R", verbose
= FALSE): NMF::snmf - Too many restarts due to too big 'beta' value
[Computation stopped after the 9th restart]

for(i in 1:k){
    plot(fit_snmfr@fit@H[i,],main=paste0("snmfr: estimated factors ",i))
}

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Session information

sessionInfo()

R version 3.6.1 (2019-07-05)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] parallel  stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
[1] NMF_0.21.0          Biobase_2.44.0      BiocGenerics_0.30.0
[4] cluster_2.1.0       rngtools_1.4        pkgmaker_0.27      
[7] registry_0.5-1      NNLM_0.4.3         

loaded via a namespace (and not attached):
 [1] tidyselect_0.2.5   xfun_0.10          purrr_0.3.2       
 [4] reshape2_1.4.3     colorspace_1.4-1   htmltools_0.4.0   
 [7] yaml_2.2.0         rlang_0.4.0        later_1.0.0       
[10] pillar_1.4.2       glue_1.3.1         withr_2.1.2       
[13] RColorBrewer_1.1-2 foreach_1.4.7      plyr_1.8.4        
[16] stringr_1.4.0      munsell_0.5.0      gtable_0.3.0      
[19] workflowr_1.5.0    codetools_0.2-16   evaluate_0.14     
[22] knitr_1.25         doParallel_1.0.15  httpuv_1.5.2      
[25] Rcpp_1.0.2         xtable_1.8-4       promises_1.1.0    
[28] backports_1.1.5    scales_1.0.0       fs_1.3.1          
[31] ggplot2_3.2.1      digest_0.6.21      stringi_1.4.3     
[34] dplyr_0.8.3        grid_3.6.1         rprojroot_1.3-2   
[37] bibtex_0.4.2       tools_3.6.1        magrittr_1.5      
[40] lazyeval_0.2.2     tibble_2.1.3       crayon_1.3.4      
[43] whisker_0.4        pkgconfig_2.0.3    gridBase_0.4-7    
[46] assertthat_0.2.1   rmarkdown_1.16     iterators_1.0.12  
[49] R6_2.4.0           git2r_0.26.1       compiler_3.6.1