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Introduction

This is an example the current greedy approach will probably not work.

rm(list = ls())
library(ebpmf.alpha)
library(flashr)
set.seed(123)
n = 150
p = 500
k= 5
L = matrix(0, nrow=n, ncol=k)
F = matrix(0, nrow=p, ncol=k)
L[1:(n/5),1] = 1
L[((n/5)+1):(2*n/5),2] = 1
L[(2 * (n/5)+1):(3*n/5),3] = 1
L[(3 * (n/5)+1):(4*n/5),4] = 1
L[(4 * (n/5)+1):(5 *n/5),5] = 1

F[1:(p/5),1] = 1+10*runif(p/5)
F[((p/5)+1):(2*p/5),2] = 1+10*runif(p/5)
F[(2 * (p/5)+1):(3*p/5),3] = 1+10*runif(p/5)
F[(3 * (p/5)+1):(4*p/5),4] = 1+10*runif(p/5)
F[(4 * (p/5)+1):(5*p/5),5] = 1+10*runif(p/5)

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

Version Author Date
23decbe zihao12 2020-06-04 
eps = 1e-4
init = NNLM::nnmf(A = X, k = k, loss = "mkl", method = "lee")
L0 = init$W
F0 = t(init$H)
init_pmf = list(L = matrix(L0[,1] + eps, ncol = 1), 
                F = matrix(F0[,1] + eps, ncol = 1))
maxiter = 200
rate = 0.6
verbose = FALSE

system.time(
  fit_pmf <- ebpmf.alpha::pmf_greedy(X = X, K = 3 * k,
                              init = init_pmf, maxiter = maxiter, rate = rate,
                              verbose = verbose)
)
   user  system elapsed 
  4.402   0.087   4.515 
system.time(
  fit_flash <- flash(data = X, Kmax = 3*k, verbose = verbose)
)
   user  system elapsed 
  3.732   0.850   4.627 
system.time(
  fit_svd <- svd(X, nu = 3*k, nv = 3*k)
)
   user  system elapsed 
  0.025   0.000   0.026 
fit_flash
Summary of flash object:
  Number of factor/loading pairs: 15
  Proportion of variance explained:
    Factor/loading 1: 0.182
    Factor/loading 2: 0.175
    Factor/loading 3: 0.177
    Factor/loading 4: 0.178
    Factor/loading 5: 0.172
    Factor/loading 6: 0.001
    Factor/loading 7: 0.001
    Factor/loading 10: 0.001
    Factor/loading 12: 0.001
    Factor/loading 13: 0.001
    Factor/loading 14: 0.001
    Factor/loading 15: 0.001
      *Factor/loadings with PVE < 0.001 are omitted from this summary.
  Value of objective function: -105999.189

look at progress from greedy pmf

plot(diff(fit_pmf$loglik))

Version Author Date
23decbe zihao12 2020-06-04

look at \(l_{ik} f_{jk}\) for pmf_greedy

I scale \(l_{Ik}, f_{Jk}\) to have Frobenius norm 1, as the other two methods

d_l = sqrt( diag(t(fit_pmf$L) %*% fit_pmf$L) )
d_f = sqrt( diag(t(fit_pmf$F) %*% fit_pmf$F) )
d = d_l*d_f
plot(d, log = "y")

Version Author Date
23decbe zihao12 2020-06-04 
Kmax = 3 *k
par(mfrow = c(k, 3))
for(k_ in 1:Kmax){
  l = fit_pmf$L[,k_]/d_l[k_]
  f = fit_pmf$F[,k_]/d_f[k_]
  lam = l %o% f 
  image(lam)
}

Version Author Date
23decbe zihao12 2020-06-04

look at \(l_{ik} f_{jk}\) for flashr

plot(fit_flash$ldf$d, log = "y")

Kmax = 3 *k
par(mfrow = c(k, 3))
for(k_ in 1:Kmax){
  l = fit_flash$ldf$l[,k_]
  f = fit_flash$ldf$f[,k_]
  lam = l %o% f 
  image(lam)
}

look at \(l_{ik} f_{jk}\) for svd

## u^t u = v^t v = I_k
plot(fit_svd$d, log = "y")

Kmax = 3 *k
par(mfrow = c(k, 3))
for(k_ in 1:Kmax){
  l = fit_svd$u[,k_]
  f = fit_svd$v[,k_]
  lam = l %o% f 
  image(lam)
}


sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] flashr_0.6-6      ebpmf.alpha_0.4.2 workflowr_1.6.2  

loaded via a namespace (and not attached):
 [1] softImpute_1.4    gtools_3.8.2      tidyselect_0.2.5  xfun_0.8         
 [5] NNLM_0.4.2        reshape2_1.4.3    purrr_0.3.4       ashr_2.2-38      
 [9] lattice_0.20-38   colorspace_1.4-1  vctrs_0.3.0       htmltools_0.3.6  
[13] yaml_2.2.0        rlang_0.4.6       mixsqp_0.3-43     later_0.8.0      
[17] pillar_1.4.4      glue_1.4.1        plyr_1.8.4        foreach_1.4.7    
[21] lifecycle_0.2.0   ebpm_0.0.1.0      stringr_1.4.0     munsell_0.5.0    
[25] gtable_0.3.0      codetools_0.2-16  evaluate_0.14     knitr_1.28       
[29] pscl_1.5.2        doParallel_1.0.15 httpuv_1.5.1      irlba_2.3.3      
[33] parallel_3.5.1    Rcpp_1.0.4.6      promises_1.0.1    backports_1.1.7  
[37] scales_1.1.1      truncnorm_1.0-8   fs_1.3.1          ggplot2_3.3.0    
[41] digest_0.6.25     stringi_1.4.3     dplyr_0.8.1       grid_3.5.1       
[45] rprojroot_1.3-2   tools_3.5.1       magrittr_1.5      tibble_3.0.1     
[49] crayon_1.3.4      whisker_0.3-2     pkgconfig_2.0.3   MASS_7.3-51.4    
[53] ellipsis_0.3.1    Matrix_1.2-17     SQUAREM_2017.10-1 assertthat_0.2.1 
[57] rmarkdown_2.1     iterators_1.0.12  R6_2.4.1          git2r_0.26.1     
[61] compiler_3.5.1