Last updated: 2021-06-17

Checks: 7 0

Knit directory: ebpmf_data_analysis/

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    Modified:   script/fit_kos_NMF_F.R
    Modified:   topicView-app/app.R

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Introduction

I want to confirm my observation that cone NMF (F norm) solution converges to where \(B, W^t\) are the same, on realistic data. Here I fit it on a document dataset with \((n, p) = (3430, 6906)\)

rm(list = ls())
source("code/cone_NMF_l2.R")
source("code/smallsim2_functions.R")
source("code/misc.R")
source("code/util.R")
set.seed(123)

Fit for 100 iterations

Note it has not converged it.

fitted = readRDS("output/fitted_kos_coneNMF_F_K20.Rds")
plot(fitted$loss)

Version Author Date
7ceb75d zihao12 2021-06-15 
fitted$runtime
    user   system  elapsed 
1024.484  428.177 1455.753

Indeed \(B, W^t\) are basically identical.

k = ncol(fitted$B)
par(mfrow = c(5, 4))
for(i in 1:k){
  plot(fitted$B[,i], fitted$W[i,], xlab = "bk",ylab = "wk", cex.lab = 1)
  abline(a = 0, b = 1, col = "blue")
  
}

Version Author Date
1f213e0 zihao12 2021-06-15

Fit for 1000 iterations

fitted = readRDS("output/fitted_kos_coneNMF_F_K20_iter1000.Rds")
plot(fitted$loss)

Version Author Date
454edc8 zihao12 2021-06-17
463e2bf zihao12 2021-06-17
06996fb zihao12 2021-06-16 
fitted$runtime
     user    system   elapsed 
10361.252  3976.731 14359.158

Indeed \(B, W^t\) are basically identical. Will show the results after 1000 iterations when ready.

k = ncol(fitted$B)
par(mfrow = c(5, 4))
for(i in 1:k){
  plot(fitted$B[,i], fitted$W[i,], xlab = "bk",ylab = "wk", cex.lab = 1)
  abline(a = 0, b = 1, col = "blue")
}

Version Author Date
454edc8 zihao12 2021-06-17
463e2bf zihao12 2021-06-17
06996fb zihao12 2021-06-16

compare with regular NMF

Initialized from coneNMF (iter100) and ran only 20 iterations till converged (rel.tol = 1e-05)

fitted_nmf = readRDS("output/fitted_kos_NMF_F_K20.Rds")
n= ncol(fitted_nmf$H)
p= nrow(fitted_nmf$W)


## mse: NMF vs coneNMF
c(min(fitted_nmf$target.loss), min(fitted$loss)/(n*p*2))
[1] 0.01400633 0.01484356

Compare L

par(mfrow = c(5, 4))
for(i in 1:k){
  plot(fitted$W[i,], fitted_nmf$H[i,],xlab = "Lk (coneNMF)",ylab = "Lk (NMF)", cex.lab = 1)
  abline(a = 0, b = 1, col = "blue")
}

Version Author Date
454edc8 zihao12 2021-06-17

Compare F

par(mfrow = c(5, 4))
for(i in 1:k){
  plot(fitted$A[,i], fitted_nmf$W[,i],xlab = "Fk (coneNMF)",ylab = "Fk (NMF)", cex.lab = 1)
  abline(a = 0, b = 1, col = "blue")
}

Version Author Date
454edc8 zihao12 2021-06-17

Is the NMF solution contained in the cone?

F_proj = readRDS("output/kos_coneFactor_F.Rds")$f_proj
par(mfrow = c(5, 4))
for(i in 1:k){
  f = fitted$A[,i]
  f_proj  = F_proj[[i]]
  plot(f, f_proj$fitted, ylab = "f_proj", cex.lab = 1)
  abline(a = 0, b = 1, col = "blue")
  
}

Version Author Date
454edc8 zihao12 2021-06-17 

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.15.7

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] pheatmap_1.0.12 mvtnorm_1.1-0   workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.5         knitr_1.28         whisker_0.3-2      magrittr_1.5      
 [5] munsell_0.5.0      colorspace_1.4-1   R6_2.4.1           rlang_0.4.5       
 [9] stringr_1.4.0      tools_3.5.1        grid_3.5.1         gtable_0.3.0      
[13] xfun_0.8           git2r_0.26.1       htmltools_0.5.0    yaml_2.2.0        
[17] digest_0.6.25      rprojroot_1.3-2    lifecycle_0.2.0    RColorBrewer_1.1-2
[21] later_1.1.0.1      promises_1.1.1     fs_1.3.1           glue_1.4.1        
[25] evaluate_0.14      rmarkdown_2.1      stringi_1.6.2      compiler_3.5.1    
[29] scales_1.1.1       backports_1.1.7    httpuv_1.5.4