Last updated: 2020-05-28

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Introduction

Here I run both SVD and non-negative matrix factorization on the zipcode training data.

SVD

Here we read in the “zipcode” training data, and extract the 2s and 3s.

z = read.table("../data/zip.train.txt")
sub = (z[,1] == 2) | (z[,1]==3)
z23 = as.matrix(z[sub,])

Now we run svd (excluding the first column which are the labels)

z23.svd = svd(z23[,-1])

Plot the first two two singular vectors, colored by group, we see the second sv separates the groups reasonably well.

plot(z23.svd$u[,1],z23.svd$u[,2],col=z23[,1])

Version Author Date
f300de6 stephens999 2018-04-19

And a histogram suggests a mixture of two Gaussians might be a reasonable start:

hist(z23.svd$u[,2],breaks=seq(-0.07,0.07,length=20))

Version Author Date
f300de6 stephens999 2018-04-19

Plot the images corresponding to first two eigenvectors

We put the eigenvector in the form of an image before plotting. Note that I have not been very careful with the limits

n = sqrt(length(z23.svd$v[,1]))
plot_zipcode_image = function(v){
  n = sqrt(length(v))
  m = matrix(v,nrow=n)
  m = apply(m,1,rev) # I had to experiment here to get the images to appear the "right way up"
  m = apply(m,1,rev) # note that applying rev twice does not result in no change...
  m = apply(m,2,rev)
  image(m)
}
plot_zipcode_image(z23.svd$v[,1])

plot_zipcode_image(z23.svd$v[,2])

Try non-negative matrix factorization

You will need to install NNLM to run this.

#library(devtools)
#devtools::install_github('linxihui/NNLM')

library(NNLM)
summary(as.vector(z23[1,]))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-1.0000 -1.0000 -1.0000 -0.4028  0.3190  3.0000 
z23_nonneg = z23[,-1] + 1
z23.nmf = nnmf(z23_nonneg,k = 2)
plot_zipcode_image(z23.nmf$H[1,])

plot_zipcode_image(z23.nmf$H[2,])

plot(z23.nmf$W[,1],z23.nmf$W[,2],col=z23[,1])

Try doing 6 and 3 instead - you see it separates them very nicely.

sub = (z[,1] == 6) | (z[,1]==3)
z36 = as.matrix(z[sub,])
summary(as.vector(z36[1,]))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-1.0000 -1.0000 -0.9870 -0.2932  0.7530  6.0000 
z36_nonneg = z36[,-1] + 1
z36.nmf = nnmf(z36_nonneg,k = 2)
plot_zipcode_image(z36.nmf$H[1,])

plot_zipcode_image(z36.nmf$H[2,])

plot(z36.nmf$W[,1],z36.nmf$W[,2],col=z36[,1])

Try doing all the digits. Here the results are messier. It is possible this is a local optimum problem as nmf is sensitive to initialization.

z_nonneg = as.matrix(z[,-1]) + 1
z.nmf = nnmf(z_nonneg,k = 12,max.iter = 100)
par(mfcol=c(3,4),mai=rep(0.2,4))
for(i in 1:12){
  plot_zipcode_image(z.nmf$H[i,])
}

Try running multiple times. Here I plot the mse trace for 3 different runs.

z.nmf2 = nnmf(z_nonneg,k = 12,max.iter = 100)
z.nmf3 = nnmf(z_nonneg,k = 12,max.iter = 100)
par(mfcol=c(1,1),mai=rep(0.5,4))
plot(z.nmf$mse,type="l")
lines(z.nmf2$mse,col=2)
lines(z.nmf3$mse,col=3)


sessionInfo()
R version 3.6.0 (2019-04-26)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Mojave 10.14.6

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] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] NNLM_0.4.4

loaded via a namespace (and not attached):
 [1] workflowr_1.6.1 Rcpp_1.0.4.6    rprojroot_1.3-2 digest_0.6.25  
 [5] later_1.0.0     R6_2.4.1        backports_1.1.5 git2r_0.26.1   
 [9] magrittr_1.5    evaluate_0.14   stringi_1.4.6   rlang_0.4.5    
[13] fs_1.3.2        promises_1.1.0  whisker_0.4     rmarkdown_2.1  
[17] tools_3.6.0     stringr_1.4.0   glue_1.4.0      httpuv_1.5.2   
[21] xfun_0.12       yaml_2.2.1      compiler_3.6.0  htmltools_0.4.0
[25] knitr_1.28