Last updated: 2025-06-26

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Knit directory: fastTopics-experiments/analysis/

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Rmd d2d8cb0 Peter Carbonetto 2025-06-26 wflow_publish("mcf7.Rmd", verbose = T, view = F)
html 1144f11 Peter Carbonetto 2025-06-26 Added another progress plot to the mcf7 example showing that the EM
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html 97d4fcd Peter Carbonetto 2025-06-25 Build site.
Rmd 05adfb4 Peter Carbonetto 2025-06-25 wflow_publish("mcf7.Rmd", verbose = T, view = F)
Rmd 727d65c Peter Carbonetto 2025-06-25 Added more structure plots to the mcf7 example.
Rmd 092a881 Peter Carbonetto 2025-06-25 Added the relative logliks to the mcf7 example.
Rmd 8a1835c Peter Carbonetto 2025-06-25 Improved the progress plot in the mcf7 analysis.
Rmd 94ffd45 Peter Carbonetto 2025-06-24 A couple small edits to the mcf7 example.
Rmd 88ac4b7 Peter Carbonetto 2025-06-24 I have a rough draft of the MCF-7 example; now I need to polish it up and put together nice figures.
html 8791b26 Peter Carbonetto 2025-06-23 Added link to the overview page.
Rmd 30dff04 Peter Carbonetto 2025-06-23 wflow_publish("index.Rmd")

This will be the new in-depth example for the paper illustrating the differences in performance of the EM and SCD methods. See here for background on the MCF-7 data set, including steps taken to prepare the data.

First load the packages used in the code below:

library(fastTopics)
library(ggplot2)
library(cowplot)

Set the seed to ensure that the results are reproducible:

set.seed(1)

Load the MCF-7 data set and initial estimate of the topic proportions:

load("../data/mcf7.RData")
dim(counts)
# [1]    41 16773

I obtain a “smart” initialization by running 4 EM iterations:

L <- L[,2:4]
control <- list(extrapolate = FALSE,numiter = 4,nc = 8)
fit0 <- init_poisson_nmf(counts,L = L,init.method = "random")
fit0 <- fit_poisson_nmf(counts,fit0 = fit0,numiter = 4,method = "em",
                        control = control,verbose = "none")

This “smart” initialization will be used as the starting point for all the comparisons.

This is what the smart initialization looks like:

topic_colors <- c("darkblue","dodgerblue","tomato")
n <- nrow(samples)
p1 <- structure_plot(fit0,grouping = samples$label,topics = c(3,1,2),
                     colors = topic_colors,loadings_order = 1:n) +
  labs(y = "topic prop.") +
  theme(axis.text.x = element_text(angle = 0,hjust = 0.5))
print(p1)

Version Author Date
97d4fcd Peter Carbonetto 2025-06-25

Now let’s run the extrapolated SCD algorithm for a decently long time to obtain a high-quality fit:

control$extrapolate <- FALSE
fit_best <- fit_poisson_nmf(counts,fit0 = fit0,numiter = 100,method = "scd",
                            control = control,verbose = "none")
control$extrapolate <- TRUE
fit_best <- fit_poisson_nmf(counts,fit0 = fit_best,numiter = 200,
                            method = "scd",control = control,
                            verbose = "none")

Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.

These are the max. residuals in the last iterations:

tail(fit_best$progress$res,n = 4)
# [1] 0.1081849 0.1081849 0.1081849 0.1011945

Here’s what the topic model looks like:

p2 <- structure_plot(fit_best,grouping = samples$label,topics = c(3,1,2),
                     colors = topic_colors,loadings_order = 1:n) +
  labs(y = "topic prop.") +
  theme(axis.text.x = element_text(angle = 0,hjust = 0.5))
print(p2)

Version Author Date
97d4fcd Peter Carbonetto 2025-06-25

Fit the topic model by performing EM updates or SCD updates, with or without extrapolation.

control$extrapolate <- FALSE
fit_em  <- fit_poisson_nmf(counts,fit0 = fit0,numiter = 100,method = "em",
                           control = control,verbose = "none")
fit_scd <- fit_poisson_nmf(counts,fit0 = fit0,numiter = 200,method = "scd",
                           control = control,verbose = "none")
fit_scd_ex <- fit_poisson_nmf(counts,fit0 = fit0,numiter = 50,method = "scd",
                              control = control,verbose = "none")
control$extrapolate <- TRUE
fit_scd_ex <- fit_poisson_nmf(counts,fit0 = fit_scd_ex,numiter = 50,
                              method = "scd",control = control,
                              verbose = "none")
fit_em_scd <- fit_poisson_nmf(counts,fit0 = fit_em,numiter = 100,
                              method = "scd",control = control,
                              verbose = "none")
control$extrapolate <- FALSE
fit_em  <- fit_poisson_nmf(counts,fit0 = fit_em,numiter = 100,method = "em",
                           control = control,verbose = "none")

Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.

This plot shows the improvement in the solution over time for the different methods:

progress_plot_colors <- c("dodgerblue","darkblue","darkorange","magenta")
ll_best <- tail(fit_best$progress$loglik.multinom,n = 1)
pdat <- rbind(cbind(fit_em$progress,data.frame(method = "em")),
              cbind(fit_scd$progress,data.frame(method = "scd")),
              cbind(fit_scd_ex$progress,data.frame(method = "scd+ex")),
              cbind(fit_em_scd$progress,data.frame(method = "em+scd+ex")))
pdat <- transform(pdat,
                  loglik.multinom = ll_best - loglik.multinom,
                  method = factor(method))
pdat2 <- subset(pdat,iter %% 50 == 1)
p3 <- ggplot(pdat,aes(x = iter,y = loglik.multinom,color = method)) +
  geom_line() +
  geom_point(data = pdat2,size = 1) +
  scale_y_continuous(trans = "log10",breaks = 10^seq(-3,7)) +
  scale_color_manual(values = progress_plot_colors) +
  labs(x = "iteration",y = "distance from best loglik") +
  theme_cowplot(font_size = 12)
print(p3)

Version Author Date
97d4fcd Peter Carbonetto 2025-06-25

Compare the log-likelihoods obtained by the different methods (relative to the log-likelihood at the “high-quality” solution):

logliks <- c("initial"   = sum(loglik_multinom_topic_model(counts,fit0)),
             "em"        = sum(loglik_multinom_topic_model(counts,fit_em)),
             "scd"       = sum(loglik_multinom_topic_model(counts,fit_scd)),
             "scd+ex"    = sum(loglik_multinom_topic_model(counts,fit_scd_ex)),
             "em+scd+ex" = sum(loglik_multinom_topic_model(counts,fit_em_scd)))
ll_best - logliks
#      initial           em          scd       scd+ex    em+scd+ex 
# 4.995810e+06 1.551685e+05 7.850426e-02 7.498864e-03 2.696458e-03

Compare the fit obtained by each method in Structure plots:

p4 <- structure_plot(fit_em,grouping = samples$label,topics = c(3,1,2),
                    colors = topic_colors,loadings_order = 1:n) +
  labs(y = "topic prop.",title = "EM") +
  theme(axis.text.x = element_text(angle = 0,hjust = 0.5))
p5 <- structure_plot(fit_scd,grouping = samples$label,topics = c(3,1,2),
                     colors = topic_colors,loadings_order = 1:n) +
  labs(y = "topic prop.",title = "SCD") +
  theme(axis.text.x = element_text(angle = 0,hjust = 0.5))
p6 <- structure_plot(fit_scd_ex,grouping = samples$label,topics = c(3,1,2),
                     colors = topic_colors) +
  labs(y = "topic prop.",title = "SCD + extrapolate") +
  theme(axis.text.x = element_text(angle = 0,hjust = 0.5))
p7 <- structure_plot(fit_em_scd,grouping = samples$label,topics = c(3,1,2),
                     colors = topic_colors) +
  labs(y = "topic prop.",title = "EM + SCD + extrapolate") +
  theme(axis.text.x = element_text(angle = 0,hjust = 0.5))
print(plot_grid(p4,p5,p6,p7,nrow = 4,ncol = 1))

Version Author Date
1144f11 Peter Carbonetto 2025-06-26

Also, let’s check that the EM updates eventually converge to the same fixed point:

control$extrapolate <- FALSE
fit_em_long  <- fit_poisson_nmf(counts,fit0 = fit0,numiter = 4000,
                                method = "em",control = control,
                                verbose = "none")

Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.

Indeed, they do:

cor(poisson2multinom(fit_best)$L,poisson2multinom(fit_em_long)$L)
#             k1          k2         k3
# k1  0.02068773  0.99999758 -0.8602272
# k2 -0.52903124 -0.85831034  0.9999983
# k3  0.99998264  0.01327648 -0.5230406

Plot the improvement in the EM updates over time:

pdat <- fit_em_long$progress
pdat <- transform(pdat,loglik.multinom = ll_best - loglik.multinom)
pdat2 <- subset(pdat,iter %% 50 == 1)
p8 <- ggplot(pdat,aes(x = iter,y = loglik.multinom)) +
  geom_line(color = "dodgerblue") +
  geom_point(data = pdat2,size = 1,color = "dodgerblue") +
  scale_y_continuous(trans = "log10",breaks = 10^seq(-2,+7)) +
  labs(x = "iteration",y = "dist. from best loglik") +
  theme_cowplot(font_size = 12)
print(p8)

Version Author Date
1144f11 Peter Carbonetto 2025-06-26

Finally, save the key plots to PDF:

ggsave("mcf7_structure_plots.pdf",
       plot_grid(p1 + ggtitle("initial"),
                 p2 + ggtitle("solution"),
                 p4,
                 p5,
                 nrow = 4,ncol = 1),
       height = 5.5,width = 4)
ggsave("mcf7_progress_plot.pdf",p3,height = 2.5,width = 4)
ggsave("mcf7_progress_plot_em.pdf",p8,height = 2,width = 3)

sessionInfo()
# R version 4.3.3 (2024-02-29)
# Platform: aarch64-apple-darwin20 (64-bit)
# Running under: macOS 15.5
# 
# Matrix products: default
# BLAS:   /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib 
# LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0
# 
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
# 
# time zone: America/Chicago
# tzcode source: internal
# 
# attached base packages:
# [1] stats     graphics  grDevices utils     datasets  methods   base     
# 
# other attached packages:
# [1] cowplot_1.1.3     ggplot2_3.5.0     fastTopics_0.7-25
# 
# loaded via a namespace (and not attached):
#  [1] gtable_0.3.4        xfun_0.42           bslib_0.6.1        
#  [4] htmlwidgets_1.6.4   ggrepel_0.9.5       lattice_0.22-5     
#  [7] quadprog_1.5-8      vctrs_0.6.5         tools_4.3.3        
# [10] generics_0.1.3      parallel_4.3.3      tibble_3.2.1       
# [13] fansi_1.0.6         highr_0.10          pkgconfig_2.0.3    
# [16] Matrix_1.6-5        data.table_1.17.4   SQUAREM_2021.1     
# [19] RcppParallel_5.1.10 lifecycle_1.0.4     truncnorm_1.0-9    
# [22] farver_2.1.1        compiler_4.3.3      stringr_1.5.1      
# [25] git2r_0.33.0        textshaping_0.3.7   progress_1.2.3     
# [28] munsell_0.5.0       RhpcBLASctl_0.23-42 httpuv_1.6.14      
# [31] htmltools_0.5.8.1   sass_0.4.9          yaml_2.3.8         
# [34] lazyeval_0.2.2      plotly_4.10.4       crayon_1.5.2       
# [37] later_1.3.2         pillar_1.9.0        jquerylib_0.1.4    
# [40] whisker_0.4.1       tidyr_1.3.1         uwot_0.2.3         
# [43] cachem_1.0.8        gtools_3.9.5        tidyselect_1.2.1   
# [46] digest_0.6.34       Rtsne_0.17          stringi_1.8.3      
# [49] reshape2_1.4.4      dplyr_1.1.4         purrr_1.0.2        
# [52] ashr_2.2-66         labeling_0.4.3      rprojroot_2.0.4    
# [55] fastmap_1.1.1       grid_4.3.3          colorspace_2.1-0   
# [58] cli_3.6.4           invgamma_1.1        magrittr_2.0.3     
# [61] utf8_1.2.4          withr_3.0.2         prettyunits_1.2.0  
# [64] scales_1.3.0        promises_1.2.1      rmarkdown_2.26     
# [67] httr_1.4.7          workflowr_1.7.1     ragg_1.2.7         
# [70] hms_1.1.3           pbapply_1.7-2       evaluate_1.0.3     
# [73] knitr_1.45          viridisLite_0.4.2   irlba_2.3.5.1      
# [76] rlang_1.1.5         Rcpp_1.0.12         mixsqp_0.3-54      
# [79] glue_1.8.0          jsonlite_1.8.8      plyr_1.8.9         
# [82] R6_2.5.1            systemfonts_1.0.6   fs_1.6.5