Automatic Grouping of Factors: Pancreas
Ziang Zhang
2025-02-12
Last updated: 2025-04-02
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single-cell-jamboree/analysis/
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Let’s try some automatic grouping of factors for the pancreas dataset, based on the grouping information provided in the metadata.
library(Matrix)
library(fastTopics)Warning: package 'fastTopics' was built under R version 4.3.3library(ggplot2)
library(cowplot)
set.seed(1)
subsample_cell_types <- function (x, n = 1000) {
cells <- NULL
groups <- levels(x)
for (g in groups) {
i <- which(x == g)
n0 <- min(n,length(i))
i <- sample(i,n0)
cells <- c(cells,i)
}
return(sort(cells))
}
load("../data/pancreas.RData")
load("../output/pancreas_factors.RData")
load("../output/pancreas_factors2.RData")source("../code/group_factors.R")A Simple Automatic Approach Based on ANOVA
Let \(l_{ki}\) denote the loading of observation \(i\) on the \(k\)th factor, and let \(G_i\) denote the grouping information (e.g. cell-type) for observation (e.g. cell) \(i\). Suppose \(G_i\) can take values in \(\{g_1, g_2, \ldots, g_L\}\) (e.g. \(L\) possible cell-types).
A straightforward way to identify group-specific factors is to perform an ANOVA on each factor’s loadings. Specifically, for the \(k\)th factor, we regress the loadings \(\boldsymbol{l}_k\) on the set of indicator variables \(\{\mathbb{I}(G_i = c_l)\}_{l=1}^L\):
\[ l_{ki} \sim \sum_{l=1}^L \beta_l \,\mathbb{I}(G_i = c_l). \]
From the regression model for each factor, we obtain a statistic \(S_k\) that measures how strongly the grouping structure explains variation in the \(k\)-th factor’s loadings. For instance, \(S_k\) could be the \(R^2\) of this regression model or the \(F\)-statistic from the ANOVA test. After computing \(\{S_k\}_{k=1}^K\), we can rank the factors by their relevance to the grouping, then choose a threshold (for example, by examining an elbow plot) to automatically select the ``group-specific’’ factors.
Below, let’s apply this approach to the pancreas dataset, using \(R^2\) as the relevance statistic.
flashier NMF
cells <- subsample_cell_types(sample_info$celltype,n = 500)
L <- fl_nmf_ldf$L
k <- ncol(L)
colnames(L) <- paste0("k",1:k)Take a look at the elbow plot:
ordered_df_tech <- ANOVA_factors(L[cells,], sample_info$tech[cells], stats = "R2")
ordered_df_celltype <- ANOVA_factors(L[cells,], sample_info$celltype[cells], stats = "R2")
par(mfrow = c(2,1))
plot(ordered_df_tech$rank, ordered_df_tech$stats, type = "o", xlab = "Rank", ylab = "R2", main = "batchtypes", ylim = c(0,1.1))
text(ordered_df_tech$rank, ordered_df_tech$stats, labels = ordered_df_tech$factor, pos = 3, cex = 0.6)
abline(h = c(0.3,0.5,0.7), col = "red", lty = 2)
plot(ordered_df_celltype$rank, ordered_df_celltype$stats, type = "o", xlab = "Rank", ylab = "R2", main = "celltypes", ylim = c(0,1.1))
text(ordered_df_celltype$rank, ordered_df_celltype$stats, labels = ordered_df_celltype$factor, pos = 3, cex = 0.6)
abline(h = c(0.3,0.5,0.7), col = "red", lty = 2)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
par(mfrow = c(1,1))Cut off the factors with \(R^2\) less than 0.7:
p1 <- structure_plot_group(L = L[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.7, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = L[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.7, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Cut off the factors with \(R^2\) less than 0.5:
p1 <- structure_plot_group(L = L[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.5, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = L[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.5, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Try reduce to the cut-off to 0.3:
p1 <- structure_plot_group(L = L[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.3, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = L[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.3, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
NMF (NNLM)
W <- nmf$W
k <- ncol(W)
d <- apply(W,2,max)
scale_cols <- function (A, b)
t(t(A) * b)
W <- scale_cols(W,1/d)
colnames(W) <- paste0("k",1:k)Take a look at the elbow plot:
ordered_df_tech <- ANOVA_factors(W[cells,], sample_info$tech[cells], stats = "R2")
ordered_df_celltype <- ANOVA_factors(W[cells,], sample_info$celltype[cells], stats = "R2")
par(mfrow = c(2,1))
plot(ordered_df_tech$rank, ordered_df_tech$stats, type = "o", xlab = "Rank", ylab = "R2", main = "batchtypes", ylim = c(0,1.1))
text(ordered_df_tech$rank, ordered_df_tech$stats, labels = ordered_df_tech$factor, pos = 3, cex = 0.6)
abline(h = c(0.3,0.5,0.7), col = "red", lty = 2)
plot(ordered_df_celltype$rank, ordered_df_celltype$stats, type = "o", xlab = "Rank", ylab = "R2", main = "celltypes", ylim = c(0,1.1))
text(ordered_df_celltype$rank, ordered_df_celltype$stats, labels = ordered_df_celltype$factor, pos = 3, cex = 0.6)
abline(h = c(0.3,0.5,0.7), col = "red", lty = 2)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
par(mfrow = c(1,1))Cut off the factors with \(R^2\) less than 0.7:
p1 <- structure_plot_group(L = W[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.7, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = W[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.7, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Cut off the factors with \(R^2\) less than 0.5:
p1 <- structure_plot_group(L = W[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.5, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = W[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.5, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Cut off the factors with \(R^2\) less than 0.3:
p1 <- structure_plot_group(L = W[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.3, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = W[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.3, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Topic model (fastTopics)
L <- poisson2multinom(pnmf)$LTake a look at the elbow plot:
ordered_df_tech <- ANOVA_factors(L[cells,], sample_info$tech[cells], stats = "R2")
ordered_df_celltype <- ANOVA_factors(L[cells,], sample_info$celltype[cells], stats = "R2")
par(mfrow = c(2,1))
plot(ordered_df_tech$rank, ordered_df_tech$stats, type = "o", xlab = "Rank", ylab = "R2", main = "batchtypes", ylim = c(0,1.1))
text(ordered_df_tech$rank, ordered_df_tech$stats, labels = ordered_df_tech$factor, pos = 3, cex = 0.6)
abline(h = c(0.3,0.5,0.7), col = "red", lty = 2)
plot(ordered_df_celltype$rank, ordered_df_celltype$stats, type = "o", xlab = "Rank", ylab = "R2", main = "celltypes", ylim = c(0,1.1))
text(ordered_df_celltype$rank, ordered_df_celltype$stats, labels = ordered_df_celltype$factor, pos = 3, cex = 0.6)
abline(h = c(0.3,0.5,0.7), col = "red", lty = 2)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
par(mfrow = c(1,1))Cut off the factors with \(R^2\) less than 0.7:
p1 <- structure_plot_group(L = L[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.7, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = L[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.7, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Cut off the factors with \(R^2\) less than 0.5:
p1 <- structure_plot_group(L = L[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.5, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = L[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.5, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Cut off the factors with \(R^2\) less than 0.3:
p1 <- structure_plot_group(L = L[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.3, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = L[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.3, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Flashier semi-NMF
L <- fl_snmf_ldf$L
x <- apply(L,2,function (x) quantile(x,0.995))
L <- scale_cols(L,1/x)
colnames(L) <- paste0("k",1:k)Take a look at the elbow plot:
ordered_df_tech <- ANOVA_factors(W[cells,], sample_info$tech[cells], stats = "R2")
ordered_df_celltype <- ANOVA_factors(W[cells,], sample_info$celltype[cells], stats = "R2")
par(mfrow = c(2,1))
plot(ordered_df_tech$rank, ordered_df_tech$stats, type = "o", xlab = "Rank", ylab = "R2", main = "batchtypes", ylim = c(0,1.1))
text(ordered_df_tech$rank, ordered_df_tech$stats, labels = ordered_df_tech$factor, pos = 3, cex = 0.6)
abline(h = c(0.3,0.5,0.7), col = "red", lty = 2)
plot(ordered_df_celltype$rank, ordered_df_celltype$stats, type = "o", xlab = "Rank", ylab = "R2", main = "celltypes", ylim = c(0,1.1))
text(ordered_df_celltype$rank, ordered_df_celltype$stats, labels = ordered_df_celltype$factor, pos = 3, cex = 0.6)
abline(h = c(0.3,0.5,0.7), col = "red", lty = 2)
par(mfrow = c(1,1))Cut off the factors with \(R^2\) less than 0.7:
p1 <- structure_plot_group(L = L[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.7, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = L[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.7, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Cut off the factors with \(R^2\) less than 0.5:
p1 <- structure_plot_group(L = L[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.5, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = L[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.5, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
Cut off the factors with \(R^2\) less than 0.3:
p1 <- structure_plot_group(L = L[cells,], group_vec = sample_info$tech[cells],
cutoff = 0.3, stats = "R2", group_name = "data-set")
p2 <- structure_plot_group(L = L[cells,], group_vec = sample_info$celltype[cells],
cutoff = 0.3, stats = "R2", group_name = "cell-type")
plot_grid(p1,p2,nrow = 2,ncol = 1)
| Version | Author | Date |
|---|---|---|
| cb4a691 | Ziang Zhang | 2025-02-12 |
sessionInfo()R version 4.3.1 (2023-06-16)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Monterey 12.7.4
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_3.5.1 fastTopics_0.6-192 Matrix_1.6-4
loaded via a namespace (and not attached):
[1] gtable_0.3.6 xfun_0.48 bslib_0.8.0
[4] htmlwidgets_1.6.4 ggrepel_0.9.6 lattice_0.22-6
[7] quadprog_1.5-8 vctrs_0.6.5 tools_4.3.1
[10] generics_0.1.3 parallel_4.3.1 tibble_3.2.1
[13] fansi_1.0.6 highr_0.11 pkgconfig_2.0.3
[16] data.table_1.16.2 SQUAREM_2021.1 RcppParallel_5.1.9
[19] lifecycle_1.0.4 truncnorm_1.0-9 farver_2.1.2
[22] compiler_4.3.1 stringr_1.5.1 git2r_0.33.0
[25] progress_1.2.3 munsell_0.5.1 RhpcBLASctl_0.23-42
[28] httpuv_1.6.15 htmltools_0.5.8.1 sass_0.4.9
[31] yaml_2.3.10 lazyeval_0.2.2 plotly_4.10.4
[34] crayon_1.5.3 later_1.3.2 pillar_1.9.0
[37] jquerylib_0.1.4 whisker_0.4.1 tidyr_1.3.1
[40] uwot_0.1.16 cachem_1.1.0 gtools_3.9.5
[43] tidyselect_1.2.1 digest_0.6.37 Rtsne_0.17
[46] stringi_1.8.4 dplyr_1.1.4 purrr_1.0.2
[49] ashr_2.2-66 labeling_0.4.3 rprojroot_2.0.4
[52] fastmap_1.2.0 grid_4.3.1 colorspace_2.1-1
[55] cli_3.6.3 invgamma_1.1 magrittr_2.0.3
[58] utf8_1.2.4 withr_3.0.2 prettyunits_1.2.0
[61] scales_1.3.0 promises_1.3.0 rmarkdown_2.28
[64] httr_1.4.7 workflowr_1.7.1 hms_1.1.3
[67] pbapply_1.7-2 evaluate_1.0.1 knitr_1.48
[70] viridisLite_0.4.2 irlba_2.3.5.1 rlang_1.1.4
[73] Rcpp_1.0.13-1 mixsqp_0.3-54 glue_1.8.0
[76] rstudioapi_0.16.0 jsonlite_1.8.9 R6_2.5.1
[79] fs_1.6.4