pancreas_celseq2_ica_02
Matthew Stephens
2026-09-16
Last updated: 2026-09-16
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Knit directory: single-cell-jamboree/analysis/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | a8d1267 | Matthew Stephens | 2026-09-16 | Add pancreas_celseq2_ica_02: rank-r ICA with cubic, logPhi, x|x| |
Introduction
A second look at ICA on the pancreas CEL-seq2 data, incorporating lessons from the first analysis (pancreas_celseq2_ica.Rmd). Key differences from the first analysis:
- Data are not centred before whitening. The mean direction becomes one of the 25 components and can be explicitly examined.
- We run rank-\(r\) (symmetric) fastICA with \(r = 25\) rather than many rank-1 starts, which is faster and avoids the post-hoc deduplication step.
- We compare three contrast functions chosen to favour one-sided/sparse sources: \(x^3\) (kurtosis/skewness), \(\log\Phi(\alpha x)\) (log-normal CDF), and \(x|x|\) (the tilting term of TLC without the log-cosh).
library(fastICA)
library(Matrix)
library(ggplot2)
library(caret)
load("../data/pancreas.RData")
set.seed(1)
i <- which(sample_info$tech == "celseq2")
sample_info <- sample_info[i, ]
counts <- counts[i, ]
x <- colSums(counts > 0)
j <- which(x > 9)
counts <- counts[, j]
a <- 1
s <- rowSums(counts)
s <- s / mean(s)
Y <- MatrixExtra::mapSparse(counts / (a * s), log1p) # NOT centredPreprocessing: SVD of uncentered data
n <- nrow(Y)
n.comp <- 25
r <- n.comp
Y.svd <- svd(Y, nu = n.comp, nv = 0)
# U: n x n.comp, orthonormal columns (left singular vectors of uncentered Y)
U_unc <- Y.svd$u[, 1:n.comp]
# Whitened row space (n.comp x n, as used by rank-r fastICA)
U_w <- sqrt(n) * t(U_unc)Helper functions
celltype_palette <- c(
"#E41A1C", "#377EB8", "#4DAF4A", "#984EA3", "#FF7F00",
"#A65628", "#F781BF", "#1B9E77", "#D95F02", "#7570B3",
"#E7298A", "#66A61E", "#E6AB02", "#A6761D", "#666666"
)
# Polar factor via eigendecomposition (avoids SVD column reordering).
polar <- function(W) {
eig <- eigen(t(W) %*% W, symmetric = TRUE)
Ainvhalf <- eig$vectors %*%
diag(1 / sqrt(pmax(eig$values, 1e-14))) %*%
t(eig$vectors)
W %*% Ainvhalf
}
prune_and_count_cluster <- function(L, tau = 0.9) {
L <- L[, apply(L, 2, sd) > 1e-10, drop = FALSE]
dist_mat <- as.dist(1 - abs(cor(L)))
hc <- hclust(dist_mat, method = "complete")
clusters <- cutree(hc, h = 1 - tau)
kept_indices <- match(unique(clusters), clusters)
cluster_sizes_table <- table(clusters)
kept_cluster_ids <- clusters[kept_indices]
cluster_sizes <- as.integer(cluster_sizes_table[as.character(kept_cluster_ids)])
list(pruned_matrix = L[, kept_indices, drop = FALSE],
cluster_sizes = cluster_sizes,
kept_indices = kept_indices,
cluster_assignments = clusters)
}
plot_loadings_matrix <- function(Lhat, label_prefix = "c:", si = sample_info,
obj_fn = function(L) colMeans(L^4),
max_panels = 25, labels = NULL) {
obj <- obj_fn(Lhat)
n_comp <- ncol(Lhat)
if (is.null(labels)) {
o <- order(obj)
Lhat <- Lhat[, o, drop = FALSE]
obj <- obj[o]
comp_labels <- make.unique(paste0(label_prefix, seq_len(n_comp),
" obj:", round(obj, 3)))
} else {
comp_labels <- make.unique(paste0(labels, " obj:", round(obj, 3)))
}
cell_order <- order(si$celltype)
df <- data.frame(
rank = rep(seq_len(nrow(Lhat)), n_comp),
celltype = rep(si$celltype[cell_order], n_comp),
loading = as.vector(Lhat[cell_order, ]),
component = factor(rep(comp_labels, each = nrow(Lhat)),
levels = comp_labels)
)
pages <- split(comp_labels,
ceiling(seq_along(comp_labels) / max_panels))
for (pg in seq_along(pages)) {
pg_labels <- pages[[pg]]
df_pg <- df[df$component %in% pg_labels, ]
df_pg$component <- factor(as.character(df_pg$component),
levels = pg_labels)
pg_title <- if (length(pages) > 1)
paste0("page ", pg, "/", length(pages)) else ""
p <- ggplot(df_pg, aes(x = rank, y = loading, color = celltype)) +
geom_point(size = 0.5, alpha = 0.7) +
geom_hline(yintercept = 0, linetype = "dashed", linewidth = 0.3) +
facet_wrap(~ component, ncol = 5, scales = "free_y") +
scale_color_manual(values = celltype_palette) +
labs(x = NULL, y = "Loading", color = "Cell type", title = pg_title) +
theme_bw(base_size = 10) +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank(),
strip.text = element_text(size = 7,
margin = margin(2, 0, 2, 0)),
strip.background = element_rect(fill = "grey90", color = NA),
legend.position = "bottom")
print(p)
}
}Contrast functions
# --- x^3 (kurtosis/skewness) ---
# g(x) = x^3, g'(x) = 3x^2, G(x) = x^4/4
fastica_update_cubic_rankr <- function(U, W) {
P <- t(U) %*% W
G <- P^3
G2 <- 3 * P^2
W <- U %*% G - sweep(W, 2, colSums(G2), "*")
polar(W)
}
objective_cubic <- function(L) colMeans(L^4)
# --- log-Phi ---
# G(x) = log Phi(alpha*x), g = alpha*h, g' = alpha^2*(-alpha*x*h - h^2)
fastica_update_logphi_rankr <- function(U, W, alpha = 2) {
P <- t(U) %*% W
u <- alpha * P
h <- exp(dnorm(u, log = TRUE) - pnorm(u, log.p = TRUE))
G <- alpha * h
G2 <- alpha^2 * (-u * h - h^2)
W <- U %*% G - sweep(W, 2, colSums(G2), "*")
polar(W)
}
objective_logphi <- function(L, alpha = 2) colMeans(pnorm(alpha * L, log.p = TRUE))
# --- x|x| (skew tilt, no log-cosh) ---
# g(x) = 2|x|, g'(x) = 2*sign(x), G(x) = x|x|
fastica_update_skew_rankr <- function(U, W) {
P <- t(U) %*% W
G <- 2 * abs(P)
G2 <- 2 * sign(P)
W <- U %*% G - sweep(W, 2, colSums(G2), "*")
polar(W)
}
objective_skew <- function(L) colMeans(L * abs(L))Rank-r fastICA: cubic contrast (x^3)
set.seed(1)
n_iter <- 500
W_cubic <- polar(matrix(rnorm(n.comp * r), n.comp, r))
for (i in seq_len(n_iter))
W_cubic <- fastica_update_cubic_rankr(U_w, W_cubic)
Lhat_cubic <- t(U_w) %*% W_cubic # n x r
plot_loadings_matrix(Lhat_cubic, label_prefix = "cub:",
obj_fn = objective_cubic)
Rank-r fastICA: log-Phi contrast (alpha = 2)
set.seed(1)
n_iter <- 500
W_lp <- polar(matrix(rnorm(n.comp * r), n.comp, r))
for (i in seq_len(n_iter))
W_lp <- fastica_update_logphi_rankr(U_w, W_lp, alpha = 2)
Lhat_lp <- t(U_w) %*% W_lp
plot_loadings_matrix(Lhat_lp, label_prefix = "lp:",
obj_fn = objective_logphi)
Rank-r fastICA: x|x| contrast
set.seed(1)
n_iter <- 500
W_skew <- polar(matrix(rnorm(n.comp * r), n.comp, r))
for (i in seq_len(n_iter))
W_skew <- fastica_update_skew_rankr(U_w, W_skew)
Lhat_skew <- t(U_w) %*% W_skew
plot_loadings_matrix(Lhat_skew, label_prefix = "sk:",
obj_fn = objective_skew)
sessionInfo()R version 4.4.2 (2024-10-31)
Platform: aarch64-apple-darwin20
Running under: macOS 26.5.2
Matrix products: default
BLAS: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.0
locale:
[1] C
time zone: America/Chicago
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] caret_7.0-1 lattice_0.22-9 ggplot2_4.0.2 Matrix_1.7-4 fastICA_1.2-7
loaded via a namespace (and not attached):
[1] tidyselect_1.2.1 timeDate_4052.112 dplyr_1.2.0
[4] farver_2.1.2 S7_0.2.1 fastmap_1.2.0
[7] pROC_1.19.0.1 promises_1.5.0 digest_0.6.39
[10] rpart_4.1.24 timechange_0.4.0 lifecycle_1.0.5
[13] survival_3.8-6 MatrixExtra_0.1.15 magrittr_2.0.4
[16] compiler_4.4.2 rlang_1.1.7 sass_0.4.10
[19] tools_4.4.2 yaml_2.3.12 data.table_1.18.2.1
[22] knitr_1.51 labeling_0.4.3 plyr_1.8.9
[25] RColorBrewer_1.1-3 workflowr_1.7.2 withr_3.0.2
[28] purrr_1.2.1 nnet_7.3-20 grid_4.4.2
[31] stats4_4.4.2 git2r_0.36.2 future_1.69.0
[34] globals_0.19.0 scales_1.4.0 iterators_1.0.14
[37] MASS_7.3-65 cli_3.6.5 rmarkdown_2.30
[40] generics_0.1.4 otel_0.2.0 future.apply_1.20.2
[43] reshape2_1.4.5 cachem_1.1.0 stringr_1.6.0
[46] splines_4.4.2 parallel_4.4.2 vctrs_0.7.2
[49] hardhat_1.4.2 jsonlite_2.0.0 listenv_0.10.0
[52] foreach_1.5.2 gower_1.0.2 jquerylib_0.1.4
[55] recipes_1.3.1 glue_1.8.0 parallelly_1.46.1
[58] codetools_0.2-20 lubridate_1.9.5 stringi_1.8.7
[61] gtable_0.3.6 later_1.4.6 tibble_3.3.1
[64] pillar_1.11.1 htmltools_0.5.9 float_0.3-3
[67] ipred_0.9-15 lava_1.8.2 R6_2.6.1
[70] rprojroot_2.1.1 evaluate_1.0.5 RhpcBLASctl_0.23-42
[73] httpuv_1.6.16 bslib_0.10.0 class_7.3-23
[76] Rcpp_1.1.1 nlme_3.1-168 prodlim_2026.03.11
[79] whisker_0.4.1 xfun_0.56 fs_1.6.6
[82] pkgconfig_2.0.3 ModelMetrics_1.2.2.2