Scaling of higher dimensions

[rcannood]

The higher dimensions of LMDS have a higher scale in comparison to MDS and PCA. Determine whether this is a problem and whether it needs to be solved.

Example code

library(tidyverse)
library(dyno)

data("fibroblast_reprogramming_treutlein")

expr <- fibroblast_reprogramming_treutlein$expression 
rownames(expr) <- colnames(expr) <- NULL

pca <- prcomp(expr, rank. = 40)$x %>% dynutils::scale_uniform()
pheatmap::pheatmap(pca, border_color = NA, cluster_cols = FALSE)

mds <- cmdscale(dynutils::calculate_distance(expr, method = "spearman"), k = 40) %>%
  dynutils::scale_uniform()
pheatmap::pheatmap(mds, border_color = NA, cluster_cols = FALSE)

lmds <- lmds::lmds(expr, distance_method = "spearman", ndim = 40, num_landmarks = 100) %>%
  dynutils::scale_uniform()
pheatmap::pheatmap(lmds, border_color = NA, cluster_cols = FALSE)

colnames(pca) <- colnames(mds) <- colnames(lmds) <- NULL

df <- bind_rows(
  pca %>% reshape2::melt(varnames = c("row", "comp")) %>% mutate(dimred = "PCA"),
  mds %>% reshape2::melt(varnames = c("row", "comp")) %>% mutate(dimred = "MDS"),
  lmds %>% reshape2::melt(varnames = c("row", "comp")) %>% mutate(dimred = "LMDS")
)
ggplot(df) + 
  geom_point(aes(comp, value, colour = dimred)) +
  facet_wrap(~dimred) +
  theme_bw()
ggsave("~/plot.png", width = 12, height = 4)

[rcannood]

By setting the number of landmarks to Inf, this effect is already greatly reduced (as can be expected, maybe), but not entirely: