localization.R

library(tidyverse)
library(invertiforms) # RoheLab/invertiforms
library(igraphdata)
library(igraph)
library(RSpectra)
library(scales)

data("enron", package = "igraphdata")

A <- enron %>%
  as_adjacency_matrix()

rank <- 10

num_tau <- 10
tau <- 10^seq(-2, 4, length.out = num_tau)

laplacians <- tibble(tau = tau) %>%
  mutate(
    scaler = map(tau, ~ RegularizedLaplacian(A, .x, .x)),
    L_tau = map(scaler, ~ transform(.x, A))
  )

decomposed <- laplacians %>%
  mutate(
    svd = map(L_tau, svds, k = rank)
  )

cumulative_participation <- function(U) {
  sum(rowSums(U^2)^2)
}

localization <- decomposed %>%
  mutate(
    u = map_dbl(svd, ~ cumulative_participation(.x$u)),
    v = map_dbl(svd, ~ cumulative_participation(.x$v))
  )

# these are the same now but might differ for rectangular A
mean_rs <- mean(rowSums(A))
mean_cs <- mean(colSums(A))

localization %>%
  select(-scaler, -L_tau, -svd) %>%
  gather(subspace, localization, u, v) %>%
  ggplot() +
  aes(tau, localization, color = subspace, group = subspace) +
  geom_line() +
  geom_vline(xintercept = mean_rs, linetype = "dashed") +
  geom_vline(xintercept = mean_cs, linetype = "dashed") +
  scale_color_viridis_d(begin = 0.15, end = 0.85) +
  scale_x_log10(
    breaks = trans_breaks("log10", function(x) 10^x),
    labels = trans_format("log10", math_format(10^.x))
  ) +
  theme_minimal()