Overlap Lasso Plot with R ggplot2

Question

I'm trying to reproduce the plot of the experiment in the paper "Group Lasso with Overlap and Graph Lasso - Jacob, Obozinksi and Vert". I was able to produce the data but I don't know where to start with the plot.

enter image description here

Here the description of the plot from the authors: "for each variable (on the vertical axis), we plot its frequency of selection in levels of gray as a function of the regularization parameter λ, both for the lasso penalty and Ω_overlap"

I'm trying a simplified version to begin with, with only 1 simulation, so instead of a scale of gray I should obtain black and white segment

I tried heatmap but I don't know how to impose the x-axis

Here is the code to produce the data

library(MLGL)

p <- 82
n <- 50

X <- rnorm(n*p)
X <- matrix(X, nrow=n, ncol=p)

y <- X[,c(26:42)] %*% c(rep(1,17)) + rnorm(50, 0, 0.5)

var <- c(1:10, 9:18, 17:26, 25:34, 33:42, 41:50, 49:58, 57:66, 65:74, 73:82)
group <- rep(1:10, each = 10)

experimento <- overlapgglasso(X, y, var, group, intercept = F)

lambda <- experimento$lambda[-1]

variabili <- 1:82

selez <- matrix(NA, ncol = 82, nrow = 99)

for (i in 1:99){
  selez[i,] <- variabili %in% experimento$var[[i+1]]
}

I tried heatmap but I don't know how to impose the x-axis.

Answer 1

I would probably convert to a data frame, then pivot into long format for plotting with ggplot:

library(ggplot2)

as.data.frame(0 + selez) |>
  setNames(variabili) |>
  cbind(lambda = lambda) |>
  tidyr::pivot_longer(-lambda) |>
  dplyr::mutate(name = factor(as.numeric(name))) |>
  ggplot(aes(lambda, name, fill = factor(value))) +
  geom_tile(aes(width = lambda/20), color = 'gray') +
  scale_fill_manual('Selez', values = c('white', 'black'), 
                    labels = c('No', 'Sì')) +
  labs(y = 'variabili') +
  coord_cartesian(expand = FALSE) +
  theme_minimal()