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boRing

Description

The goal of boRing is to provide an easy metric to determine whether a multivariate empirical distribution is likely unimodal (that is, a boring distribution) or not. The “boringness” index is based on the idea that the density of observations should decrease monotonically with the the distance to the center of mass of an unimodal empirical distribution.

The computation of the “boringness” index is done as follows:

  1. We compute the center of mass and the covariance matrix of the empirical distribution (weighted observations are allowed in boRing).

  2. From the center of mass and the covariance matrix, we compute the Mahalanobis distance of each observation to the center of mass of the distribution.

  3. We order the observations based on their Mahalanobis distance (from closest to furthest away).

  4. We compute the Spearman correlation between the negative Mahalanobis distances of the ordered observations and the weighted density of the observations up to each computed distance. If the correlation is close to 1, it indicates that the density of observations decreases monotonically with the distance to the center of mass of the distribution and, hence, that the distribution is likely unimodal (or, boring).

Installation

At this time, boRing is not yet available on CRAN.

You can install the development version of boRing from GitHub with:

# install.packages("devtools")
devtools::install_github("swarm-lab/boRing")

Performance tip

boRing depends on RcppEigen for computing efficiently the weighted covariance matrix of the empirical distribution as well as the Mahalanobis distances of the observations. Provided that your compiler allows it, a significant performance increase can be obtained by adding the -O3 optimization flag to the CXXFLAGS line in your local .R/Makevars file. If you don’t know where your local .R/Makevars file is located, install the usethis package and then run usethis::edit_r_makevars().

Example 

library(MASS)
library(ggplot2)
library(patchwork)
library(boRing)

distr1 <- mvrnorm(500, c(0, 0), matrix(c(3, 0.5, 0.5, 1), 2, 2))
distr2 <- mvrnorm(500, c(0, 0), matrix(c(3, 0.5, 0.5, 1), 2, 2))

xlim <- c(min(distr1[, 1], distr2[, 1]), max(distr1[, 1], distr2[, 1]) + 8)
ylim <- c(min(distr1[, 2], distr2[, 2]), max(distr1[, 2], distr2[, 2]) + 8)

g <- lapply(0:8, function(offset) {
  dt <- data.frame(
    x = c(distr1[, 1], distr2[, 1] + offset),
    y = c(distr1[, 2], distr2[, 2] + offset),
    dist = c(rep("A", nrow(distr1)), rep("B", nrow(distr1)))
  )

  idx <- boring(dt[, 1:2])

  ggplot(dt) +
    aes(x, y) +
    stat_density_2d(aes(fill = after_stat(level)),
      geom = "polygon",
      n = 100, bins = 10, show.legend = FALSE
    ) +
    geom_point(aes(color = dist), size = 0.25, alpha = 0.5) +
    labs(title = paste0("Boringness index: ", round(idx, 3))) +
    coord_equal(xlim = xlim, ylim = ylim) +
    scale_fill_viridis_c(option = "plasma") +
    scale_color_brewer(palette = "Dark2") +
    theme_bw() +
    theme(legend.position = "none")
})

wrap_plots(g)