Plot showing relationship between entropy and gini in relation to proportion of event (and that gini and entropy follow same pattern).

gini_entropy_similarity.R

library(tidyverse)

df_metrics <- tibble(
  prob = seq.int(0.001, 0.999, length.out = 999),
  entropy = -2 * (prob * log(prob) + (1-prob)*log(1-prob)),
  gini_index = 4 * prob * (1 - prob)
) %>% 
  gather(entropy, gini_index, key = "purity_metric", value = "value")

ggplot(df_metrics, aes(x = prob, y = value, colour = purity_metric))+
  geom_line()+
  facet_wrap(~purity_metric, scales = "free_y", ncol = 1)+
  labs(title = "Plot of entropy and gini vs proportion of binary outcome after one split", 
       subtitle = "number of regions = 2 ;  number of outcomes = 2", 
       x = "proportion K")