A theoretical comparison plot showing Gini impurity and entropy (information gain) as splitting criteria for decision trees across the probability range [0, 1]. Both curves are displayed on the same axes to illustrate their similar behavior and slight differences. This educational visualization helps understand the mathematical foundation of tree-based algorithms and why both criteria lead to similar tree structures in practice.
""" anyplot.ai
line-impurity-comparison: Gini Impurity vs Entropy Comparison
Library: letsplot 4.10.1 | Python 3.13.13
Quality: 91/100 | Updated: 2026-05-29
"""
import os
import numpy as np
import pandas as pd
from lets_plot import *
from lets_plot.export import ggsave
LetsPlot.setup_html()
# Theme tokens — Imprint palette, theme-adaptive chrome
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
# Data
p = np.linspace(0, 1, 200)
# Gini impurity: 2p(1 - p)
gini = 2 * p * (1 - p)
# Entropy: -p log2(p) - (1-p) log2(1-p), normalized to [0, 1]
with np.errstate(divide="ignore", invalid="ignore"):
entropy = -p * np.log2(p) - (1 - p) * np.log2(1 - p)
entropy = np.nan_to_num(entropy, nan=0.0)
# Main curves data — Gini first so it gets Imprint position 1 (#009E73)
df = pd.DataFrame(
{
"p": np.tile(p, 2),
"impurity": np.concatenate([gini, entropy]),
"metric": ["Gini: 2p(1−p)"] * len(p) + ["Entropy (normalized)"] * len(p),
}
)
# Shaded region between curves
ribbon_df = pd.DataFrame({"p": p, "gini": gini, "entropy": entropy})
# Open circle markers at maxima (unified, no unused columns)
markers_df = pd.DataFrame(
{"p": [0.5, 0.5], "impurity": [1.0, 0.5], "metric": ["Entropy (normalized)", "Gini: 2p(1−p)"]}
)
# Arrow pointing to peak area
arrow_df = pd.DataFrame({"x": [0.5], "y": [0.93], "xend": [0.5], "yend": [0.86]})
# Annotations
main_label_df = pd.DataFrame({"p": [0.5], "impurity": [0.97], "label": ["Maximum uncertainty at p = 0.5"]})
region_label_df = pd.DataFrame(
{"p": [0.72], "impurity": [0.6], "label": ["Shaded region:\ndifference between metrics"]}
)
# Shifted inward (0.07 / 0.93) to avoid left/right edge clipping
boundary_df = pd.DataFrame(
{"p": [0.07, 0.93], "impurity": [0.06, 0.06], "label": ["p → 0: both → 0", "p → 1: both → 0"], "hjust": [0.0, 1.0]}
)
# Plot
plot = (
ggplot()
# Shaded ribbon between curves
+ geom_ribbon(
data=ribbon_df,
mapping=aes(x="p", ymin="gini", ymax="entropy"),
fill=IMPRINT_PALETTE[2],
alpha=0.12,
tooltips="none",
)
# Main curves with interactive tooltips
+ geom_line(
data=df,
mapping=aes(x="p", y="impurity", color="metric"),
size=1.5,
tooltips=layer_tooltips()
.format("@p", ".2f")
.format("@impurity", ".3f")
.line("@metric")
.line("p = @p")
.line("impurity = @impurity"),
)
# Vertical guide at p=0.5
+ geom_vline(xintercept=0.5, color=INK_SOFT, size=0.5, linetype="dashed")
# Arrow from annotation to entropy maximum
+ geom_segment(
aes(x="x", y="y", xend="xend", yend="yend"),
data=arrow_df,
color=INK_SOFT,
size=0.6,
arrow=arrow(angle=25, length=8, type="closed"),
)
# Open circle markers at maxima — unified, border color from metric scale
+ geom_point(
aes(x="p", y="impurity", color="metric"),
data=markers_df,
size=6,
shape=21,
fill=PAGE_BG,
stroke=2,
tooltips="none",
)
# Annotation: maximum uncertainty label
+ geom_text(
data=main_label_df,
mapping=aes(x="p", y="impurity", label="label"),
size=4,
color=INK,
fontface="bold italic",
)
# Annotation: shaded region explanation
+ geom_text(
data=region_label_df,
mapping=aes(x="p", y="impurity", label="label"),
size=3.5,
color=INK_SOFT,
fontface="italic",
)
# Annotations: boundary behavior at p→0 and p→1
+ geom_text(
data=boundary_df,
mapping=aes(x="p", y="impurity", label="label", hjust="hjust"),
size=3,
color=INK_MUTED,
fontface="italic",
)
# Scales — Imprint palette canonical order
+ scale_color_manual(values=[IMPRINT_PALETTE[0], IMPRINT_PALETTE[1]])
+ scale_x_continuous(breaks=list(np.arange(0, 1.1, 0.1)), limits=[0, 1])
+ scale_y_continuous(breaks=list(np.arange(0, 1.2, 0.2)), limits=[-0.06, 1.05])
# Labels
+ labs(
x="Probability of class 1 (p)",
y="Impurity measure (normalized)",
title="line-impurity-comparison · python · letsplot · anyplot.ai",
subtitle="Both criteria peak at maximum uncertainty (p = 0.5), explaining why Gini and entropy yield similar tree structures",
color="",
)
# Canvas: 800×450 × scale=4 → 3200×1800 px
+ ggsize(800, 450)
+ theme_minimal()
+ theme(
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
axis_text=element_text(size=10, color=INK_SOFT),
axis_title=element_text(size=12, color=INK),
plot_title=element_text(size=16, face="bold", color=INK),
plot_subtitle=element_text(size=10, color=INK_SOFT, face="italic"),
legend_text=element_text(size=10, color=INK_SOFT),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_position="bottom",
panel_grid_major=element_line(color=INK_SOFT, size=0.2),
panel_grid_minor=element_blank(),
axis_line=element_blank(),
axis_ticks=element_blank(),
plot_margin=[20, 20, 10, 10],
)
)
# Save — PNG + HTML (interactive)
ggsave(plot, f"plot-{THEME}.png", path=".", scale=4)
ggsave(plot, f"plot-{THEME}.html", path=".")
Part of Gini Impurity vs Entropy Comparison on anyplot.ai.