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: chartjs 4.4.7 | JavaScript 22.23.2
// Quality: 89/100 | Created: 2026-08-26
const t = window.ANYPLOT_TOKENS;
// --- Data (in-memory, deterministic) ----------------------------------------
// Splitting-criterion curves across the full probability range [0, 1].
const POINTS = 100;
const probabilities = Array.from({ length: POINTS }, (_, i) => i / (POINTS - 1));
const log2 = (x) => Math.log(x) / Math.log(2);
const giniPoints = probabilities.map((p) => ({ x: p, y: 2 * p * (1 - p) }));
const entropyPoints = probabilities.map((p) => {
// Edge cases: 0 * log2(0) is undefined, defined as 0 by convention.
const term1 = p === 0 ? 0 : -p * log2(p);
const term2 = p === 1 ? 0 : -(1 - p) * log2(1 - p);
return { x: p, y: term1 + term2 };
});
// --- Mount -------------------------------------------------------------------
const canvas = document.createElement("canvas");
document.getElementById("container").appendChild(canvas);
// --- Custom plugin: annotate the shared maximum at p = 0.5 -------------------
const maxImpurityAnnotation = {
id: "maxImpurityAnnotation",
afterDatasetsDraw(chart) {
const { ctx, chartArea, scales } = chart;
const x = scales.x.getPixelForValue(0.5);
ctx.save();
ctx.strokeStyle = t.inkSoft;
ctx.lineWidth = 1.5;
ctx.setLineDash([6, 5]);
ctx.beginPath();
ctx.moveTo(x, chartArea.top);
ctx.lineTo(x, chartArea.bottom);
ctx.stroke();
ctx.setLineDash([]);
ctx.fillStyle = t.ink;
ctx.font = "16px sans-serif";
ctx.textAlign = "center";
ctx.fillText("Max impurity at p = 0.5", x, chartArea.top - 10);
ctx.restore();
},
};
Chart.register(maxImpurityAnnotation);
// --- Chart ---------------------------------------------------------------------
new Chart(canvas, {
type: "line",
data: {
datasets: [
{
label: "Gini Impurity: 2p(1-p)",
data: giniPoints,
borderColor: t.palette[0],
backgroundColor: t.palette[0],
borderWidth: 4,
pointRadius: 0,
tension: 0,
},
{
label: "Entropy: -p·log₂(p) - (1-p)·log₂(1-p)",
data: entropyPoints,
borderColor: t.palette[1],
backgroundColor: t.palette[1],
borderWidth: 3,
borderDash: [10, 6],
pointRadius: 0,
tension: 0,
},
],
},
options: {
responsive: true,
maintainAspectRatio: false,
animation: false,
parsing: false,
plugins: {
title: {
display: true,
text: "line-impurity-comparison · javascript · chartjs · anyplot.ai",
color: t.ink,
font: { size: 22 },
padding: { top: 10, bottom: 34 },
},
legend: {
position: "bottom",
labels: { color: t.ink, font: { size: 16 }, usePointStyle: true },
},
},
scales: {
x: {
type: "linear",
min: 0,
max: 1,
title: { display: true, text: "Probability of Positive Class (p)", color: t.ink, font: { size: 18 } },
ticks: { color: t.inkSoft, font: { size: 14 }, stepSize: 0.1 },
grid: { display: false },
},
y: {
min: 0,
max: 1,
title: { display: true, text: "Impurity Measure", color: t.ink, font: { size: 18 } },
ticks: { color: t.inkSoft, font: { size: 14 } },
grid: { color: t.grid },
},
},
},
});
Part of Gini Impurity vs Entropy Comparison on anyplot.ai.