Chernoff faces visualize multivariate data by mapping each variable to a facial feature (eye size, mouth curvature, face width, nose length, etc.), transforming each observation into a unique cartoon face. This technique leverages humans' innate ability to recognize and distinguish faces, making it easier to identify patterns, clusters, and outliers across multiple dimensions simultaneously.
""" anyplot.ai
chernoff-basic: Chernoff Faces for Multivariate Data
Library: plotnine 0.15.4 | Python 3.13.13
Quality: 91/100 | Updated: 2026-05-15
"""
import os
import numpy as np
import pandas as pd
from plotnine import (
aes,
coord_fixed,
element_rect,
element_text,
facet_wrap,
geom_path,
geom_point,
geom_polygon,
ggplot,
labs,
scale_fill_manual,
theme,
theme_void,
)
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"
np.random.seed(42)
# Data: Car performance metrics with more extreme outliers
car_data = {
"observation_id": ["Compact A", "Compact B", "Sedan A", "Sedan B", "SUV A", "SUV B"],
"category": ["Compact", "Compact", "Sedan", "Sedan", "SUV", "SUV"],
"engine_power": [100, 150, 180, 220, 280, 320],
"fuel_efficiency": [38, 30, 26, 22, 18, 15],
"safety_rating": [3.9, 4.5, 4.8, 4.2, 4.6, 4.9],
"comfort_score": [3.0, 3.6, 4.5, 4.1, 4.0, 4.4],
}
sample_df = pd.DataFrame(car_data)
# Normalize data to 0-1 range for facial feature mapping
normalized = sample_df[["engine_power", "fuel_efficiency", "safety_rating", "comfort_score"]].apply(
lambda col: (col - col.min()) / (col.max() - col.min() + 1e-10)
)
face_widths = 0.6 + normalized["engine_power"] * 0.4
face_heights = 0.8 + normalized["fuel_efficiency"] * 0.4
eye_sizes = 0.08 + normalized["safety_rating"] * 0.1
mouth_curvatures = -0.3 + normalized["comfort_score"] * 0.6
# Build data for all faces
all_data = []
for idx in range(len(sample_df)):
obs_id = sample_df["observation_id"].iloc[idx]
category = sample_df["category"].iloc[idx]
fw = face_widths.iloc[idx]
fh = face_heights.iloc[idx]
es = eye_sizes.iloc[idx]
mc = mouth_curvatures.iloc[idx]
# Face outline
theta = np.linspace(0, 2 * np.pi, 50)
fx = fw * np.cos(theta)
fy = fh * np.sin(theta)
for i in range(len(fx)):
all_data.append({"observation_id": obs_id, "category": category, "part": "face", "x": fx[i], "y": fy[i]})
# Left eye
theta = np.linspace(0, 2 * np.pi, 20)
ex = -fw * 0.35 + es * np.cos(theta)
ey = fh * 0.25 + es * np.sin(theta)
for i in range(len(ex)):
all_data.append({"observation_id": obs_id, "category": category, "part": "left_eye", "x": ex[i], "y": ey[i]})
# Right eye
ex = fw * 0.35 + es * np.cos(theta)
ey = fh * 0.25 + es * np.sin(theta)
for i in range(len(ex)):
all_data.append({"observation_id": obs_id, "category": category, "part": "right_eye", "x": ex[i], "y": ey[i]})
# Left pupil (larger for visibility)
all_data.append(
{"observation_id": obs_id, "category": category, "part": "left_pupil", "x": -fw * 0.35, "y": fh * 0.25}
)
# Right pupil (larger for visibility)
all_data.append(
{"observation_id": obs_id, "category": category, "part": "right_pupil", "x": fw * 0.35, "y": fh * 0.25}
)
# Mouth
x_mouth = np.linspace(-fw * 0.25, fw * 0.25, 20)
y_mouth = -fh * 0.35 + mc * (((x_mouth) / (fw * 0.25)) ** 2 - 1)
for i in range(len(x_mouth)):
all_data.append(
{"observation_id": obs_id, "category": category, "part": "mouth", "x": x_mouth[i], "y": y_mouth[i]}
)
# Nose
all_data.append({"observation_id": obs_id, "category": category, "part": "nose", "x": 0, "y": fh * 0.1})
all_data.append({"observation_id": obs_id, "category": category, "part": "nose", "x": 0, "y": -fh * 0.1})
# Left eyebrow
x_brow = np.linspace(-fw * 0.35 - es, -fw * 0.35 + es, 10)
y_brow = fh * 0.45 + 0.05 * (x_brow + fw * 0.35) / es
for i in range(len(x_brow)):
all_data.append(
{"observation_id": obs_id, "category": category, "part": "left_eyebrow", "x": x_brow[i], "y": y_brow[i]}
)
# Right eyebrow
x_brow = np.linspace(fw * 0.35 - es, fw * 0.35 + es, 10)
y_brow = fh * 0.45 - 0.05 * (x_brow - fw * 0.35) / es
for i in range(len(x_brow)):
all_data.append(
{"observation_id": obs_id, "category": category, "part": "right_eyebrow", "x": x_brow[i], "y": y_brow[i]}
)
plot_df = pd.DataFrame(all_data)
# Okabe-Ito palette
category_colors = {"Compact": "#009E73", "Sedan": "#C475FD", "SUV": "#4467A3"}
anyplot_theme = theme(
figure_size=(16, 9),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
plot_title=element_text(size=24, weight="bold", color=INK, ha="center"),
plot_subtitle=element_text(size=16, color=INK_SOFT, ha="center"),
legend_position="bottom",
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_title=element_text(size=16, color=INK),
legend_text=element_text(size=14, color=INK_SOFT),
strip_text=element_text(size=14, color=INK, weight="bold"),
)
plot = (
ggplot()
# Face outline (filled polygon)
+ geom_polygon(
data=plot_df[plot_df["part"] == "face"],
mapping=aes(x="x", y="y", group="observation_id", fill="category"),
color=INK_SOFT,
size=1.5,
)
# Eyes (white/elevated filled)
+ geom_polygon(
data=plot_df[plot_df["part"] == "left_eye"],
mapping=aes(x="x", y="y", group="observation_id"),
fill=ELEVATED_BG,
color=INK_SOFT,
size=0.8,
)
+ geom_polygon(
data=plot_df[plot_df["part"] == "right_eye"],
mapping=aes(x="x", y="y", group="observation_id"),
fill=ELEVATED_BG,
color=INK_SOFT,
size=0.8,
)
# Pupils (larger for visibility)
+ geom_point(data=plot_df[plot_df["part"] == "left_pupil"], mapping=aes(x="x", y="y"), color=INK_SOFT, size=5)
+ geom_point(data=plot_df[plot_df["part"] == "right_pupil"], mapping=aes(x="x", y="y"), color=INK_SOFT, size=5)
# Mouth
+ geom_path(
data=plot_df[plot_df["part"] == "mouth"],
mapping=aes(x="x", y="y", group="observation_id"),
color=INK_SOFT,
size=1.2,
)
# Nose
+ geom_path(
data=plot_df[plot_df["part"] == "nose"],
mapping=aes(x="x", y="y", group="observation_id"),
color=INK_SOFT,
size=1,
)
# Eyebrows
+ geom_path(
data=plot_df[plot_df["part"] == "left_eyebrow"],
mapping=aes(x="x", y="y", group="observation_id"),
color=INK_SOFT,
size=1.2,
)
+ geom_path(
data=plot_df[plot_df["part"] == "right_eyebrow"],
mapping=aes(x="x", y="y", group="observation_id"),
color=INK_SOFT,
size=1.2,
)
# Facet by observation
+ facet_wrap("~observation_id", ncol=3)
# Colors (Okabe-Ito palette)
+ scale_fill_manual(values=category_colors)
# Labels
+ labs(
title="chernoff-basic · plotnine · anyplot.ai",
subtitle="Car Performance: Power/Efficiency/Safety/Comfort mapped to facial features",
fill="Category",
)
# Theme
+ theme_void()
+ anyplot_theme
+ coord_fixed(ratio=1)
)
plot.save(f"plot-{THEME}.png", dpi=300)
Part of Chernoff Faces for Multivariate Data on anyplot.ai.