Andrews Curves for Multivariate Data — Matplotlib

Andrews curves visualization transforms multivariate observations into smooth Fourier series curves. Each data point is represented as a continuous function where variable values become coefficients in a Fourier expansion, producing distinctive wave patterns. This technique enables visual comparison of multivariate patterns, cluster identification, and outlier detection—observations with similar values across variables produce similar curves, while outliers appear as distinctly different patterns.

Andrews Curves for Multivariate Data rendered with Matplotlib

Python source (Matplotlib)

""" anyplot.ai
andrews-curves: Andrews Curves for Multivariate Data
Library: matplotlib 3.10.9 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-15
"""

import os

import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets import load_iris
from sklearn.preprocessing import StandardScaler


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"
BRAND = "#009E73"
IMPRINT = ["#009E73", "#C475FD", "#4467A3"]

# Data
np.random.seed(42)
iris = load_iris()
X = iris.data
y = iris.target
species_names = ["Setosa", "Versicolor", "Virginica"]

# Normalize data to prevent dominant variables
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# Generate t values from -π to π
t = np.linspace(-np.pi, np.pi, 200)

# Build Andrews curve transformation matrix
# f(t) = x1/sqrt(2) + x2*sin(t) + x3*cos(t) + x4*sin(2t) + ...
n_features = X_scaled.shape[1]
basis = np.zeros((len(t), n_features))
basis[:, 0] = 1 / np.sqrt(2)
for i in range(1, n_features):
    freq = (i + 1) // 2
    if i % 2 == 1:
        basis[:, i] = np.sin(freq * t)
    else:
        basis[:, i] = np.cos(freq * t)

# Compute all Andrews curves: each row of X_scaled dot basis.T gives one curve
curves = X_scaled @ basis.T  # shape: (150, 200)

# Plot
fig, ax = plt.subplots(figsize=(16, 9), facecolor=PAGE_BG)
ax.set_facecolor(PAGE_BG)

# Plot Andrews curves for each observation
for i in range(len(curves)):
    ax.plot(t, curves[i], color=IMPRINT[y[i]], alpha=0.4, linewidth=2.5)

# Create legend with sample lines
for idx, species in enumerate(species_names):
    ax.plot([], [], color=IMPRINT[idx], linewidth=3, label=species, alpha=0.4)

# Style
ax.set_xlabel("t (radians)", fontsize=20, color=INK)
ax.set_ylabel("f(t)", fontsize=20, color=INK)
ax.set_title("andrews-curves · matplotlib · anyplot.ai", fontsize=24, fontweight="medium", color=INK)
ax.tick_params(axis="both", labelsize=16, colors=INK_SOFT)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
for s in ("left", "bottom"):
    ax.spines[s].set_color(INK_SOFT)
ax.yaxis.grid(True, alpha=0.15, linewidth=0.8, color=INK)

# Legend styling
leg = ax.legend(fontsize=16, loc="upper right")
if leg:
    leg.get_frame().set_facecolor(ELEVATED_BG)
    leg.get_frame().set_edgecolor(INK_SOFT)
    leg.get_frame().set_linewidth(0.8)
    plt.setp(leg.get_texts(), color=INK_SOFT)

# Set x-axis ticks at meaningful positions
ax.set_xticks([-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi])
ax.set_xticklabels(["-π", "-π/2", "0", "π/2", "π"], fontsize=16)

plt.tight_layout()
plt.savefig(f"plot-{THEME}.png", dpi=300, bbox_inches="tight", facecolor=PAGE_BG)

Part of Andrews Curves for Multivariate Data on anyplot.ai.

Andrews Curves for Multivariate Data — Matplotlib

Python source (Matplotlib)

Other implementations