PCA Biplot in Python: How to Make and Interpret Scores and Loadings

A PCA biplot is one of the fastest ways to understand a multivariate dataset. It shows sample separation and variable direction in the same figure, which makes it useful for metabolomics, spectroscopy, materials data, and any workflow where interpretation matters as much as compression.

Minimal PCA biplot code

The important part is not just running PCA. You need to standardize features, scale the loading vectors sensibly, and label axes with explained variance.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler

rng = np.random.default_rng(7)
X = rng.normal(size=(60, 5))
X[:, 0] += np.linspace(-2, 2, 60)
X[:, 1] += X[:, 0] * 0.7

X_scaled = StandardScaler().fit_transform(X)
pca = PCA(n_components=2)
scores = pca.fit_transform(X_scaled)
loadings = pca.components_.T

fig, ax = plt.subplots(figsize=(7, 6))
ax.scatter(scores[:, 0], scores[:, 1], alpha=0.75)

for i, (lx, ly) in enumerate(loadings):
    ax.arrow(0, 0, lx * 2.5, ly * 2.5, head_width=0.08, color="crimson")
    ax.text(lx * 2.7, ly * 2.7, f"V{i+1}", color="crimson")

ax.axhline(0, color="gray", lw=0.8)
ax.axvline(0, color="gray", lw=0.8)
ax.set_xlabel(f"PC1 ({pca.explained_variance_ratio_[0]:.1%})")
ax.set_ylabel(f"PC2 ({pca.explained_variance_ratio_[1]:.1%})")
ax.set_title("PCA Biplot")
plt.tight_layout()

Common mistakes

• Skipping standardization when variables use different units.
• Using too many loadings arrows so the figure becomes unreadable.
• Forcing interpretation from weak PCs that explain very little variance.
• Not explaining whether the arrows represent correlations or raw loadings.