PCA Biplot with Scores and Loading Vectors — Plotly

A PCA biplot simultaneously displays both observation scores (as points) and variable loadings (as arrows) in the principal component space. This dual representation is essential for interpreting PCA results, revealing how observations relate to each other and which original variables drive the separation along each principal component. The length and direction of loading arrows indicate variable importance and correlation with the components.

PCA Biplot with Scores and Loading Vectors rendered with Plotly

Python source (Plotly)

""" anyplot.ai
biplot-pca: PCA Biplot with Scores and Loading Vectors
Library: plotly 6.7.0 | Python 3.13.13
Quality: 86/100 | Updated: 2026-05-17
"""

import os

import numpy as np
import plotly.graph_objects as go
from sklearn.datasets import load_iris
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler


# Theme tokens
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"
GRID = "rgba(26,26,23,0.10)" if THEME == "light" else "rgba(240,239,232,0.10)"

# Okabe-Ito palette (first series is always #009E73)
IMPRINT = ["#009E73", "#C475FD", "#4467A3"]

# Load data
iris = load_iris()
X = iris.data
y = iris.target
feature_names = iris.feature_names
target_names = iris.target_names

# Standardize and perform PCA
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
pca = PCA(n_components=2)
scores = pca.fit_transform(X_scaled)
loadings = pca.components_.T * np.sqrt(pca.explained_variance_)

# Variance explained
var_explained = pca.explained_variance_ratio_ * 100

# Create figure
fig = go.Figure()

# Plot scores for each group
for i, target in enumerate(target_names):
    mask = y == i
    fig.add_trace(
        go.Scatter(
            x=scores[mask, 0],
            y=scores[mask, 1],
            mode="markers",
            marker={"size": 14, "color": IMPRINT[i], "opacity": 0.8, "line": {"width": 1, "color": PAGE_BG}},
            name=target.capitalize(),
            legendgroup=target,
        )
    )

# Scale loadings for visibility (relative to score spread)
score_scale = max(np.abs(scores).max(axis=0))
loading_scale = max(np.abs(loadings).max(axis=0))
scale_factor = score_scale / loading_scale * 0.9

# Plot loading arrows
arrow_color = INK_SOFT
for loading, name in zip(loadings, feature_names, strict=False):
    x_end = loading[0] * scale_factor
    y_end = loading[1] * scale_factor

    # Arrow line
    fig.add_trace(
        go.Scatter(
            x=[0, x_end],
            y=[0, y_end],
            mode="lines",
            line={"color": arrow_color, "width": 3},
            showlegend=False,
            hoverinfo="skip",
        )
    )

    # Arrowhead using annotation
    fig.add_annotation(
        x=x_end,
        y=y_end,
        ax=0,
        ay=0,
        xref="x",
        yref="y",
        axref="x",
        ayref="y",
        showarrow=True,
        arrowhead=2,
        arrowsize=1.5,
        arrowwidth=3,
        arrowcolor=arrow_color,
    )

    # Variable label with offset to avoid overlap
    label_offsets = {
        "sepal length": (0.15, 0.3),
        "sepal width": (0.1, 0.25),
        "petal length": (0.15, -0.35),
        "petal width": (0.15, 0.15),
    }
    clean_name = name.replace(" (cm)", "")
    dx, dy = label_offsets.get(clean_name, (0.1, 0.1))
    offset_x = x_end + dx
    offset_y = y_end + dy
    xanchor = "left" if x_end > 0 else "right"
    fig.add_annotation(
        x=offset_x,
        y=offset_y,
        text=clean_name,
        showarrow=False,
        font={"size": 16, "color": arrow_color},
        xanchor=xanchor,
        yanchor="middle",
    )

# Layout
fig.update_layout(
    title={
        "text": "biplot-pca · plotly · anyplot.ai",
        "font": {"size": 28, "color": INK},
        "x": 0.5,
        "xanchor": "center",
    },
    paper_bgcolor=PAGE_BG,
    plot_bgcolor=PAGE_BG,
    font={"color": INK},
    xaxis={
        "title": {"text": f"PC1 ({var_explained[0]:.1f}%)", "font": {"size": 22, "color": INK}},
        "tickfont": {"size": 18, "color": INK_SOFT},
        "zeroline": True,
        "zerolinewidth": 1,
        "zerolinecolor": arrow_color,
        "gridcolor": GRID,
        "gridwidth": 1,
        "linecolor": INK_SOFT,
    },
    yaxis={
        "title": {"text": f"PC2 ({var_explained[1]:.1f}%)", "font": {"size": 22, "color": INK}},
        "tickfont": {"size": 18, "color": INK_SOFT},
        "zeroline": True,
        "zerolinewidth": 1,
        "zerolinecolor": arrow_color,
        "gridcolor": GRID,
        "gridwidth": 1,
        "linecolor": INK_SOFT,
        "scaleanchor": "x",
        "scaleratio": 1,
    },
    legend={
        "font": {"size": 18, "color": INK_SOFT},
        "x": 0.02,
        "y": 0.98,
        "xanchor": "left",
        "yanchor": "top",
        "bgcolor": ELEVATED_BG,
        "bordercolor": INK_SOFT,
        "borderwidth": 1,
    },
    margin={"l": 80, "r": 80, "t": 100, "b": 80},
)

# Save outputs
fig.write_image(f"plot-{THEME}.png", width=1600, height=900, scale=3)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")

Part of PCA Biplot with Scores and Loading Vectors on anyplot.ai.

PCA Biplot with Scores and Loading Vectors — Plotly

Python source (Plotly)

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