A line plot showing the cumulative proportion of explained variance as a function of the number of Principal Component Analysis (PCA) components. This visualization helps determine the optimal number of components to retain by displaying the trade-off between dimensionality reduction and information preservation. The cumulative curve typically exhibits an elbow pattern where additional components yield diminishing returns, and horizontal threshold lines (e.g., 90%, 95%) guide component selection decisions.
""" anyplot.ai
line-pca-variance-cumulative: Cumulative Explained Variance for PCA Component Selection
Library: plotly 6.7.0 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-29
"""
import sys
sys.path = sys.path[1:] # prevent this file from shadowing the installed plotly package
import os
import numpy as np
import plotly.graph_objects as go
from sklearn.datasets import load_wine
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
# Theme tokens — Imprint palette chrome
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(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
# Imprint categorical palette — data colors are theme-independent
BRAND = "#009E73" # position 1 — cumulative variance line (always first series)
BAR_COLOR = "#4467A3" # position 3 — individual variance bars
ELBOW_COLOR = "#C475FD" # position 2 — elbow marker accent
AMBER = "#DDCC77" # semantic anchor — 90% warning threshold
RED = "#AE3030" # position 5 — 95% critical threshold
# Data — PCA on Wine dataset
wine = load_wine()
X_scaled = StandardScaler().fit_transform(wine.data)
pca = PCA().fit(X_scaled)
explained_variance = pca.explained_variance_ratio_
cumulative_variance = np.cumsum(explained_variance) * 100
n_components = np.arange(1, len(explained_variance) + 1)
# Threshold crossings
threshold_90_idx = int(np.argmax(cumulative_variance >= 90))
threshold_95_idx = int(np.argmax(cumulative_variance >= 95))
threshold_90_comp = threshold_90_idx + 1
threshold_95_comp = threshold_95_idx + 1
# Elbow: first component where marginal gain drops below mean gain
individual_pct = explained_variance * 100
elbow_idx = int(np.argmax(individual_pct < individual_pct.mean()))
elbow_comp = elbow_idx + 1
elbow_var = float(cumulative_variance[elbow_idx])
title = "line-pca-variance-cumulative · python · plotly · anyplot.ai"
# Plot
fig = go.Figure()
# Individual variance bars (secondary context)
bar_fill = "rgba(68,103,163,0.30)"
bar_edge = "rgba(68,103,163,0.55)"
fig.add_trace(
go.Bar(
x=n_components,
y=explained_variance * 100,
marker={"color": bar_fill, "line": {"width": 1, "color": bar_edge}},
name="Individual variance",
hovertemplate="PC%{x}<br>Individual: %{y:.1f}%<extra></extra>",
)
)
# Cumulative variance line — primary series (Imprint position 1)
fig.add_trace(
go.Scatter(
x=n_components,
y=cumulative_variance,
mode="lines+markers",
line={"color": BRAND, "width": 4, "shape": "spline"},
marker={"size": 12, "color": BRAND, "line": {"width": 2, "color": PAGE_BG}},
name="Cumulative variance",
hovertemplate="PC%{x}<br>Cumulative: %{y:.1f}%<extra></extra>",
)
)
# Dummy traces so threshold lines appear in the legend
fig.add_trace(
go.Scatter(
x=[None], y=[None], mode="lines", line={"color": AMBER, "width": 2.5, "dash": "dash"}, name="90% threshold"
)
)
fig.add_trace(
go.Scatter(
x=[None], y=[None], mode="lines", line={"color": RED, "width": 2.5, "dash": "dash"}, name="95% threshold"
)
)
# Horizontal threshold lines — placed on opposite sides to avoid label crowding
fig.add_hline(
y=90,
line_dash="dash",
line_color=AMBER,
line_width=2.5,
annotation_text="90%",
annotation_position="top right",
annotation_font={"size": 14, "color": AMBER},
)
fig.add_hline(
y=95,
line_dash="dash",
line_color=RED,
line_width=2.5,
annotation_text="95%",
annotation_position="top left",
annotation_font={"size": 14, "color": RED},
)
# Vertical drop lines from threshold crossings to x-axis
fig.add_shape(
type="line",
x0=threshold_90_comp,
x1=threshold_90_comp,
y0=0,
y1=90,
line={"color": AMBER, "width": 1.5, "dash": "dot"},
)
fig.add_shape(
type="line",
x0=threshold_95_comp,
x1=threshold_95_comp,
y0=0,
y1=95,
line={"color": RED, "width": 1.5, "dash": "dot"},
)
# Elbow marker — diamond outline for visual distinction
fig.add_trace(
go.Scatter(
x=[elbow_comp],
y=[elbow_var],
mode="markers",
marker={"size": 22, "color": ELEVATED_BG, "line": {"width": 3, "color": ELBOW_COLOR}, "symbol": "diamond"},
showlegend=False,
hovertemplate=f"Elbow: PC{elbow_comp}<br>Cumulative: {elbow_var:.1f}%<extra></extra>",
)
)
# Elbow annotation with arrow
fig.add_annotation(
x=elbow_comp,
y=elbow_var,
text=f"<b>Elbow</b> — PC{elbow_comp}<br>{elbow_var:.0f}% variance",
showarrow=True,
arrowhead=2,
arrowsize=1.4,
arrowwidth=1.8,
arrowcolor=ELBOW_COLOR,
ax=-65,
ay=-55,
font={"size": 12, "color": ELBOW_COLOR},
bgcolor=ELEVATED_BG,
bordercolor=ELBOW_COLOR,
borderwidth=1.5,
borderpad=5,
)
# Layout
fig.update_layout(
autosize=False,
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
title={"text": title, "font": {"size": 16, "color": INK}, "x": 0.5, "xanchor": "center"},
xaxis={
"title": {"text": "Principal Component", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"tickmode": "linear",
"tick0": 1,
"dtick": 1,
"showgrid": False,
"zeroline": False,
"showline": True,
"linewidth": 1,
"linecolor": INK_SOFT,
},
yaxis={
"title": {"text": "Explained Variance (%)", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"range": [0, 105],
"showgrid": True,
"gridwidth": 1,
"gridcolor": GRID,
"zeroline": False,
"showline": True,
"linewidth": 1,
"linecolor": INK_SOFT,
},
legend={
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
"font": {"size": 10, "color": INK_SOFT},
"x": 0.02,
"y": 0.40,
},
font={"color": INK},
margin={"t": 80, "b": 60, "l": 80, "r": 40},
bargap=0.4,
)
# Save
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Cumulative Explained Variance for PCA Component Selection on anyplot.ai.