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: plotnine 0.15.4 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-29
"""
import os
import numpy as np
import pandas as pd
from plotnine import (
aes,
element_blank,
element_line,
element_rect,
element_text,
geom_col,
geom_hline,
geom_line,
geom_point,
geom_segment,
geom_text,
ggplot,
labs,
scale_x_continuous,
scale_y_continuous,
theme,
theme_minimal,
)
from sklearn.datasets import load_wine
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
# Theme tokens — Imprint palette, theme-adaptive chrome
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint palette
BRAND = "#009E73" # Imprint position 1 — ALWAYS first series
IMPRINT_RED = "#AE3030" # Imprint matte red — semantic anchor for elbow emphasis
# Data — PCA on the Wine dataset (13 features)
X_scaled = StandardScaler().fit_transform(load_wine().data)
pca = PCA().fit(X_scaled)
n_components = np.arange(1, len(pca.explained_variance_ratio_) + 1)
cumulative_var = np.cumsum(pca.explained_variance_ratio_) * 100
individual_var = pca.explained_variance_ratio_ * 100
df = pd.DataFrame({"component": n_components, "cumulative": cumulative_var, "individual": individual_var})
# Elbow detection via maximum second-derivative change
diffs = np.diff(cumulative_var)
elbow_idx = int(np.argmax(np.abs(np.diff(diffs)))) + 1
elbow_c = int(n_components[elbow_idx])
elbow_v = cumulative_var[elbow_idx]
elbow_df = pd.DataFrame(
{"component": [elbow_c], "cumulative": [elbow_v], "label": [f"Elbow: {elbow_c} components\n({elbow_v:.1f}%)"]}
)
# Threshold reference lines
thresholds = pd.DataFrame({"y": [90.0, 95.0, 99.0], "label": ["90%", "95%", "99%"], "x": [12.5, 12.5, 12.5]})
# Title fontsize — scaled by length per plot-generator.md formula
title_str = "line-pca-variance-cumulative · python · plotnine · anyplot.ai"
n = len(title_str)
ratio = 67 / n if n > 67 else 1.0
title_fontsize = max(8, round(12 * ratio))
# Plot
plot = (
ggplot(df, aes(x="component", y="cumulative"))
# Threshold dashed reference lines (structural chrome — INK_SOFT)
+ geom_hline(yintercept=90.0, linetype="dashed", color=INK_SOFT, size=0.5, alpha=0.6)
+ geom_hline(yintercept=95.0, linetype="dashed", color=INK_SOFT, size=0.5, alpha=0.6)
+ geom_hline(yintercept=99.0, linetype="dashed", color=INK_SOFT, size=0.5, alpha=0.6)
# Individual variance as translucent bars — contextual background layer
+ geom_col(aes(y="individual"), fill=BRAND, width=0.5, alpha=0.15, show_legend=False)
# Vertical drop-line from elbow to x-axis
+ geom_segment(
data=elbow_df,
mapping=aes(x="component", xend="component", y=0, yend="cumulative"),
linetype="dotted",
color=IMPRINT_RED,
size=0.6,
alpha=0.6,
)
# Main cumulative variance line
+ geom_line(color=BRAND, size=1.0)
# Data point markers — PAGE_BG fill for theme-adaptive white circles
+ geom_point(color=BRAND, size=2.5, fill=PAGE_BG, stroke=1.2, shape="o")
# Highlighted elbow point
+ geom_point(
data=elbow_df,
mapping=aes(x="component", y="cumulative"),
color=IMPRINT_RED,
size=5.0,
fill=IMPRINT_RED,
stroke=1.5,
shape="o",
alpha=0.9,
)
# Elbow annotation
+ geom_text(
data=elbow_df,
mapping=aes(x="component", y="cumulative", label="label"),
ha="left",
va="bottom",
size=3.0,
color=IMPRINT_RED,
fontweight="bold",
nudge_x=0.4,
nudge_y=2.5,
)
# Threshold labels
+ geom_text(
data=thresholds,
mapping=aes(x="x", y="y", label="label"),
ha="right",
va="bottom",
size=2.5,
color=INK_MUTED,
nudge_y=0.5,
)
# Scales
+ scale_x_continuous(breaks=n_components, labels=[str(i) for i in n_components], expand=(0.02, 0.4))
+ scale_y_continuous(
limits=(0, 102), breaks=[0, 20, 40, 60, 80, 100], labels=["0%", "20%", "40%", "60%", "80%", "100%"]
)
+ labs(x="Number of Principal Components", y="Cumulative Explained Variance (%)", title=title_str)
+ theme_minimal()
+ theme(
figure_size=(8, 4.5),
text=element_text(size=7, color=INK_SOFT),
axis_title=element_text(size=10, color=INK),
axis_text=element_text(size=8, color=INK_SOFT),
plot_title=element_text(size=title_fontsize, color=INK, ha="left"),
panel_grid_major_x=element_blank(),
panel_grid_minor=element_blank(),
panel_grid_major_y=element_line(color=INK, size=0.3, alpha=0.12),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
panel_border=element_rect(color=INK_SOFT, fill=None),
axis_line_x=element_line(color=INK_SOFT, size=0.4),
axis_ticks_major_x=element_line(color=INK_SOFT, size=0.3),
plot_margin=0.02,
)
)
# Save
plot.save(f"plot-{THEME}.png", dpi=400, width=8, height=4.5, units="in", verbose=False)
Part of Cumulative Explained Variance for PCA Component Selection on anyplot.ai.