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: pygal 3.1.0 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-29
"""
import os
import numpy as np
import pygal
from pygal.style import Style
# 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 = (
"#009E73", # brand green — always first series
"#C475FD", # lavender
"#4467A3", # blue
"#BD8233", # ochre
"#AE3030",
"#2ABCCD",
"#954477",
"#99B314",
)
# Data — realistic PCA variance ratios for a 13-feature Wine-like dataset
eigenvalues = np.array([4.73, 2.51, 1.45, 0.92, 0.85, 0.64, 0.55, 0.35, 0.29, 0.21, 0.17, 0.13, 0.08])
explained_variance_ratio = eigenvalues / eigenvalues.sum()
individual_variance = explained_variance_ratio * 100
cumulative_variance = np.cumsum(explained_variance_ratio) * 100
n_components = len(cumulative_variance)
component_labels = [str(i) for i in range(1, n_components + 1)]
# Detect elbow: where slope drops below 35% of the initial slope
slopes = np.diff(cumulative_variance)
elbow_idx = int(np.argmax(slopes < slopes[0] * 0.35))
# Threshold crossings
cross_90 = int(np.searchsorted(cumulative_variance, 90))
cross_95 = int(np.searchsorted(cumulative_variance, 95))
# Style — Imprint palette, theme-adaptive tokens, 3200×1800 canvas sizing
custom_style = Style(
background=PAGE_BG,
plot_background=PAGE_BG,
foreground=INK,
foreground_strong=INK,
foreground_subtle=INK_SOFT, # INK_SOFT (not INK_MUTED) for legible tick labels against green fill
colors=IMPRINT_PALETTE,
opacity=0.38, # semi-transparent fill so y-axis labels remain legible beneath the green area
opacity_hover=1.0,
stroke_opacity=1.0,
stroke_opacity_hover=1.0,
stroke_width=2.5,
dot_opacity=1.0,
guide_stroke_color=INK_MUTED,
guide_stroke_dasharray="2,12", # longer gap — guides recede behind data
major_guide_stroke_color=INK_SOFT,
major_guide_stroke_dasharray="8,12", # longer gap for major guides at 90%/95%
title_font_size=66,
label_font_size=56,
major_label_font_size=44,
legend_font_size=44,
value_font_size=36,
tooltip_font_size=34,
font_family="Helvetica, Arial, sans-serif",
title_font_family="Helvetica, Arial, sans-serif",
label_font_family="Helvetica, Arial, sans-serif",
legend_font_family="Helvetica, Arial, sans-serif",
value_font_family="Helvetica, Arial, sans-serif",
major_label_font_family="Helvetica, Arial, sans-serif",
transition="200ms",
)
# Chart
chart = pygal.Line(
width=3200,
height=1800,
title="line-pca-variance-cumulative · python · pygal · anyplot.ai",
x_title="Number of Components",
y_title="Cumulative Explained Variance (%)",
style=custom_style,
show_dots=True,
dots_size=10,
show_only_major_dots=False,
show_y_guides=True,
show_x_guides=False,
legend_at_bottom=True,
legend_at_bottom_columns=4,
legend_box_size=26,
truncate_legend=-1,
range=(0, 105),
secondary_range=(0, 55), # individual variance secondary axis; wider margin ensures labels are visible
margin=30,
margin_bottom=90,
margin_left=220, # wider left margin so y-axis labels sit clearly outside the green fill
margin_right=220, # wider right margin for secondary-axis tick labels on right side
margin_top=40,
print_values=True,
print_values_position="top",
value_formatter=lambda x: "",
spacing=20,
show_minor_x_labels=True,
tooltip_fancy_mode=True,
tooltip_border_radius=10,
interpolate="cubic",
interpolation_precision=200,
human_readable=False,
no_data_text="No variance data",
)
# Axes — custom y-tick positions highlight the decision thresholds
chart.x_labels = component_labels
# Mark the three decision-point components as major x-labels (bold, guided)
chart.x_labels_major = [str(elbow_idx + 1), str(cross_90 + 1), str(cross_95 + 1)]
chart.y_labels = [0, 20, 40, 60, 80, 90, 95, 100]
chart.y_labels_major = [90, 95] # major guide lines drawn at the two decision thresholds
# Annotations at key decision points
annotations = {
elbow_idx: lambda x: f"Elbow: n={elbow_idx + 1} ({x:.0f}%)",
cross_90: lambda x: f"90%: n={cross_90 + 1}",
cross_95: lambda x: f"95%: n={cross_95 + 1}",
}
# Cumulative variance — brand green filled area, thick primary stroke for visual hierarchy
cumulative_values = [
{"value": round(v, 1), "label": f"PC{i + 1}", "formatter": annotations.get(i, lambda x: "")}
for i, v in enumerate(cumulative_variance)
]
chart.add(
"Cumulative Variance",
cumulative_values,
stroke_style={"width": 10, "linecap": "round", "linejoin": "round"},
fill=True,
)
# 90% threshold — lavender dashed, thinner to reinforce secondary role
chart.add(
"90% Threshold",
[{"value": 90, "label": "90% variance threshold", "formatter": lambda x: ""} for _ in range(n_components)],
show_dots=False,
fill=False,
stroke_style={"width": 3, "dasharray": "22, 12", "linecap": "round"},
)
# 95% threshold — blue dotted, thinner for visual hierarchy
chart.add(
"95% Threshold",
[{"value": 95, "label": "95% variance threshold", "formatter": lambda x: ""} for _ in range(n_components)],
show_dots=False,
fill=False,
stroke_style={"width": 3, "dasharray": "8, 10", "linecap": "round"},
)
# Individual variance on secondary Y-axis — ochre with larger dots for salience
# Per-point formatters serve as secondary-axis labels for components with meaningful variance
individual_values = [
{"value": round(v, 1), "label": f"PC{i + 1}: {v:.1f}%", "formatter": lambda x: f"{x:.1f}%" if x > 3 else ""}
for i, v in enumerate(individual_variance)
]
chart.add(
"Individual Variance (%)",
individual_values,
secondary=True,
stroke_style={"width": 8, "linecap": "round", "linejoin": "round"},
show_dots=True,
dots_size=11,
fill=False,
)
# Save PNG and interactive HTML
chart.render_to_png(f"plot-{THEME}.png")
with open(f"plot-{THEME}.html", "wb") as f:
f.write(chart.render())
Part of Cumulative Explained Variance for PCA Component Selection on anyplot.ai.