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feat(pygal): implement biplot-pca (#3474)
## Implementation: `biplot-pca` - pygal Implements the **pygal** version of `biplot-pca`. **File:** `plots/biplot-pca/implementations/pygal.py` **Parent Issue:** #3417 --- :robot: *[impl-generate workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/20853044084)* --------- Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com> Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
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‎plots/biplot-pca/implementations/pygal.py‎

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""" pyplots.ai
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biplot-pca: PCA Biplot with Scores and Loading Vectors
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Library: pygal 3.1.0 | Python 3.13.11
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Quality: 82/100 | Created: 2026-01-09
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"""
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import math
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import pygal
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from pygal.style import Style
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from sklearn.datasets import load_iris
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from sklearn.decomposition import PCA
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from sklearn.preprocessing import StandardScaler
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# Load and prepare data
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iris = load_iris()
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X = iris.data
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y = iris.target
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feature_names = iris.feature_names
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target_names = iris.target_names
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# Standardize features
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X_scaled = StandardScaler().fit_transform(X)
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# Perform PCA
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pca = PCA(n_components=2)
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scores = pca.fit_transform(X_scaled)
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loadings = pca.components_.T # Shape: (n_features, n_components)
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variance_explained = pca.explained_variance_ratio_ * 100
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# Use correlation biplot scaling
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score_range = max(scores[:, 0].max() - scores[:, 0].min(), scores[:, 1].max() - scores[:, 1].min())
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loading_scale = score_range * 0.4
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unit_circle_radius = loading_scale
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# Custom style for 4800x2700 px canvas
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species_colors = ["#306998", "#FFD43B", "#2ECC71"] # Blue, Yellow, Green for species
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unit_circle_color = "#AAAAAA" # Gray for unit circle reference
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# Distinct colors for each loading vector (colorblind-friendly)
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loading_colors = ["#E41A1C", "#984EA3", "#FF7F00", "#377EB8"] # Red, Purple, Orange, Blue
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custom_style = Style(
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background="white",
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plot_background="white",
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foreground="#333333",
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foreground_strong="#333333",
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foreground_subtle="#666666",
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colors=tuple(species_colors + [unit_circle_color] + loading_colors),
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title_font_size=72,
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label_font_size=48,
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major_label_font_size=42,
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legend_font_size=42,
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tooltip_font_size=36,
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stroke_width=4,
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opacity=0.85,
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opacity_hover=0.95,
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)
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# Create XY chart for biplot
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chart = pygal.XY(
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width=4800,
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height=2700,
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style=custom_style,
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title="biplot-pca · pygal · pyplots.ai",
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x_title=f"PC1 ({variance_explained[0]:.1f}%)",
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y_title=f"PC2 ({variance_explained[1]:.1f}%)",
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show_legend=True,
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legend_at_bottom=True,
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legend_box_size=36,
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dots_size=14,
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stroke=False,
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show_x_guides=True,
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show_y_guides=True,
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truncate_legend=50,
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explicit_size=True,
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)
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# Add score points for each species (class)
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for i, name in enumerate(target_names):
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mask = y == i
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points = [(float(scores[j, 0]), float(scores[j, 1])) for j in range(len(y)) if mask[j]]
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chart.add(name.capitalize(), points, stroke=False, dots_size=14)
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# Create unit circle for loading magnitude reference
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circle_points = []
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for angle in range(0, 361, 3):
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rad = math.radians(angle)
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circle_points.append((unit_circle_radius * math.cos(rad), unit_circle_radius * math.sin(rad)))
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chart.add("Unit Circle", circle_points, stroke=True, show_dots=False, stroke_style={"width": 3, "dasharray": "10,8"})
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# Full feature names for legend clarity
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full_names = ["Sepal Length", "Sepal Width", "Petal Length", "Petal Width"]
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# Add each loading vector as line arrow with arrowhead
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for i, full_name in enumerate(full_names):
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tip_x = float(loadings[i, 0] * loading_scale)
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tip_y = float(loadings[i, 1] * loading_scale)
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# Calculate arrow geometry for line-style arrow
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dx, dy = tip_x, tip_y
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length = math.sqrt(dx * dx + dy * dy)
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ux = dx / length if length > 0 else 0
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uy = dy / length if length > 0 else 0
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px, py = -uy, ux # Perpendicular vector
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# Smaller arrowhead for cleaner line appearance
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head_len = 0.08 * loading_scale
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head_wid = 0.04 * loading_scale
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hb_x = tip_x - ux * head_len
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hb_y = tip_y - uy * head_len
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# Line arrow: origin to tip with small arrowhead triangle
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arrow_line = [
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(0.0, 0.0),
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(tip_x, tip_y),
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(hb_x + px * head_wid, hb_y + py * head_wid),
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(tip_x, tip_y),
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(hb_x - px * head_wid, hb_y - py * head_wid),
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(tip_x, tip_y),
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]
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chart.add(full_name, arrow_line, stroke=True, show_dots=False, fill=False, stroke_style={"width": 5})
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# Save PNG output only
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chart.render_to_png("plot.png")

‎plots/biplot-pca/metadata/pygal.yaml‎

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library: pygal
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specification_id: biplot-pca
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created: '2026-01-09T13:18:36Z'
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updated: '2026-01-09T13:44:46Z'
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generated_by: claude-opus-4-5-20251101
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workflow_run: 20853044084
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issue: 3417
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python_version: 3.13.11
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library_version: 3.1.0
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preview_url: https://storage.googleapis.com/pyplots-images/plots/biplot-pca/pygal/plot.png
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preview_thumb: https://storage.googleapis.com/pyplots-images/plots/biplot-pca/pygal/plot_thumb.png
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preview_html: https://storage.googleapis.com/pyplots-images/plots/biplot-pca/pygal/plot.html
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quality_score: 82
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review:
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strengths:
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- Excellent use of the Iris dataset providing realistic, interpretable context
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- 'Correct variance explained percentages on axis labels (PC1: 73.0%, PC2: 22.9%)'
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- Colorblind-friendly palette distinguishes species and loading vectors effectively
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- Unit circle provides appropriate reference for loading magnitudes
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- Good canvas utilization and overall layout
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weaknesses:
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- Loading vectors rendered as thick filled shapes that obscure underlying data points
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- should be thin line arrows
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- Legend labels are truncated (Sepal L., Petal W.) despite full names defined in
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code
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- Arrow rendering creates visual clutter near the origin where all four vectors
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originate
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- No explicit random seed (though dataset is deterministic)
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image_description: 'The plot displays a PCA biplot of the Iris dataset on a 4800x2700
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white canvas. Three species are shown as scatter points: Setosa (blue, clustered
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on the left), Versicolor (yellow, in the middle), and Virginica (green, on the
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right). A dashed red/pink unit circle is centered at the origin for loading magnitude
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reference. Four loading vectors are rendered as large filled arrow shapes originating
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from the origin: Sepal Width (purple, pointing upward), Sepal Length (brown/red,
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pointing upper-right), Petal Length (orange, pointing right), and Petal Width
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(teal, pointing right). The axis labels correctly show "PC1 (73.0%)" and "PC2
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(22.9%)". The title "biplot-pca · pygal · pyplots.ai" appears at the top. A legend
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appears in the top-left corner showing all series with abbreviated labels.'
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criteria_checklist:
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visual_quality:
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score: 32
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max: 40
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items:
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- id: VQ-01
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name: Text Legibility
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score: 9
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max: 10
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passed: true
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comment: Title and axis labels are clearly readable at full size; tick labels
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are appropriately sized
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- id: VQ-02
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name: No Overlap
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score: 6
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max: 8
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passed: true
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comment: The thick filled arrow shapes overlap with each other near the origin
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and partially obscure data points
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- id: VQ-03
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name: Element Visibility
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score: 6
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max: 8
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passed: true
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comment: Scatter points are visible but the loading arrows are excessively
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thick and filled, obscuring some data
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- id: VQ-04
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name: Color Accessibility
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score: 5
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max: 5
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passed: true
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comment: Good colorblind-safe palette with blue, yellow, green for species
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and distinct colors for loadings
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- id: VQ-05
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name: Layout Balance
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score: 4
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max: 5
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passed: true
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comment: Good use of canvas space; legend positioning is reasonable but slightly
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crowds the top-left
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- id: VQ-06
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name: Axis Labels
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score: 2
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max: 2
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passed: true
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comment: 'Descriptive labels with variance percentages: PC1 (73.0%) and PC2
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(22.9%)'
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- id: VQ-07
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name: Grid & Legend
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score: 0
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max: 2
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passed: false
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comment: Legend uses abbreviated labels (Sepal L.) instead of full names;
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too many legend entries
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spec_compliance:
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score: 23
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max: 25
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items:
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- id: SC-01
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name: Plot Type
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score: 8
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max: 8
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passed: true
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comment: Correct PCA biplot showing scores and loadings
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- id: SC-02
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name: Data Mapping
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score: 5
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max: 5
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passed: true
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comment: PC1 on X-axis, PC2 on Y-axis, correct mapping
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- id: SC-03
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name: Required Features
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score: 4
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max: 5
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passed: true
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comment: Has scores, loadings, unit circle, variance labels; loading labels
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are truncated
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- id: SC-04
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name: Data Range
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score: 3
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max: 3
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passed: true
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comment: All data points visible within axes
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- id: SC-05
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name: Legend Accuracy
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score: 2
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max: 2
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passed: true
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comment: Legend entries correctly identify species and loading vectors
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- id: SC-06
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name: Title Format
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score: 1
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max: 2
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passed: true
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comment: Title format is correct but uses hyphen instead of middle dot separator
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data_quality:
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score: 18
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max: 20
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items:
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- id: DQ-01
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name: Feature Coverage
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score: 7
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max: 8
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passed: true
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comment: Shows clear separation of species along PC1; all loading directions
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visible
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- id: DQ-02
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name: Realistic Context
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score: 7
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max: 7
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passed: true
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comment: Uses the classic Iris dataset, a real and widely understood scenario
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- id: DQ-03
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name: Appropriate Scale
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score: 4
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max: 5
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passed: true
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comment: Standardized PCA scores with appropriate scaling; unit circle provides
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good reference
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code_quality:
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score: 6
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max: 10
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items:
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- id: CQ-01
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name: KISS Structure
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score: 3
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max: 3
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passed: true
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comment: 'Linear flow: imports, data, PCA, chart setup, rendering'
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- id: CQ-02
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name: Reproducibility
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score: 0
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max: 3
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passed: false
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comment: No random seed set; uses deterministic dataset but no explicit seed
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- id: CQ-03
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name: Clean Imports
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score: 2
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max: 2
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passed: true
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comment: All imports are used
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- id: CQ-04
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name: No Deprecated API
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score: 1
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max: 1
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passed: true
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comment: Current API usage
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- id: CQ-05
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name: Output Correct
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score: 0
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max: 1
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passed: false
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comment: Saves as plot.png correctly
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library_features:
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score: 3
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max: 5
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items:
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- id: LF-01
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name: Distinctive Features
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score: 3
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max: 5
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passed: true
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comment: Uses XY chart, custom Style, dashed stroke for unit circle, legend_at_bottom
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- demonstrates pygal capabilities but arrows are not rendered elegantly
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verdict: APPROVED
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impl_tags:
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dependencies:
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- sklearn
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techniques:
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- annotations
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- layer-composition
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patterns:
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- dataset-loading
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- iteration-over-groups
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dataprep:
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- pca
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- normalization
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styling:
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- alpha-blending

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