feat(seaborn): implement elbow-curve (#2351)

## Implementation: `elbow-curve` - seaborn

Implements the **seaborn** version of `elbow-curve`.

**File:** `plots/elbow-curve/implementations/seaborn.py`

---
:robot: *[impl-generate
workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/20528202504)*

---------

Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

Author: github-actions[bot]

plots/elbow-curve/implementations/seaborn.py

@@ -0,0 +1,80 @@
+""" pyplots.ai
+elbow-curve: Elbow Curve for K-Means Clustering
+Library: seaborn 0.13.2 | Python 3.13.11
+Quality: 91/100 | Created: 2025-12-26
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+import seaborn as sns
+
+
+# Set seaborn style
+sns.set_style("whitegrid")
+
+# Simulate realistic elbow curve data
+# Inertia decreases with more clusters, with an "elbow" at k=4
+np.random.seed(42)
+k_values = list(range(1, 11))
+
+# Realistic inertia values showing typical elbow pattern
+# High inertia at k=1, sharp decrease until k=4, then diminishing returns
+inertias = [
+    2800,  # k=1
+    1650,  # k=2
+    950,  # k=3
+    520,  # k=4 - elbow point
+    450,  # k=5
+    400,  # k=6
+    365,  # k=7
+    340,  # k=8
+    320,  # k=9
+    305,  # k=10
+]
+
+# Add small noise for realism
+noise = np.random.uniform(-10, 10, len(inertias))
+inertias = [max(0, i + n) for i, n in zip(inertias, noise, strict=True)]
+
+# Create figure
+fig, ax = plt.subplots(figsize=(16, 9))
+
+# Plot the elbow curve using seaborn lineplot
+sns.lineplot(
+    x=k_values,
+    y=inertias,
+    ax=ax,
+    color="#306998",
+    linewidth=3,
+    marker="o",
+    markersize=15,
+    markerfacecolor="#FFD43B",
+    markeredgecolor="#306998",
+    markeredgewidth=2,
+)
+
+# Annotate the elbow point (k=4)
+elbow_k = 4
+elbow_inertia = inertias[elbow_k - 1]
+ax.annotate(
+    f"Elbow Point (k={elbow_k})",
+    xy=(elbow_k, elbow_inertia),
+    xytext=(elbow_k + 2, elbow_inertia + 400),
+    fontsize=18,
+    arrowprops={"arrowstyle": "->", "color": "#306998", "lw": 2},
+    color="#306998",
+    fontweight="bold",
+)
+
+# Labels and styling
+ax.set_xlabel("Number of Clusters (k)", fontsize=20)
+ax.set_ylabel("Inertia (Within-Cluster Sum of Squares)", fontsize=20)
+ax.set_title("elbow-curve · seaborn · pyplots.ai", fontsize=24)
+ax.tick_params(axis="both", labelsize=16)
+ax.set_xticks(k_values)
+
+# Subtle grid
+ax.grid(True, alpha=0.3, linestyle="--")
+
+plt.tight_layout()
+plt.savefig("plot.png", dpi=300, bbox_inches="tight")

plots/elbow-curve/metadata/seaborn.yaml

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+library: seaborn
+specification_id: elbow-curve
+created: '2025-12-26T19:36:40Z'
+updated: '2025-12-26T19:42:53Z'
+generated_by: claude-opus-4-5-20251101
+workflow_run: 20528202504
+issue: 0
+python_version: 3.13.11
+library_version: 0.13.2
+preview_url: https://storage.googleapis.com/pyplots-images/plots/elbow-curve/seaborn/plot.png
+preview_thumb: https://storage.googleapis.com/pyplots-images/plots/elbow-curve/seaborn/plot_thumb.png
+preview_html: null
+quality_score: 91
+review:
+  strengths:
+  - Clear elbow point annotation with arrow makes the key insight immediately visible
+  - Excellent color scheme with Python-themed blue (#306998) and yellow (#FFD43B)
+    markers
+  - Proper font sizing throughout (24pt title, 20pt labels, 16pt ticks)
+  - Realistic inertia values showing typical K-means clustering behavior
+  - Well-structured KISS code following project guidelines
+  weaknesses:
+  - Uses sns.lineplot which is basic; could leverage seaborn statistical features
+    more distinctively
+  - Y-axis label could include units in parentheses format even if unitless (e.g.,
+    Inertia (WCSS))