spec: add elbow-curve specification (#2335)

## New Specification: `elbow-curve`

Related to #2333

---

### specification.md

# elbow-curve: Elbow Curve for K-Means Clustering

## Description

An elbow curve visualizes the relationship between the number of
clusters (k) and within-cluster sum of squares (inertia/distortion) in
K-means clustering. The plot helps identify the optimal number of
clusters by finding the "elbow point" where adding more clusters yields
diminishing returns in reducing inertia. This is a fundamental
diagnostic tool for unsupervised learning parameter selection.

## Applications

- Selecting the optimal number of clusters (k) in K-means clustering
analysis
- Customer segmentation to determine natural groupings in behavioral
data
- Image compression parameter selection for color quantization
- Document clustering to identify topic groupings in text corpora

## Data

- `k_values` (numeric) - Number of clusters tested (typically 1 to 10 or
15)
- `inertia` (numeric) - Within-cluster sum of squares for each k value
- Size: 8-15 different k values for clear elbow visualization
- Example: Scikit-learn's `KMeans.inertia_` attribute across multiple k
values

## Notes

- X-axis shows number of clusters (k), y-axis shows inertia/distortion
- The elbow point is where the rate of decrease sharply changes
- Consider annotating or highlighting the optimal k value
- Use markers at each data point to show discrete k values tested
- A smooth connecting line helps visualize the curve shape

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plots/elbow-curve/specification.md

@@ -0,0 +1,27 @@
+# elbow-curve: Elbow Curve for K-Means Clustering
+
+## Description
+
+An elbow curve visualizes the relationship between the number of clusters (k) and within-cluster sum of squares (inertia/distortion) in K-means clustering. The plot helps identify the optimal number of clusters by finding the "elbow point" where adding more clusters yields diminishing returns in reducing inertia. This is a fundamental diagnostic tool for unsupervised learning parameter selection.
+
+## Applications
+
+- Selecting the optimal number of clusters (k) in K-means clustering analysis
+- Customer segmentation to determine natural groupings in behavioral data
+- Image compression parameter selection for color quantization
+- Document clustering to identify topic groupings in text corpora
+
+## Data
+
+- `k_values` (numeric) - Number of clusters tested (typically 1 to 10 or 15)
+- `inertia` (numeric) - Within-cluster sum of squares for each k value
+- Size: 8-15 different k values for clear elbow visualization
+- Example: Scikit-learn's `KMeans.inertia_` attribute across multiple k values
+
+## Notes
+
+- X-axis shows number of clusters (k), y-axis shows inertia/distortion
+- The elbow point is where the rate of decrease sharply changes
+- Consider annotating or highlighting the optimal k value
+- Use markers at each data point to show discrete k values tested
+- A smooth connecting line helps visualize the curve shape

plots/elbow-curve/specification.yaml

@@ -0,0 +1,30 @@
+# Specification-level metadata for elbow-curve
+# Auto-synced to PostgreSQL on push to main
+
+spec_id: elbow-curve
+title: Elbow Curve for K-Means Clustering
+
+# Specification tracking
+created: 2025-12-26T19:28:09Z
+updated: null
+issue: 2333
+suggested: MarkusNeusinger
+
+# Classification tags (applies to all library implementations)
+# See docs/concepts/tagging-system.md for detailed guidelines
+tags:
+  plot_type:
+    - line
+    - curve
+  data_type:
+    - numeric
+    - discrete
+  domain:
+    - general
+    - statistics
+    - machine-learning
+  features:
+    - basic
+    - clustering
+    - optimization
+    - diagnostic