spec: add elbow-curve specification

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New Specification: elbow-curve

Related to #2333

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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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