Feature/adding elbow score

[Mahatav]

Summary

This PR adds elbow method analysis alongside the existing silhouette-based cluster selection to provide complementary validation metrics for K-means clustering decisions.

Changes

New Functionality:

• Added compute_elbow_scores() function to calculate within-cluster sum of squares (inertia) across the k-range
• Integrated the elbow score computation into the main clustering pipeline
• Exports elbow scores to CSV for both branching and PR datasets

Implementation Details:

• Computes inertia for k values from 2 to 10 (matching silhouette range)
• Reuses existing KMeans parameters (n_init=25, random_state=42) for consistency
• Processes both datasets in parallel within the existing loop
• Follows established naming convention: elbow_scores_{suffix}.csv

New Outputs

Per dataset, a new CSV is generated:

• data/outputs/branching/elbow_scores_branching.csv
• data/outputs/pr/elbow_scores_pr.csv

CSV Schema:

• k - Number of clusters tested (2 to 10)
• inertia - Within-cluster sum of squares (lower indicates tighter clusters)

Why This Matters:

The elbow method complements silhouette analysis by providing an alternative perspective on cluster quality:

• Silhouette: Measures cluster separation quality (higher = better distinct clusters)
• Elbow: Measures compactness via inertia (look for the "elbow point" where diminishing returns begin)

Researchers can now cross-validate clustering decisions using both metrics and identify cases where the methods agree or disagree about optimal k.

[AdaraPutri]

can we add a guard here? so that the elbow requires at least 3 teams (since k starts at 2, and k_max is currently capped to n-1 which would return an empty curve)

maybe something like this:

elbow_scores = None
if X.shape[0] >= 3:
    elbow_scores = compute_elbow_scores(X)
else:
    print("[INFO] Skipping elbow scores (need >= 3 teams).")

[AdaraPutri]

if compute_elbow_scores() returns an empty k list, this line is still writing an empty csv. can we add a check that elbow_scores["k"] is non empty else skip the csv production?

something like this:

if elbow_scores and elbow_scores["k"]:
    elbow_df = pd.DataFrame(elbow_scores)
    elbow_df.to_csv(elbow_fp, index=False)
    print(f"[OK] Wrote: {elbow_fp}")
else:
    print("[INFO] Skipping elbow CSV (no valid k range).")

[AdaraPutri]

hey Manu, great job with this PR! I’ve added two inline comments around small guard / edge-case handling. one additional thought: since the elbow score is mainly used to visually inspect the curve, could you also add a simple matplotlib visualization alongside the csv?

[Mahatav]

Hey, just made the changes!

[AdaraPutri]

thanks for adding the guard Manu, the edge cases are protected now. could you still add the matplotlib graphing? it would have the number of clusters as the x-axis and the inertia value as the y-axis. something that would look like this graph:

[AdaraPutri]

thanks for adding the plot Manu, it looks good now! approved.

[d2r3v]

Looks Good. Ready to merge.