Greedy matching evaluation

Greedy Matching for Clustering Evaluation

To evaluate clustering performance against ground truth (expert) points, we need to match predicted centroids to expert points.

Algorithm

1. Compute all pairwise standard Euclidean distances between predicted centroids and expert points.
2. Filter pairs with distance > max_dist (e.g., 100 pixels).
3. Sort remaining pairs by distance (closest first).
4. Iteratively pick the closest pair, ensuring each centroid and each expert point is matched at most once.

F1 Score Calculation

• True Positives (TP): Number of matched pairs.
• False Positives (FP): Number of unmatched predicted centroids.
• False Negatives (FN): Number of unmatched expert points.
• Precision = TP / (TP + FP)
• Recall = TP / (TP + FN)
• F1 = 2 * (Precision * Recall) / (Precision + Recall) (Handle division by zero)

Python Implementation

import numpy as np
from scipy.spatial.distance import cdist

def evaluate_clustering(centroids, experts, max_dist=100):
    if len(centroids) == 0:
        return 0.0, np.nan
    if len(experts) == 0:
        return 0.0, np.nan

    distances = cdist(centroids, experts, metric='euclidean')
    
    # Greedy matching
    indices = np.where(distances <= max_dist)
    pairs = sorted(zip(indices[0], indices[1]), key=lambda x: distances[x[0], x[1]])
    
    matched_centroids = set()
    matched_experts = set()
    match_distances = []
    
    for c_idx, e_idx in pairs:
        if c_idx not in matched_centroids and e_idx not in matched_experts:
            matched_centroids.add(c_idx)
            matched_experts.add(e_idx)
            match_distances.append(distances[c_idx, e_idx])
            
    tp = len(matched_centroids)
    fp = len(centroids) - tp
    fn = len(experts) - tp
    
    precision = tp / (tp + fp) if (tp + fp) > 0 else 0
    recall = tp / (tp + fn) if (tp + fn) > 0 else 0
    f1 = 2 * precision * recall / (precision + recall) if (precision + recall) > 0 else 0
    
    avg_delta = np.mean(match_distances) if len(match_distances) > 0 else np.nan
    
    return f1, avg_delta