Run1 dbscan custom distance clustering

Overview

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a clustering algorithm that groups points based on density. This implementation uses a custom distance metric that weights x and y dimensions asymmetrically.

Custom Distance Metric

The distance between points a and b is:

d(a, b) = sqrt((w * Δx)² + ((2 - w) * Δy)²)

Where:

• w = shape_weight parameter (0.9–1.9)
• Δx = difference in x-coordinates
• Δy = difference in y-coordinates

Interpretation:

• When w = 1.0: Standard Euclidean distance
• When w > 1.0: y-distances are attenuated (points closer in y-direction are grouped together more easily)
• When w < 1.0: x-distances are attenuated (points closer in x-direction are grouped together more easily)

DBSCAN Parameters

• epsilon (eps): Maximum distance between two points for them to be in the same neighborhood
• min_samples: Minimum number of points in a neighborhood for a point to be considered a core point

Implementation Notes

1. Use scikit-learn's DBSCAN with a custom metric function or distance matrix
2. Compute cluster centroids as the mean (x, y) of all points in each cluster
3. Ignore noise points (label = -1) when computing centroids
4. Return only valid clusters (at least 1 cluster found)