run2_custom-distance-metrics

Fast Custom Distance Metrics in Scikit-Learn

To effectively use custom distance metrics with DBSCAN, it is highly recommended to precompute the distance matrix. Python scalar functions passed to metric are typically too slow. Instead, use numpy broadcasting to compute the matrix.

Installation

Ensure you have scikit-learn and numpy installed: pip install scikit-learn numpy

Usage

import numpy as np
from sklearn.cluster import DBSCAN

def custom_dist_matrix(points, w):
    """
    Computes a distance matrix for N points.
    d(a, b) = sqrt((w * Δx)^2 + ((2 - w) * Δy)^2)
    """
    points = np.asarray(points)
    # Broadcasting to find all pairwise differences
    dx = w * (points[:, 0:1] - points[:, 0:1].T)
    dy = (2 - w) * (points[:, 1:2] - points[:, 1:2].T)
    return np.sqrt(dx**2 + dy**2)

# X is an N by 2 array of points
# dist_matrix = custom_dist_matrix(X, w=1.5)
# db = DBSCAN(eps=10, min_samples=5, metric='precomputed').fit(dist_matrix)