dbscan-custom-metric

name	dbscan-custom-metric
description	How to run DBSCAN clustering with a custom anisotropic distance metric using sklearn and scipy. Use this skill whenever the user needs to cluster spatial points with a weighted or shape-adjusted distance, such as attenuating x vs y distances differently, or when DBSCAN needs a non-Euclidean metric defined as a callable. Covers cluster centroid computation and noise-point handling.

DBSCAN with Custom Distance Metric

Overview

sklearn.cluster.DBSCAN accepts metric='precomputed' or a callable. For runtime-efficient custom metrics, use metric='precomputed' with a precomputed distance matrix, or pass a Python callable directly.

Custom Anisotropic Metric

For the shape-weighted metric d(a, b) = sqrt((w*Δx)² + ((2-w)*Δy)²):

import numpy as np
from sklearn.cluster import DBSCAN

def make_metric(shape_weight):
    w = shape_weight
    def metric(a, b):
        dx = w * (a[0] - b[0])
        dy = (2 - w) * (a[1] - b[1])
        return np.sqrt(dx*dx + dy*dy)
    return metric

def run_dbscan(points_xy, epsilon, min_samples, shape_weight):
    """points_xy: np.ndarray of shape (N, 2)"""
    if len(points_xy) < min_samples:
        return np.array([])  # no clusters possible

    metric = make_metric(shape_weight)
    db = DBSCAN(eps=epsilon, min_samples=min_samples, metric=metric)
    labels = db.fit_predict(points_xy)
    return labels

Computing Cluster Centroids

After fitting, compute the mean (x, y) of each non-noise cluster:

def compute_centroids(points_xy, labels):
    """Returns list of (cx, cy) for each unique cluster label >= 0."""
    unique_labels = set(labels) - {-1}
    centroids = []
    for lbl in sorted(unique_labels):
        mask = labels == lbl
        cx = points_xy[mask, 0].mean()
        cy = points_xy[mask, 1].mean()
        centroids.append((cx, cy))
    return centroids  # list of (x, y) tuples

Performance Notes

• For large datasets, prefer metric='precomputed' with scipy's cdist:

  from scipy.spatial.distance import cdist
  D = cdist(points_xy, points_xy, metric=metric)
  db = DBSCAN(eps=epsilon, min_samples=min_samples, metric='precomputed')
  labels = db.fit_predict(D)
  

• For grid search parallelism, pass the metric as a closure (not a lambda that captures mutable state).

Edge Cases

• If fewer than min_samples points exist: return no clusters (empty labels).
• If all points are labeled -1 (noise): no clusters found.
• Empty points_xy array: skip DBSCAN, return empty centroids.