dbscan-custom-metric

DBSCAN with Custom Distance Metrics

Overview

scikit-learn's DBSCAN accepts a metric parameter that can be a callable Python function. When using a custom metric, set algorithm='ball_tree' or algorithm='brute' (default 'auto' may not support custom callables).

Installation

pip install scikit-learn numpy

Custom Metric Definition

A custom metric must accept two 1D arrays and return a scalar distance.

import numpy as np

def weighted_euclidean(a, b, w=1.0):
    """
    Weighted Euclidean distance:
      d(a, b) = sqrt((w * Δx)² + ((2 - w) * Δy)²)

    When w=1: standard Euclidean distance.
    w>1: attenuates y-distances (stretches x influence).
    w<1: attenuates x-distances (stretches y influence).
    """
    dx = a[0] - b[0]
    dy = a[1] - b[1]
    return np.sqrt((w * dx)**2 + ((2 - w) * dy)**2)

Using with DBSCAN

DBSCAN requires a metric with a fixed signature (a, b) -> float. Use functools.partial or a closure to bind parameters:

from sklearn.cluster import DBSCAN
from functools import partial
import numpy as np

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

# Run DBSCAN
points = np.array([[x1, y1], [x2, y2], ...])  # shape (N, 2)
dbscan = DBSCAN(eps=epsilon, min_samples=min_samples, metric=make_metric(1.2))
labels = dbscan.fit_predict(points)

Important: When using a custom callable metric, sklearn uses algorithm='brute' internally. You do NOT need to pass a precomputed distance matrix — just pass the raw points array.

Extracting Cluster Centroids

import numpy as np

def get_cluster_centroids(points, labels):
    """
    Returns array of centroids for each cluster (excluding noise label -1).
    points: np.array of shape (N, 2)
    labels: np.array of cluster labels from DBSCAN
    """
    unique_labels = set(labels) - {-1}  # exclude noise
    centroids = []
    for label in unique_labels:
        mask = labels == label
        centroid = points[mask].mean(axis=0)
        centroids.append(centroid)
    return np.array(centroids) if centroids else np.empty((0, 2))