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Implementing a weighted Euclidean distance metric for DBSCAN to account for anisotropic spatial features.
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| name | dbscan-custom-metric-weighting |
| description | Implementing a weighted Euclidean distance metric for DBSCAN to account for anisotropic spatial features. |
When clustering spatial data where features (like x and y coordinates) have different importance or scales, a custom distance metric can be used with sklearn.cluster.DBSCAN.
The formula provided: $d(a, b) = \sqrt{(w \cdot \Delta x)^2 + ((2 - w) \cdot \Delta y)^2}$ allows for "stretching" or "compressing" the influence of horizontal vs vertical distances.
Implementation with Scikit-Learn:
To use this with DBSCAN, you can define a function and pass it to the metric parameter.
from sklearn.cluster import DBSCAN
import numpy as np
def custom_dist(a, b, w):
dx = a[0] - b[0]
dy = a[1] - b[1]
return np.sqrt((w * dx)**2 + ((2 - w) * dy)**2)
# Using it in DBSCAN (note: using lambda to pass the weight)
db = DBSCAN(eps=epsilon, min_samples=min_samples,
metric=lambda u, v: custom_dist(u, v, weight))
clusters = db.fit_predict(points)
Alternatively, for performance during grid search, precomputing the distance matrix or using a vectorized function inside the metric argument is recommended.