Mahalanobis distance measures point-to-distribution distance by accounting for data covariance and correlations, making it superior for multivariate outlier detection and clustering. Unlike Euclidean distance, which treats features independently and is sensitive to scale, Mahalanobis is scale-invariant and creates elliptical boundaries rather than circular ones. [1, 2, 3, 4]
Key Differences:
- Correlation & Variance: Mahalanobis considers how variables change together (covariance), while Euclidean treats variables as independent.
- Scale Invariance: Mahalanobis accounts for the scale of measurements, whereas Euclidean requires scaling/normalization.
- Use Cases: Mahalanobis is better for anomaly detection and finding data clusters, while Euclidean is ideal for straightforward geometric calculations in uniform space.
- Shape/Boundary: Euclidean creates circular or spherical boundaries, while Mahalanobis creates elliptical boundaries. [1, 2, 4, 5, 6]
Mahalanobis Distance Advantages:
- Outlier Detection: It accurately calculates the atypicality of points compared to a central distribution.
- Dimensionality Handling: It effectively handles data where variables are not independent. [2, 7, 8]
Euclidean Distance Advantages:
- Simplicity: Easier to compute, requiring only the standard distance formula (ruler-like measurement).
- Interpretability: Intuitive interpretation of physical distance. [7, 9, 10]
Note: If variables are uncorrelated and have equal variance, Mahalanobis distance equals Euclidean distance. [9]
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