Implementing the Mahalanobis Distance in Python

Below you will find a Jupyter Notebook that explores the Mahalanobis distance in depth.
It begins with the theoretical foundations and practical applications, followed by multiple Python implementations (NumPy, JAX, TensorFlow, SciPy) to ensure correctness and compare performance.
The notebook validates these implementations, benchmarks them across low- and high-dimensional datasets, and illustrates the geometric intuition behind the Mahalanobis distance through visualizations and whitening transformations.
Finally, it demonstrates the close connection to the Chi-square distribution and applies the method to a simple anomaly detection task.

The aim is to provide both a solid theoretical understanding and practical tools for applying the Mahalanobis distance in real-world scenarios.

👉 A more theoretical discussion of the Mahalanobis distance and its connection to the Chi-square distribution can be found here.

👉 For estimating the covariance matrix and mean in a streaming or batch-incremental fashion, see Online and Batch-Incremental Estimation of Covariance Matrices.