title	emoji	colorFrom	colorTo	sdk	sdk_version	app_file	pinned	tags	description
Mahalanobis Distance	🤗	blue	red	gradio	3.19.1	app.py	false	evaluate metric	Compute the Mahalanobis Distance Mahalonobis distance is the distance between a point and a distribution. And not between two distinct points. It is effectively a multivariate equivalent of the Euclidean distance. It was introduced by Prof. P. C. Mahalanobis in 1936 and has been used in various statistical applications ever since [source: https://www.machinelearningplus.com/statistics/mahalanobis-distance/]

Metric Card for Mahalanobis Distance

Metric Description

Mahalonobis distance is the distance between a point and a distribution (as opposed to the distance between two points), making it the multivariate equivalent of the Euclidean distance.

It is often used in multivariate anomaly detection, classification on highly imbalanced datasets and one-class classification.

How to Use

At minimum, this metric requires two lists of datapoints:

>>> mahalanobis_metric = evaluate.load("mahalanobis")
>>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])

Inputs

• X (list): data points to be compared with the reference_distribution.
• reference_distribution (list): data points from the reference distribution that we want to compare to.

Output Values

mahalanobis (array): the Mahalonobis distance for each data point in X.

>>> print(results)
{'mahalanobis': array([0.5])}

Values from Popular Papers

N/A

Example

>>> mahalanobis_metric = evaluate.load("mahalanobis")
>>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])
>>> print(results)
{'mahalanobis': array([0.5])}

Limitations and Bias

The Mahalanobis distance is only able to capture linear relationships between the variables, which means it cannot capture all types of outliers. Mahalanobis distance also fails to faithfully represent data that is highly skewed or multimodal.

Citation

@inproceedings{mahalanobis1936generalized,
  title={On the generalized distance in statistics},
  author={Mahalanobis, Prasanta Chandra},
  year={1936},
  organization={National Institute of Science of India}
}

@article{de2000mahalanobis,
  title={The Mahalanobis distance},
  author={De Maesschalck, Roy and Jouan-Rimbaud, Delphine and Massart, D{\'e}sir{\'e} L},
  journal={Chemometrics and intelligent laboratory systems},
  volume={50},
  number={1},
  pages={1--18},
  year={2000},
  publisher={Elsevier}
}

Further References

-Wikipedia -- Mahalanobis Distance

-Machine Learning Plus -- Mahalanobis Distance