# Lipschitz Continuity of Mahalanobis Distances and Bilinear Forms

arXiv: https://arxiv.org/abs/1604.01376 · HTML: https://mlsanity.com/paper/1604.01376/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2016.

## Built on by (most cited first, 1 of 1)

- [Global Ground Metric Learning with Applications to scRNA data](https://mlsanity.com/paper/2506.15383/) (2025)

## Abstract (arXiv)

Many theoretical results in the machine learning domain stand only for functions that are Lipschitz continuous. Lipschitz continuity is a strong form of continuity that linearly bounds the variations of a function. In this paper, we derive tight Lipschitz constants for two families of metrics: Mahalanobis distances and bounded-space bilinear forms. To our knowledge, this is the first time the Mahalanobis distance is formally proved to be Lipschitz continuous and that such tight Lipschitz constants are derived.