# Bregman Divergences for Infinite Dimensional Covariance Matrices

arXiv: https://arxiv.org/abs/1403.4334 · HTML: https://mlsanity.com/paper/1403.4334/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2014.

## Built on by (most cited first, 12 of 12)

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- [Conditionally Whitened Generative Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2509.20928/) (2025)
- [Symmetrizing Bregman Divergence on the Cone of Positive Definite Matrices: Which Mean to Use and Why](https://mlsanity.com/paper/2603.28917/) (2026)
- [Generalising maximum mean discrepancy: kernelised functional Bregman divergences](https://mlsanity.com/paper/2604.24047/) (2026)
- [CPDA: Class-Conditional Path Distribution Alignment for Unsupervised Time-Series Domain Adaptation](https://mlsanity.com/paper/2608.09193/) (2026)

## Abstract (arXiv)

We introduce an approach to computing and comparing Covariance Descriptors (CovDs) in infinite-dimensional spaces. CovDs have become increasingly popular to address classification problems in computer vision. While CovDs offer some robustness to measurement variations, they also throw away part of the information contained in the original data by only retaining the second-order statistics over the measurements. Here, we propose to overcome this limitation by first mapping the original data to a high-dimensional Hilbert space, and only then compute the CovDs. We show that several Bregman divergences can be computed between the resulting CovDs in Hilbert space via the use of kernels. We then exploit these divergences for classification purposes. Our experiments demonstrate the benefits of our approach on several tasks, such as material and texture recognition, person re-identification, and action recognition from motion capture data.