# Inductive Geometric Matrix Midranges

arXiv: https://arxiv.org/abs/2006.01508 · HTML: https://mlsanity.com/paper/2006.01508/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [Differential geometry with extreme eigenvalues in the positive semidefinite cone](https://mlsanity.com/paper/2304.07347/) (2023)
- [Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm](https://mlsanity.com/paper/2207.00818/) (2022)
- [Geometric statistics with subspace structure preservation for SPD matrices](https://mlsanity.com/paper/2407.03382/) (2024)

## Abstract (arXiv)

Covariance data as represented by symmetric positive definite (SPD) matrices are ubiquitous throughout technical study as efficient descriptors of interdependent systems. Euclidean analysis of SPD matrices, while computationally fast, can lead to skewed and even unphysical interpretations of data. Riemannian methods preserve the geometric structure of SPD data at the cost of expensive eigenvalue computations. In this paper, we propose a geometric method for unsupervised clustering of SPD data based on the Thompson metric. This technique relies upon a novel "inductive midrange" centroid computation for SPD data, whose properties are examined and numerically confirmed. We demonstrate the incorporation of the Thompson metric and inductive midrange into X-means and K-means++ clustering algorithms.