# Probabilistic Learning Vector Quantization on Manifold of Symmetric Positive Definite Matrices

arXiv: https://arxiv.org/abs/2102.00667 · HTML: https://mlsanity.com/paper/2102.00667/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 37 references that are in the map.
- First posted on arXiv 1 Feb 2021.

## Builds on (most cited first, 4 of 4)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernels](https://mlsanity.com/paper/1412.0265/) (2014)
- [A review of learning vector quantization classifiers](https://mlsanity.com/paper/1509.07093/) (2015)
- [Riemannian Metric Learning for Symmetric Positive Definite Matrices](https://mlsanity.com/paper/1501.02393/) (2015)

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

- [RSAVQ: Riemannian Sensitivity-Aware Vector Quantization for Large Language Models](https://mlsanity.com/paper/2510.01240/) (2025)

## Abstract (arXiv)

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive definite matrices, which are inherently points that live on a curved Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, traditional Euclidean machine learning algorithms yield poor results on such data. In this paper, we generalize the probabilistic learning vector quantization algorithm for data points living on the manifold of symmetric positive definite matrices equipped with Riemannian natural metric (affine-invariant metric). By exploiting the induced Riemannian distance, we derive the probabilistic learning Riemannian space quantization algorithm, obtaining the learning rule through Riemannian gradient descent. Empirical investigations on synthetic data, image data , and motor imagery EEG data demonstrate the superior performance of the proposed method.