# Mixture Probabilistic Principal Geodesic Analysis

arXiv: https://arxiv.org/abs/1909.01412 · HTML: https://mlsanity.com/paper/1909.01412/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2019.

## Built on by (most cited first, 4 of 4)

- [Deep Spherical Manifold Gaussian Kernel for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2105.02089/) (2021)
- [MGAug: Multimodal Geometric Augmentation in Latent Spaces of Image Deformations](https://mlsanity.com/paper/2312.13440/) (2023)
- [Probabilistic Geometric Principal Component Analysis with application to neural data](https://mlsanity.com/paper/2509.18469/) (2025)
- [Disentanglement Beyond Generative Models with Riemannian ICA](https://mlsanity.com/paper/2605.22531/) (2026)

## Abstract (arXiv)

Dimensionality reduction on Riemannian manifolds is challenging due to the complex nonlinear data structures. While probabilistic principal geodesic analysis~(PPGA) has been proposed to generalize conventional principal component analysis (PCA) onto manifolds, its effectiveness is limited to data with a single modality. In this paper, we present a novel Gaussian latent variable model that provides a unique way to integrate multiple PGA models into a maximum-likelihood framework. This leads to a well-defined mixture model of probabilistic principal geodesic analysis (MPPGA) on sub-populations, where parameters of the principal subspaces are automatically estimated by employing an Expectation Maximization algorithm. We further develop a mixture Bayesian PGA (MBPGA) model that automatically reduces data dimensionality by suppressing irrelevant principal geodesics. We demonstrate the advantages of our model in the contexts of clustering and statistical shape analysis, using synthetic sphere data, real corpus callosum, and mandible data from human brain magnetic resonance~(MR) and CT images.