Poster
Probabilistic Principal Geodesic Analysis
Miaomiao Zhang · Tom Fletcher

Sat Dec 7th 07:00 -- 11:59 PM @ Harrah's Special Events Center, 2nd Floor #None

Principal geodesic analysis (PGA) is a generalization of principal component analysis (PCA) for dimensionality reduction of data on a Riemannian manifold. Currently PGA is defined as a geometric fit to the data, rather than as a probabilistic model. Inspired by probabilistic PCA, we present a latent variable model for PGA that provides a probabilistic framework for factor analysis on manifolds. To compute maximum likelihood estimates of the parameters in our model, we develop a Monte Carlo Expectation Maximization algorithm, where the expectation is approximated by Hamiltonian Monte Carlo sampling of the latent variables. We demonstrate the ability of our method to recover the ground truth parameters in simulated sphere data, as well as its effectiveness in analyzing shape variability of a corpus callosum data set from human brain images.

Author Information

Miaomiao Zhang (MIT)
Tom Fletcher (University of Utah)

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