# Learning Subspaces of Different Dimension

arXiv: https://arxiv.org/abs/1404.6841 · HTML: https://mlsanity.com/paper/1404.6841/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2014.

## Built on by (most cited first, 2 of 2)

- [Sequential Gibbs Posteriors with Applications to Principal Component Analysis](https://mlsanity.com/paper/2310.12882/) (2023)
- [Extrinsic Bayesian Optimizations on Manifolds](https://mlsanity.com/paper/2212.13886/) (2022)

## Abstract (arXiv)

We introduce a Bayesian model for inferring mixtures of subspaces of different dimensions. The key challenge in such a mixture model is specification of prior distributions over subspaces of different dimensions. We address this challenge by embedding subspaces or Grassmann manifolds into a sphere of relatively low dimension and specifying priors on the sphere. We provide an efficient sampling algorithm for the posterior distribution of the model parameters. We illustrate that a simple extension of our mixture of subspaces model can be applied to topic modeling. We also prove posterior consistency for the mixture of subspaces model. The utility of our approach is demonstrated with applications to real and simulated data.