Abstract

We introduce a Bayesian model for inferring mixtures of subspaces of different dimensions. The model allows flexible and efficient learning of a density supported in an ambient space which in fact can concentrate around some lower-dimensional space. 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. The utility of our approach is demonstrated with applications to real and simulated data.

摘要

我们引入了一个贝叶斯模型来推断不同维度子空间的混合。该模型允许灵活有效地学习环境空间中支持的密度，实际上可以集中在一些低维空间周围。这种混合模型的关键挑战是在不同维度的子空间上指定先验分布。我们通过将子空间或 Grassmann 流形嵌入到相对低维的球体中并在球体上指定先验来解决这一挑战。我们为模型参数的后验分布提供了一种有效的采样算法。我们说明了我们的混合子空间模型的简单扩展可以应用于主题建模。我们的方法的实用性通过对真实数据和模拟数据的应用得到证明。