Learning Subspaces of Different Dimensions
Learning Subspaces of Different Dimensions
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DOI：
10.1080/10618600.2021.2000420
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发表时间：
2014-04
影响因子：
2.4
通讯作者：
Brian St. Thomas;Lizhen Lin;Lek-Heng Lim;Sayan Mukherjee
中科院分区：
文献类型：
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作者：
Brian St. Thomas;Lizhen Lin;Lek-Heng Lim;Sayan Mukherjee
摘要本文介绍了一种贝叶斯模型，用于推断不同维数的子空间的混合。该模型允许灵活有效地学习周围空间中支持的密度，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格拉斯曼流形嵌入到相对低维的球体中并指定球体上的先验来解决这一挑战。我们提供了一个有效的采样算法的模型参数的后验分布。我们说明了子空间混合模型的简单扩展可以应用于主题建模。我们的方法的效用证明与应用程序的真实的和模拟数据。
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.