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arXiv 1909.01412cs.LGcs.CVstat.ML
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混合概率主测地线分析

Mixture Probabilistic Principal Geodesic Analysis

Lehigh University（理海大学）；University of Virginia（弗吉尼亚大学）

Youshan Zhang, Jiarui Xing, Miaomiao Zhang

备注：
Seventh MICCAI Workshop on Mathematical Foundations of Computational Anatomy
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摘要：

由于黎曼流形上复杂的非线性数据结构，黎曼流形上的非线性约简具有挑战性。概率主测地线分析（PPGA）是将传统的主成分分析（PCA）推广到流形上的一种方法，但其有效性仅限于单一模态的数据。在本文中，我们提出了一种新的高斯潜变量模型，提供了一种独特的方式来集成多个PGA模型到一个最大似然框架。这导致一个定义良好的混合模型的概率主测地线分析（MPPGA）的子种群，其中的主子空间的参数自动估计采用期望最大化算法。我们进一步开发了一个混合贝叶斯PGA（MBPGA）模型，通过抑制不相关的主测地线自动降低数据的维数。我们证明了我们的模型在聚类和统计形状分析的背景下，使用合成的球体数据，真实的胼胝体，和下颌骨数据从人脑磁共振~（MR）和CT图像的优势。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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