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Sequentially spherical data modeling with hidden Markov models and its application to fMRI data analysis

机译：用隐马尔可夫模型顺序球形数据建模及其在FMRI数据分析中的应用

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摘要

Due to the reason that spherical data (i.e. L-2 normalized vectors) are often involved with various real life applications (such as anomaly detection, gesture recognition, intrusion detection in networks, gene expression data analysis, etc.), spherical data modeling has recently become an important research topic. In this work, we address the problem of modeling sequentially spherical data through continuous hidden Markov models (HMMs). Instead of adopting Gaussian mixture models (GMMs) as the emission distributions as in common continuous HMMs, we propose a continuous HMM by considering the mixture of von Mises-Fisher (VMF) distributions as its emission densities. Then, we systematically propose an effective method based on variational Bayes (VB) to learn the VMF-based HMM. The developed learning method has the following merits: (1) It is convergence-guaranteed; (2) It can be optimized with closed-form solutions. The proposed VMF-HMM with VB learning is validated by conducting experiments on both simulated sequential spherical data and a real application about fMRI data analysis. (C) 2020 Elsevier B.V. All rights reserved.
机译：由于球面数据（即L-2归一化载体）通常涉及各种真实寿命应用（例如异常检测，手势识别，网络中的入侵检测，基因表达数据分析等），球面数据建模具有最近成为一个重要的研究主题。在这项工作中，我们通过连续隐马尔可夫模型（HMMS）来解决依次球形数据建模问题。代替将高斯混合物模型（GMMS）作为常见连续HMMS作为发射分布，而不是通过将Von Mises-Fisher（VMF）分布作为其排放密度的混合物提出连续的HMM。然后，我们系统地提出了一种基于变分贝叶斯（VB）的有效方法，以学习基于VMF的HMM。开发的学习方法具有以下优点：（1）它是融合 - 保证; （2）可以用闭合溶液进行优化。通过在模拟顺序球面数据上进行实验和关于FMRI数据分析的实际应用来验证具有VB学习的提出的VMF-HMM。 （c）2020 Elsevier B.v.保留所有权利。

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