Tensor envelope mixture model for simultaneous clustering and multiway dimension reduction
Tensor envelope mixture model for simultaneous clustering and multiway dimension reduction
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DOI：
10.1111/biom.13486
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发表时间：
2021-05
期刊：
影响因子：
1.9
通讯作者：
Kai Deng;Xin Zhang
中科院分区：
文献类型：
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作者：
Kai Deng;Xin Zhang
以多维数组的形式，张量数据在现代科学研究和生物医学应用中变得越来越普遍，例如计算生物学，脑成像分析和过程监控系统。这些数据本质上是异构的，具有复杂的依赖关系和结构。因此，对张量数据的特别降维方法可能缺乏统计效率，并且可能掩盖重要的发现。基于模型的聚类是多元统计和无监督学习的基石;然而，现有的方法和算法不是为张量变量样本设计的。在这篇文章中，我们提出了一个张量包络混合模型（TEMM）的同时聚类和多维降维的张量数据。TEMM将张量结构保持降维纳入混合建模，并大大减少了自由参数和估计变异性的数量。开发了一种期望最大化型算法来获得聚类均值和协方差的基于似然的估计，这些估计被联合参数化并约束到一系列称为张量包络的低维子空间上。我们证明了令人鼓舞的实证性能，所提出的方法在广泛的模拟研究和真实的数据应用程序相比，现有的矢量和张量聚类方法。
In the form of multidimensional arrays, tensor data have become increasingly prevalent in modern scientific studies and biomedical applications such as computational biology, brain imaging analysis, and process monitoring system. These data are intrinsically heterogeneous with complex dependencies and structure. Therefore, ad‐hoc dimension reduction methods on tensor data may lack statistical efficiency and can obscure essential findings. Model‐based clustering is a cornerstone of multivariate statistics and unsupervised learning; however, existing methods and algorithms are not designed for tensor‐variate samples. In this article, we propose a tensor envelope mixture model (TEMM) for simultaneous clustering and multiway dimension reduction of tensor data. TEMM incorporates tensor‐structure‐preserving dimension reduction into mixture modeling and drastically reduces the number of free parameters and estimative variability. An expectation‐maximization‐type algorithm is developed to obtain likelihood‐based estimators of the cluster means and covariances, which are jointly parameterized and constrained onto a series of lower dimensional subspaces known as the tensor envelopes. We demonstrate the encouraging empirical performance of the proposed method in extensive simulation studies and a real data application in comparison with existing vector and tensor clustering methods.