Tensor envelope mixture model for simultaneous clustering and multiway dimension reduction

Kai Deng and Xin Zhang

Biometrics, 2022, vol. 78, issue 3, 1067-1079

Abstract: 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.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/biom.13486

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:biomet:v:78:y:2022:i:3:p:1067-1079

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0006-341X

Access Statistics for this article

More articles in Biometrics from The International Biometric Society
Bibliographic data for series maintained by Wiley Content Delivery ().