March 2024 Tensor mixture discriminant analysis with applications to sensor array data analysis
Xuesong Hou, Qing Mai, Hui Zou
Author Affiliations +
Ann. Appl. Stat. 18(1): 626-641 (March 2024). DOI: 10.1214/23-AOAS1804


Sensor arrays are often used to identify chemicals by measuring properly chosen chemical interactions. Machine learning techniques are of vital importance to accurately recognize a chemical based on the sensor array measurements. However, sensor array data often take the form of matrices (i.e, two-way tensors), and the concentration levels may have a complex impact on the measurements. Hence, existing linear and/or vector classification methods may be inadequate for sensor array data. In this article we propose a novel tensor mixture discriminant analysis (TMDA) model carefully tailored for the classification of sensor array data. We model the distribution of each chemical by a mixture of tensor normal distributions. TMDA leverages the tensor structure for better estimation and prediction, while the mixed tensor normal component accounts for the possibly varying concentration levels. The TMDA model can also be viewed as an approximation of the potentially nonnormal measurements. An efficient expectation-maximization algorithm is developed to fit the TMDA model. The application of TMDA on two sensor array datasets demonstrates its superior performance to many popular competitors.

Funding Statement

Qing Mai is supported in part by NSF Grant CCF 1908969.
Hui Zou is supported in part by NSF Grants 2015120 and 2220286.


We sincerely thank the Associate Editor and referees for their helpful comments and suggestions which greatly improved the quality of this paper.


Download Citation

Xuesong Hou. Qing Mai. Hui Zou. "Tensor mixture discriminant analysis with applications to sensor array data analysis." Ann. Appl. Stat. 18 (1) 626 - 641, March 2024.


Received: 1 June 2022; Revised: 1 July 2023; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1804

Keywords: Sensor arrays , tensor data classification , tensor normal mixtures

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 1 • March 2024
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