Tensor mixture discriminant analysis with applications to sensor array data analysis

Abstract

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.