Matrix Discriminant Analysis With Application to Colorimetric Sensor Array Data

With the rapid development of nano-technology, a "colorimetric sensor array" (CSA) which is referred to as an optical electronic nose has been developed for the identification of toxicants. Unlike traditional sensors which rely on a single chemical interaction, CSA can measure multiple chemical interactions by using chemo-responsive dyes. The color changes of the chemo-responsive dyes are recorded before and after exposure to toxicants and serve as a template for classification. The color changes are digitalized in the form of a matrix with rows representing dye effects and columns representing the spectrum of colors. Thus, matrix-classification methods are highly desirable. In this article, we develop a novel classification method, matrix discriminant analysis (MDA), which is a generalization of linear discriminant analysis (LDA) for the data in matrix form. By incorporating the intrinsic matrix-structure of the data in discriminant analysis, the proposed method can improve CSA's sensitivity and more importantly, specificity. A penalized MDA method, PMDA, is also introduced to further incorporate sparsity structure in discriminant function. Numerical studies suggest that the proposed MDA and PMDA methods outperform LDA and other competing discriminant methods for matrix predictors. The asymptotic consistency of MDA is also established. R code and data are available online as supplementary material.