Recently, a low cost yet highly sensitive colorimetric sensor array (CSA) for the detection and identification of volatile chemical toxicants has been developed. Classification analysis holds the key to the success of the array in discriminating multiple toxicants. The data output by the CSA are in the form of matrices, which render many traditional classification methods inapplicable. In this talk, I will introduce a matrix discriminant analysis method which can be viewed as a generalization of the conventional LDA method to the data in matrices form. By incorporating the intrinsic matrix structure of the data, the proposed method can greatly improve the sensitivity, and more importantly, the specificity of toxicants classification using the CSA. To further reduce the misclassification rate, I will introduce the $l_1$ penalty into the proposed matrix discriminant analysis to shrink the effect of the discriminant-irrelevant predictors. Two algorithms are developed to estimate parameters in the matrix discriminant analyses. Numerical studies suggest that the proposed matrix discriminant methods outperform the traditional LDA method. The asymptotic consistency is also established to provide the insight of the excellence of the empirical performance.
University of Illinois at Urbana-Champaign
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