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Sparse Linear Discriminant Analysis for Multi-view Structured Data

Classification methods that leverage the strengths of data from multiple sources (multi-view data) simultaneously have enormous potential to yield more powerful findings than two step methods: association followed by classification. We propose two methods, sparse integrative discriminant analysis (SIDA) and SIDA with incorporation of network information (SIDANet), for joint association and classification studies. The methods consider the overall association between multi-veiw data, and the separation within each view in choosing discriminant vectors that are associated and optimally separate subjects into different classes. SIDANet is among the first methods to incorporate prior structural information in joint association and classification studies. It uses the normalized Laplacian of a graph to smooth coefficients of predictor variables, thus encouraging selection of predictors that are connected and behave similarly. We demonstrate the effectiveness of our methods on a set of synthetic and real datasets. Our findings underscore the benefit of joint association and classification methods if the goal is to correlate multi-view data and to perform classification.