Sparse Linear Discriminant Analysis for Multiview Structured Data

Classification methods that leverage the strengths of data from multiple sources (multiview 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 multiview 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. We demonstrate the effectiveness of our methods on a set of synthetic datasets and explore their use in identifying potential nontraditional risk factors that discriminate healthy patients at low versus high risk for developing atherosclerosis cardiovascular disease in 10 years. Our findings underscore the benefit of joint association and classification methods if the goal is to correlate multiview data and to perform classification.