A sparse multi-class classifier for biomarker screening

We introduce an approach to sparsity penalized multi-class classifier design that accounts for multi-block structure of the data. The unified multi-class classifier is parameterized by a set of weights defined over the classes and over the blocks. The proposed sparse multi-block multi-class classifier imposes structured sparsity on the weights so that the same variables are selected for all classes and all blocks. The classifier is trained to minimize an objective function that captures the unified miss-classification probabilities of error over the classes in addition to the sparsity of the weights. The optimization of the objective function is implemented by a convex augmented Lagrangian and variable splitting method. This results in a classifier that automatically selects biomarkers for inclusion or exclusion in the classifier and results in significantly improved classifier performance. The approach is illustrated on publicly available longitudinal gene microarray data.