Multicategory Vertex Discriminant Analysis for High-Dimensional Data

• Activity Number: 589
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Tongtong Wu*+ and Kenneth Lange
• Companies: University of Maryland and University of California, Los Angeles
• Keywords: classification ; coordinate descent ; Euclidean penalty ; lasso penalty ; regular simplex ; variable selection

Abstract

In response to the challenges of data mining, discriminant analysis continues to evolve as a vital branch of statistics. Our recently introduced method of vertex discriminant analysis (VDA) is ideally suited to handle multiple categories and an excess of predictors over training cases. This talk explores an elaboration of VDA that conducts classification and variable selection simultaneously. Adding lasso (L1-norm) and Euclidean penalties to the VDA loss function eliminates unnecessary predictors. Lasso penalties apply to each predictor coefficient separately; Euclidean penalties group the collective coefficients of a single predictor. With these penalties in place, cyclic coordinate descent accelerates estimation of all coefficients. Our tests on simulated and benchmark real data demonstrate the virtues of penalized VDA in model building and prediction in high-dimensional settings.