On the Penalty Functions for Two-Way Regularized Matrix Decomposition

• Activity Number: 43
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Senmao Liu*
• Companies: Texas A&M University
• Keywords: matrix decomposition ; two-way regularization ; invariance

Abstract

Matrix decomposition (or low-rank matrix approximation) plays an important role in various statistical learning problems. Regularization has been introduced to matrix decomposition to achieve stability, especially when the row or column dimension is high. When both the row and column domains of the matrix are structured, it is natural to employ a two-way regularization penalty in low-rank matrix approximation. This talk discusses the importance of considering invariance when designing the two-way penalty and shows some un-desirable properties of the penalty used in the literature when the invariance is ignored. This is a joint work with Jianhua Huang.