Noniterative Joint and Individual Variation Explained

• Activity Number: 178
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Qing Feng* and James Stephen Marron and Jan Hannig
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina and The University of North Carolina at Chapel Hill
• Keywords: Multi-block data analysis ; PCA ; High dimensions ; Data visualization ; Data integration

Abstract

Multi-block data sets are concatenations of multiple feature blocks measured on a common set of experimental subjects. Analyzing such data sets encounters challenges in normalizing and interpreting the data blocks with their intrinsic structures taken into consideration, which motivates the development of Non-iterative Joint and Individual Variation Explained (Non-iterative JIVE). This method provides a direct linear algebra computation for a two-block data set decomposing the variation in the data matrices into three types of structure: a low-rank approximation of the joint variation across the blocks, low-rank approximations of the individual variation for each block, and residual noise. The separation between these components is driven by a principal angles analysis which resolves some normalization issues. Thresholds involved can be chosen by random matrix theory or through a scale space approach, which is greatly facilitated by the non-iterative algorithm. An application to a mortality data set successfully reveals common and distinct modes of variations which are well correlated with historical events.