Low-Rank Modeling Across Multiple High-Dimensional Data Sets

• Activity Number: 451
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Eric F Lock*+
• Companies: The University of North Carolina at Chapel Hill
• Keywords: Principal Components Analysis (PCA) ; Singular Value Decomposition (SVD) ; Data fusion ; Data integration ; Multi-block data

Abstract

Research in a number of fields now requires the analysis of datasets in which multiple high-dimensional types of data are available for a common set of objects. We propose a general decomposition of variation for the integrated analysis of such datasets. This decomposition partitions structured variation into a low-rank term capturing joint variation across all datatypes, low-rank terms capturing joint variation across pairs of datatypes, and low rank terms capturing structured variation individual to each datatype. This decomposition quantifies the amount of joint variation between datatypes, reduces the dimensionality of the data in an insightful way, and provides new directions for the visual exploration of joint and individual structure. This approach represents an extension of the Joint and Individual Variation Explained (JIVE) method, and has close connections with Principal Components Analysis (PCA).

This talk describes joint work with Andrew Nobel, J.S. Marron and Katherine Hoadley.