Algorithms and Approaches for Analyzing Massive Structured Data with Sparse Generalized PCA

• Activity Number: 402
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Frederick Campbell*+ and Genevera Allen
• Companies: and Rice University
• Keywords: Sparsity ; Multivariate Analysis ; Statistical Computing ; PCA ; Correlated Data ; Unsupervised Learning

Abstract

Technological advances have led to the proliferation of large complex data-sets, such as those found in genetics, neuroimaging, and climate studies. Many of these data sets are high dimensional and exhibit known dependencies, like spatial and temporal structures. Recently, Allen et. al (2011) introduced Sparse Generalized Principal Component Analysis (GPCA) which extends PCA and Sparse PCA to work with structured, high-dimensional data by permitting heteroscedasticity in the matrix errors. Through a series of case studies, we present flexible approaches for modeling structure in environmental, biomedical imaging and remote sensing data. We illustrate the advantages of Sparse GPCA for exploratory data analysis, feature selection, and dimension reduction. Lastly, we provide timing results comparing several fast algorithms for fitting Sparse GPCA, and present software packages in R and Matlab to encourage flexible analysis of structured data using Sparse GPCA.