Generalized Principal Component Analysis

• Activity Number: 698
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Andrew Landgraf* and Yoonkyung Lee
• Companies: The Ohio State University and The Ohio State University
• Keywords: Binary data ; Dimensionality reduction ; PCA ; Logistic PCA ; Count data

Abstract

Principal component analysis (PCA) is very useful for a wide variety of data analysis tasks, but its implicit link to the Gaussian distribution can be undesirable for discrete data such as binary responses, counts, or categories. We generalize PCA to handle various types of data using the generalized linear model framework. In contrast to the existing approach of matrix factorizations for exponential family data, our generalized PCA provides low-rank estimates of the natural parameters by projecting the saturated model parameters. A practical algorithm which can incorporate missing data and weights is developed to solve for the projection matrix. Further, when there are far more variables than observations, our generalized PCA formulation and algorithm can be extended to include sparsity constraints, which enhances its stability and interpretability.