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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
Abstract #317524
Title: Generalized Principal Component Analysis
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

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.

Authors who are presenting talks have a * after their name.

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