Trend-Filtered Projections for PCA

• Activity Number: 553
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Liubo Li* and Vincent Vu
• Companies: The Ohio State University and The Ohio State University
• Keywords: PCA ; ADMM ; convex optimization ; trend filtering ; convex relaxation ; smoothing

Abstract

Principal component analysis is one of the most widely used dimension reduction techniques. In this article, we propose an approach for performing smoothed PCA of densely observed functional data that combines ideas from recent developments in convex relaxation of PCA and L1 trend filtering of time series. Our method produces smooth estimates that are locally adapted, and based on a convex optimization problem that is solved by an alternating direction method of multipliers (ADMM) algorithm. We describe the method and the algorithm in detail and illustrate it through a simulation study.