Trend-Filtered Projection for Principal Component Analysis
Liubo Li · OhioLink ETD Center (Ohio Library and Information Network) · 2017
Principal component analysis is one of the most widely used dimension reduction techniques.We propose an approach for performing smoothed PCA of data that is observed over a dense and equally spaced grid.The proposed approach combines ideas from recent developments in convex relaxation of PCA and l 1 Trend Filtering of time series.Our method produces smooth estimates of the projection matrix of the principal subspace that are locally adaptive, and is based on a convex optimization problem that is solved by an augmented alternating direction method of multipliers (augADMM) algorithm.We describe the method and the algorithm in detail and compare the proposed method with existing methods by a numerical study.The effect of the choice of a penalty on the estimates given by the proposed method is also illustrated in a numerical study.Moreover, we present applications of the proposed method to real data and demonstrate its effectiveness.I would like to thank my advisor,