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Trend-Filtered Projection for Principal Component Analysis

Li, Liubo, Li
http://rave.ohiolink.edu/etdc/view?acc_num=osu1503277234178696

Abstract Details

2017, Doctor of Philosophy, Ohio State University, Statistics.
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.
Vincent Vu (Advisor)
Yoonkyung Lee (Advisor)
Sebastian Kurtek (Committee Member)
94 p.
Statistics
Convex relaxation, Trend filtering, Local Adaptiveness, Smoothed PCA

Recommended Citations

Citations

  • Li, Li, L. (2017). Trend-Filtered Projection for Principal Component Analysis [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1503277234178696

    APA Style (7th edition)

  • Li, Li, Liubo. Trend-Filtered Projection for Principal Component Analysis. 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1503277234178696.

    MLA Style (8th edition)

  • Li, Li, Liubo. "Trend-Filtered Projection for Principal Component Analysis." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1503277234178696

    Chicago Manual of Style (17th edition)

osu1503277234178696
488
© 2017, some rights reserved.Creative Commons License Trend-Filtered Projection for Principal Component Analysis by Liubo Li Li is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.