Integrating Data Transformation in Principal Components Analysis

Type
Article

Authors
Maadooliat, Mehdi
Huang, Jianhua Z.
Hu, Jianhua

KAUST Grant Number
KUS-CI-016-04

Online Publication Date
2015-03-31

Print Publication Date
2015-01-02

Date
2015-03-31

Abstract
Principal component analysis (PCA) is a popular dimension reduction method to reduce the complexity and obtain the informative aspects of high-dimensional datasets. When the data distribution is skewed, data transformation is commonly used prior to applying PCA. Such transformation is usually obtained from previous studies, prior knowledge, or trial-and-error. In this work, we develop a model-based method that integrates data transformation in PCA and finds an appropriate data transformation using the maximum profile likelihood. Extensions of the method to handle functional data and missing values are also developed. Several numerical algorithms are provided for efficient computation. The proposed method is illustrated using simulated and real-world data examples.

Citation
Maadooliat M, Huang JZ, Hu J (2015) Integrating Data Transformation in Principal Components Analysis. Journal of Computational and Graphical Statistics 24: 84–103. Available: http://dx.doi.org/10.1080/10618600.2014.891461.

Acknowledgements
We thank an associate editor and two anonymous referees for their constructive and thoughtful comments that helped us tremendously in revising the manuscript. Maadooliat and Hu were partially supported by the National Science Foundation (grants DMS-0706818), the National Institutes of Health (grants R01GM080503-01A1, R21CA129671), and the National Cancer Institute (grant CA97007). Huang was partially supported by the National Science Foundation (grants DMS-0606580, DMS-0907170). Huang and Maadooliat were partially supported by King Abdullah University of Science and Technology (grant KUS-CI-016-04).

Publisher
Informa UK Limited

Journal
Journal of Computational and Graphical Statistics

DOI
10.1080/10618600.2014.891461

PubMed ID
25914514

PubMed Central ID
PMC4408558

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