Integrating Data Transformation in Principal Components Analysis.
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.
Department of Mathematics, Statistics and Computer Science, Marquette University, WI.
Mehdi
M
Maadooliat
Department of Statistics, Texas A&M University, College Station, TX.
Jianhua Z
JZ
Huang
Department of Biostatistics, Division of Quantitative Sciences, The University of Texas MD Anderson Cancer Center, Houston, TX.
Jianhua
J
Hu
Functional PCA; Missing data; PCA; Profile likelihood; Transformation model