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.
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).