Integrating Data Transformation in Principal Components Analysis.

Area of Science:

• Statistics
• Data Science
• Machine Learning

Background:

• Principal Component Analysis (PCA) is crucial for reducing high-dimensional data complexity.
• Skewed data distributions often necessitate data transformation before PCA, typically determined empirically.
• Existing methods lack integrated, data-driven approaches for transformation selection.

Purpose of the Study:

• To develop a novel model-based method for integrating data transformation within PCA.
• To automatically determine optimal data transformations using maximum profile likelihood.
• To extend the method for functional data and handle missing values.

Main Methods:

• A model-based approach integrating data transformation and PCA.
• Utilizing maximum profile likelihood for optimal transformation selection.
• Developing numerical algorithms for computational efficiency and extensions for functional data and missing values.

Main Results:

• Demonstrated effectiveness of the integrated transformation-PCA method on simulated and real-world datasets.
• Successful handling of skewed data distributions.
• Efficient computation through provided numerical algorithms.

Conclusions:

• The proposed method offers a robust and data-driven approach to dimensionality reduction for skewed data.
• It provides a more principled way to select data transformations compared to empirical methods.
• The extensions enhance its applicability to diverse and complex datasets.