Best Subset Solution Path for Linear Dimension Reduction Models Using Continuous Optimization.

Area of Science:

• Multivariate Statistics
• Machine Learning
• Data Science

Background:

• Variable selection is challenging in high-dimensional data, where the number of variables exceeds observations.
• Principal Component Analysis (PCA) and Partial Least Squares (PLS) are popular linear dimension-reduction techniques.
• Interpreting principal components can be difficult with a large number of original variables.

Purpose of the Study:

• To integrate the best subset solution path method into PCA and PLS frameworks.
• To address the interpretability challenge of principal components in high-dimensional data.
• To offer a new approach for identifying the most relevant variables for dimension reduction.

Main Methods:

• Casting the best subset solution path method into PCA and PLS frameworks.
• Utilizing a continuous optimization algorithm for the best subset solution path.
• Empirical studies and analysis of two real-world datasets.

Main Results:

• The proposed approach demonstrates efficacy in providing a best subset solution path.
• Successful application of the algorithm to PCA and PLS frameworks.
• Validation through the analysis of two distinct real datasets.

Conclusions:

• The novel method enhances the interpretability of principal components by selecting the most relevant variables.
• The continuous optimization algorithm provides an effective solution for best subset selection in PCA and PLS.
• The approach offers a valuable tool for high-dimensional data analysis across various scientific fields.