Solving Partial Least Squares Regression via Manifold Optimization Approaches.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Partial Least Squares Regression (PLSR) is widely used for analyzing relationships between data sets.
• Existing PLSR methods optimize models in Euclidean space sequentially, often leading to suboptimal solutions.
• The successive calculation of factors in traditional PLSR can result in mutually orthogonal but not globally optimal factors.

Purpose of the Study:

• To develop a novel approach for Partial Least Squares Regression (PLSR) that avoids suboptimal solutions.
• To adapt the Statistically Inspired Modification of PLSR (SIMPLSR) for optimization on Riemannian manifolds.
• To introduce a sparse SIMPLSR method on Riemannian manifolds for improved performance.

Main Methods:

• Transforming SIMPLSR into optimization problems on Riemannian manifolds.
• Developing new optimization algorithms to compute all PLSR factors simultaneously.
• Proposing a sparse SIMPLSR model tailored for Riemannian manifolds.

Main Results:

• The proposed algorithms calculate all PLSR factors concurrently, preventing suboptimal solutions.
• Experiments show lower classification error rates compared to traditional Euclidean-based linear regression methods.
• The sparse SIMPLSR on Riemannian manifolds demonstrates effectiveness and simplicity.

Conclusions:

• Optimizing PLSR on Riemannian manifolds offers a superior alternative to Euclidean space methods.
• Simultaneous calculation of factors on manifolds avoids suboptimality and enhances model performance.
• The novel sparse SIMPLSR on Riemannian manifolds provides a powerful tool for classification problems.