Partial Least Squares Regression on Riemannian Manifolds and Its Application in Classifications

TL;DR

This paper introduces novel Partial Least Squares Regression models on Riemannian manifolds, enabling globally optimal solutions and improving performance in pattern recognition and classification tasks.

Contribution

It develops Riemannian manifold-based PLSR models and optimization algorithms that achieve globally optimal solutions, surpassing traditional Euclidean-based methods.

Findings

Proposed models outperform Euclidean-based PLSR in experiments.

Algorithms achieve globally optimal solutions avoiding local minima.

Enhanced classification accuracy demonstrated in pattern recognition tasks.

Abstract

Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two datasets. However, most of algorithm implementations of PLSR may only achieve a suboptimal solution through an optimization on the Euclidean space. In this paper, we propose several novel PLSR models on Riemannian manifolds and develop optimization algorithms based on Riemannian geometry of manifolds. This algorithm can calculate all the factors of PLSR globally to avoid suboptimal solutions. In a number of experiments, we have demonstrated the benefits of applying the proposed model and algorithm to a variety of learning tasks in pattern recognition and object classification.