Parameter-free nonlinear partial least squares regression model for image classification

Abstract

Partial least squares regression (PLSR) is a linear regression model suitable for handling data with high dimensions and small samples. However, a large amount of nonlinear structure data exists in real life, and PLSR may be not good at handling this type of data. Motivated by this, we propose a parameter-free, nonlinear PLSR model called estimating optimal transformations PLSR. First, we use the EOT model to transform a nonlinear data structure into a linear data structure without additional parameters by maximizing the correlation between data samples. In addition, the traditional PLSR model often uses a greedy algorithm, leading to suboptimal solutions. To obtain more accurate numerical solutions, we propose using manifold optimization for the PLSR model. Compared to the other existing PLSR models, our proposed model achieves lower classification error rates on several different types of datasets. The experimental results further confirm the importance of our proposed nonlinear data transformation and manifold optimization for feature extraction with nonlinear structure data.