A Sparse Semismooth Newton-Based Manifold Algorithm for Partial Least Squares

Partial least squares (PLS) is a famous dimensionality reduction tool, which is widely used in signal processing. Although a lot of solvers exist in the literature, to the best of our knowledge, there are no fast optimization algorithms available for high-domensional PLS problems. To this end, we first construct a sparse and robust PLS model with good prediction performance and efficient feature selection. More importantly, we develop a semismooth Newton-based manifold proximal gradient algorithm by exploiting the sparse structure. Numerical comparisons validate its higher efficiency over state-of-the-art algorithms.