Manifold optimization is ubiquitous in computational and applied mathematics, statistics,
engineering, machine learning, physics, chemistry, etc. One of the main challenges usually …

In this paper, we study the generalized subdifferentials and the Riemannian gradient
subconsistency that are the basis for non-Lipschitz optimization on embedded submanifolds …

This paper is devoted to studying an augmented Lagrangian method for solving a class of
manifold optimization problems, which have nonsmooth objective functions and nonlinear …

This paper investigates fairness and bias in Canonical Correlation Analysis (CCA), a widely
used statistical technique for examining the relationship between two sets of variables. We …

Robust low-rank matrix completion (RMC), or robust principal component analysis with
partially observed data, has been studied extensively for computer vision, signal processing …

Clustering is a key technique in segmenting data into different groups of similar
observations. As clustering is an unsupervised learning method, the latent cluster …

Riemannian optimization has drawn a lot of attention due to its wide applications in practice.
Riemannian stochastic first-order algorithms have been studied in the literature to solve …

Spectral clustering is one of the fundamental unsupervised learning methods and is widely
used in data analysis. Sparse spectral clustering (SSC) imposes sparsity to the spectral …

We consider optimization problems over the Stiefel manifold whose objective function is the
summation of a smooth function and a nonsmooth function. Existing methods for solving this …

2,1 norm minimization with orthogonality constraints, which comprise a feasible region
called the Stiefel manifold, has wide applications in statistics and data science. The state-of …