Solving Sparse PCA Based On The Optimization Methods On Riemannian Manifolds

PCA is a popular tool in data analysis, dimension reduction and visualization. Sparse PCA is an improved method in order to overcome the difficulty of the interpre-tation of principal component in the PCA calculation. Sparse PCA is a manifold con-strained optimization problem. However, the effect is not very well when calculating the problem by taking the spherical constraint as an equality constraint. In this paper, we attempt to transform the nonlinear constrained optimization problem into an opti-mization problem on Riemannian manifolds. We also establish a line-search method on Riemannian manifolds to solve it. During the process of algorithm building, we give the determination and calculation method of the descent direction of non-smooth func-tions on Riemannian manifold in detail. At last, this paper verify the convergence and feasibility of our algorithm by numerical experiments.