Following the entire solution path of sparse principal component analysis by coordinate-pairwise algorithm

In this paper we derive an algorithm to follow the entire solution path of the sparse principal component analysis (PCA) problem. The core idea is to iteratively identify the pairwise variables along which the objective function of the sparse PCA model can be largely increased, and then incrementally update the coefficients of the two variables so selected by a small stepsize. The new algorithm dominates on its capability of providing a computational shortcut to attain the entire spectrum of solutions of the sparse PCA problem, which is always beneficial to real applications. The proposed algorithm is simple and easy to be implemented. The effectiveness of our algorithm is empirically verified by a series of experiments implemented on synthetic and real problems, as compared with other typical sparse PCA methods.