Feature extraction based on Lp-norm generalized principal component analysis

In this paper, we propose Lp-norm generalized principal component analysis (PCA) by maximizing a class of convex objective functions. The successive linearization technique is used to solve the proposed optimization model. It is interesting to note that the closed-form solution of the subproblem in the algorithm can be achieved at each iteration. Meanwhile, we theoretically prove the convergence of the proposed method under proper conditions. It is observed that sparse or non-sparse projection vectors can be obtained due to the applications of the Lp norm. In addition, one deflation scheme is also utilized to obtain many projection vectors. Finally, a series of experiments on face images and UCI data sets are carried out to demonstrate the effectiveness of the proposed method.

► We propose Lp-norm generalized PCA by maximizing the convex objective function. ► The successive linearization technique is used to solve the optimization model. ► We provide a complete proof of convergence for our method under proper conditions. ► One deflation scheme is also used to obtain many projection vectors. ► The experiments are done to demonstrate the effectiveness of the proposed method.