Method For Robust Principal Component Analysis Based On L_p Norm

Robust Principal Component analysis can separate a low-rank matrix and a sparse matrix from a given data matrix.It can be applied in many area of engineering,such as Video Surveillance,Face Recognition,Image alignment.Robust principal component analysis problem has attracted many scholars attentions on it,and they have proposed several algorithms to solve the model,such as proximal gradient method(PGM),alternating direction multiplier method(ADMM)and Frank-Wolfe method.These methods can converge and have a good performance in computing speed.But these methods all need to calculate the singular value decomposition,and the singular value decomposition costs too much time,and l1-norm is not the perfect approximation of l0-norm,the sparse component may be not strictly sparse but rather approximately sparse.In practice it may lead to significantly biased estimates.In this paper,we present the following improved method:1.We propose a non-convex RPCA model based on l1/2-norm in order to obtain better solutions.By applying the half threshold algorithm to calculate the l1/2norm,we then use alternating direction multiplier method to solve the model.The weak convergence analysis of the algorithm is also given.Numerical experiments show the efficiency of the algorithm.2.Based on the l1/2 RPCA model,we add a weighted matrix to the sparse component of the model to treat each element differently and highlight the effect of each element,use lp norm to replace l1/2-norm.We use the generalized soft threshold algorithm to calculate the lp norm,and we compare the selection of p values in(0,1)through experiments.the experimental results show that the corresponding model has good recoverability,the selection of p influences the running time and the experiment results...