Robust Principal Component Analysis Based On Hybrid Truncation Nuclear Norm

With the rapid development of computer technology and artificial intelligence,people need to collect,process and analyze tensor data with higher dimensions and more complex structures.However,in practical life,due to factors such as weather,object occlusion,and communication interference,tensor data may be lost or noisy during the collection process.How to effectively recover high-quality tensor data from degraded data by utilizing the low rank properties of tensors is an important research topic in the field of machine learning.The low rank recovery model proposed based on tensor singular value decomposition uses tensor nuclear norm to relax the rank function.It requires minimizing all singular values simultaneously,which inevitably increase the penalty for larger singular values and cause excessive shrinkage.This is not conducive to characterizing the low rank structure of tensors.When the original tensor data has fewer known elements,the tensor nuclear norm recovery model is unstable.A tensor robust principal component analysis model with hybird truncated nuclear norm is proposed to address the above shortcomings.Firstly,a hybird truncated nuclear norm of tensor nuclear norm and tensor Frobenius norm is defined,and this hybird truncated nuclear norm is used to approximate the rank function of the tensor.The tensor hybird truncated nuclear norm minimize,m n()i m n-r singular values,which effectively solves the problem of over shrinking of the nuclear norm regularization.The introduction of tensor truncated Frobenius norm also improves the stability of the model.Secondly,an effective method for solving the proximal operator of hybird truncated nuclear norm was proposed.The optimization model was solved using the alternating direction multiplier method.In order to reduce computational complexity,an adaptive method for changing penalty parameters was proposed.Finally,the effectiveness of this method was demonstrated through experimental results of synthetic and real data.