Research On Low Rank Matrix Recovery And Deep Cascade Broad Learning System

In recent years,low rank matrix recovery and deep learning as two powerful tools have attracted considerable attention in numerous fields of pattern recognition,image processing and computer vision,which could effectively analyze and deal with redundant information and noise perturbation in data.However,the existing low rank matrix recovery methods have problems such as poor approximation ability and stability.The deep learning method involves many parameters,complicated structure and time-consuming in the training process.These defects greatly affect the performance of the algorithm.This dissertation develops systematic research and discussion from the two perspectives of low rank matrix recovery and deep learning.Based on the discussion of existing algorithm,a series of effective algorithms are designed by integrating the methods such as rank approximation and broad learning system.Then these algorithms are applied to the practical applications including image denoising,image completion and recommendation system.The specific research work is summarized as follows:1.A rank approximation method for mixture noise removal of hyperspectral images is proposed.Hyperspectral images contain various types of noises,and how to remove the mixture noises is extremely important for subsequent processing.Conventional methods require some specific prior knowledge of noises and they can deal with only one or two kinds of noises.Nevertheless,the existing low rank matrix recovery methods always cannot effectively approximate the rank function,thereby affecting the denoising performance.In order to overcome these problems,we construct a smoothing function to directly approximate the rank function,and propose a smooth rank approximation(SRA)model to handle the mixture noises of hyperspectral images.Further,according to the difference of convex strategy and the augmented Lagrange optimization method,we design an effective SRA algorithm and analyze its convergence,ensuring the effectiveness of the proposed algorithm.Experimental results show that the SRA algorithm can quickly and effectively remove the mixed noises of hyperspectral image.2.A hybrid truncation norm(HTN)regularization method based on matrix completion is presented.For data with incomplete or missing entries,a common approach is to use matrix rank minimization to convert it into a matrix completion problem.However,traditional methods based on nuclear norm and its variants do not approximate the rank function very well.In recent years,truncated nuclear norm has been considered as a good substitute of the rank function due to their excellent performance,but the stability remains a challenge.Based on this,we introduce a new truncated Frobenius norm,and propose a hybrid truncated norm model that integrates the truncated Frobenius norm with the truncated nuclear norm in order to improve the effectiveness of the model and enhance its stability.To address this model,we design an effective two-step iterative algorithm and give the corresponding adaptive penalty parameter selection rules.Further,the convergence of the proposed method is analyzed.Experimental results illustrate that the HTN method can effectively improve the restoration effect and promote the stability of the model.3.An adaptive regularization deep cascade broad learning system is built.Most deep learning methods would be subjected to a great number of parameters,complicated structures,time-consuming and involve highly nonconvex optimization problems.Broad learning system(BLS)provides an effective learning framework for processing large-scale data,has the ability to learn quickly,and has achieved good effects in areas such as pattern recognition.In order to enable BLS to extract more sufficient data information and achieve good stability,we propose an adaptive regularization deep cascade broad learning system(DCBLS).This method attempts to extract more effective information from the data by building two deep structures,and then fuses and transmits the two deep structures to the output layer so that we can establish a convex regularized deep cascade broad learning system model,thereby enhancing the stability of the model and improving the representation ability of the model.Further,it is usually difficult to deal with large-scale data due to the cases such as storage of computers,a parallelization framework of the proposed DCBLS is presented.Meanwhile,an adaptive regularization parameter selection strategy based on some assumptions is given.Later,we discuss the stability and error estimates of the proposed model.Experimental results verify the effectiveness and efficiency of the proposed DCBLS in comparison with the state-of-the-art approaches for image denoising.