Robust Low-rank Matrix Factorization And Its Application

With the development of scientific technology,we have been pushed to the waves of big data processing.In addition to the 5V characteristics,namely,Velocity,Variety,Value and Veracity,big data also has a very important feature named high-dimensional.When the dimension of the data is very high and the available information of the data is limited,it often causes the problem of insufficient sampling,and the data is easy to be contaminated by noise.Thus it is a great challenge to construct a model to discover the structure implied in the data and to predict the unknown space properly.How to model these high-dimensional data effectively? How to mine the potential structure of data informatively and fatherly predict the unknown space accurately? All these problem are very important and challenging.According to recent scientific researches,we can see that high-dimensional data is not really irregular.Through reasonable sparse or low-rank hypothesis,we can explore the correlationship among different data samples and the correlationship among various features of the data,and then make a wise decision or inference.However,due to the fact that the data itself may have been corrupted by various unknown forms of noises,such as Gaussian noise,sparse random noise,specific sample noise,anomalous samples,etc.,the data samples are distributed with different deviations from the subspaces.Under such a situation,the estimation of the data distribution,classification,prediction and many other applications have great challenges.In this paper,we apply the low-rank matrix decomposition method in high dimensional data classification and denoising.To simplify the complex computation,enhance the separability among different class,make thorough advantage of label informations,a simplified and robust low-rank matrix factorization model and a semi-supervised low-rank learning method are proposed.In the field of image processing and computer vision,Low rank matrix factorization is widely used to model the low-rank background of video frames.Low-rank matrix factorization can not only restore the background of the image completely,but also detect the moving object.However,due to the existence of small amplitude changes and lighting changes in the background,the moving objects detection results are easy to be disturbed by the false alarms.To solve these problems,this paper proposes a robust low rank matrix factorization method based on the Bayesian hierarchical model.It utilizes the Poisson factor analyses and considers the spacial continuity of the objects and the parameter adaptiveness of the model.The works of this paper are summarized as follows:Firstly,to settle the problem existed in the low-rank graph based semi-supervised classification,such as highly complex computation,low separability among different classes in the obtained low-rank representation and the conflict between sparse and low-rank constraints,a simplified sparse consistent and low-rank representation method is proposed.The sparse consistent constraint is a Two-dimensional sparse.The low-rank representation in the proposed method is not only sparse in the hidden representation but also share a similar sparse pattern within the same subspace.The proposed method make the low-rank representation sparse with the correlationship between different samples considered.Thus,it not only enhanced the separability among different subspaces but also speed up the convergence of the model.The experimental result show that the proposed method manages to obtain an acceptable classification results even when the data is heavily corrupted.Secondly,in the traditional low-rank graph based semi-supervised classification method,the classification process is sensitive to the distribution of the labeled data and the construction of the low-rank graph is not directly related to the final classification results.To settle these problems,a graph laplacian constrained semi-supervised low-rank matrix factorization method for classification is proposed.By imposing a similar low-rank graph relationship on the data space and the label space.The label information is propagated to the low-rank matrix construction procedure,which results in the iterative updating between the label prediction and graph construction,and finally,a more proper resolution is obtained.Thirdly,in the application of saliency detection,it is often the case that there exist some bright in color while widely distributed false objects in the area of background.To recognize the true saliency objects from these false ones,a global contrast and local consistency regularized low-rank matrix factorization method is proposed.The global contrast measure combines the boundary connectivity and the distribution of a super-pixel and the proposed model has its sparse part adaptive to the input data.The experimental results demonstrate that the proposed model with adaptive sparse constraint is capable of avoiding the false objects of highly boundary connectivity and of widely distributed.It enhances the accuracy of saliency detection results.Fourthly,moving objects detection is the key technology of objects recognition,objects tracing and action perception.When applied in moving objects detection,the existed lowrank matrix factorization based methods are sensitive to the switching lights and dynamic backgrounds.To settle this issue,a Bayesian hierarchical model based robust non-negative low-rank matrix factorization method is proposed.It considers both the continuousness and compactness of the objects.And at the same time,to save the efforts for tuning the parameters between the low-rank and sparse constrains,a proper prior and super-prior for the lowrank and sparse parts are provided.The experimental results demonstrate that the proposed model is capable of both detecting smooth and continues moving objects and recovering the background with more details.Fifthly,the existed low-rank matrix factorization methods are batch learning based,and thus it is not scalable to data of large size and not possible to realize the online processing in moving objects detection.To settle these problems,a self-representation based low-rank matrix factorization method is proposed.It enables a new sample processing by learning a mapping process which is in corresponding to the generative of the data.Thus,it meets the online processing of the video properly.The model is trained with mini-batch,thus it is scalable to large-scale data.Due to the fact that a mapping directly from the input data is sensitive to over-fitting,a mapping from the recovery error is adopted.It reduced the complexity of the model and at the same time speed up the convergence.