Research And Application Of Low-Rank Recovery For Multi-subspace Manifold Data

The rapid development of modern data and information makes the collected information very different from the past.Different from the simple low-dimensional data in the past,high-dimensional data with thousands of dimensions such as images and videos is readily available.In such a rapidly expanding data era,effectively utilizing these higher dimensional and highly unstructured data is an important task in the context of this era.Especially in some practi-cal applications in the field of graphics computing vision,computer science,text information un-derstanding,and biological information mining,the processed data has the characteristics of high dimension,huge data,complex content,and unknown types.And the number and di-mension will continue to increase over time.How to find meaningful and regular infor-mation hidden in a large amount of high dimensional information,and to extract the hid-den features of these data,while at the same time building a model with predictive function,are important research directions at this stage.Manifold learning was first proposed in two consecutive articles in Science in 2000,in which it was proposed that high dimensional data is distributed in a manifold state in a high di-mensional spatial structure.When processing these high dimensional manifold data,it should be expanded into low-dimensional space for processing.The idea of manifolds guides a direc-tion for nonlinear dimensionality reduction methods.This paper studies high-dimensional man-ifold data.Since the specific manifold structure of the data itself in the high-dimensional space cannot be detected,this paper extracts the multi-subspace structure of the high-dimensional manifold data through the low-rank recovery method to effectively indicate the effect of the classification algorithm.It is divided into three stages to solve the above problems: 1.Under the participation of unlabeled information,low-rank multi-subspace extraction is performed on all high-dimensional manifold data,and the extracted multi-subspace structure data is used for the classification algorithm? 2.Carry out low-rank extraction of multi-subspace structure of high-dimensional manifold data through label guidance,and simultaneously train to obtain a classifier suitable for the multi-subspace structure data? 3.Under the guidance of only a few labels,perform low-rank recovery of high-dimensional manifold data and incomplete labeling of unlabeled data,and train a classifier suitable for the multi-subspace structure at the same time.The main research contents and contributions of this thesis include:1.A data representation learning method that combines sparse dictionary representa-tion and low-rank self-representation is proposed.The data representation with multi-subspace structure extracted by the low-rank self-representation model fuses the sparse reconstruction of each data extracted by sparse dictionary learning to construct a new data representation method.The extracted data representation is used in the classifi-cation algorithm to improve the classification accuracy of the algorithm.In addition,in order to efficiently solve the joint data representation model,this paper proposes a general low-rank representation learning model,and obtains its closed-form solu-tion through strict mathematical derivation,thereby greatly improving the calculation speed of the model.Finally,it is verified that the joint data representation can bet-ter improve the accuracy of the classification algorithm and obtain a more accurate dictionary on high-dimensional manifold data such as handwritten fonts,faces,and objects.2.A robust multiple logistic regression model using nonlinear terms to learn the nonlinear relationship between label information and data is proposed.A more robust nonlinear classifier is learned while adding multi-subspace information related to labels in the process of data low-rank recovery.The research uses the alternating direction multi-plier method to solve the non-convex nonlinear model and prove its convergence.The performance effect of the algorithm is verified by comparative experiments on im-age restoration and classification and recognition of high-dimensional manifold data such as artificially synthesized data,handwritten font data,face image data,and object recognition data.3.A labeled-robust regression model that can simultaneously perform low-rank recov-ery,label completion,and classification training of high-dimensional manifold data is proposed.Firstly,a nuclear norm model for low-rank recovery of multi-subspaces in-volving labels is proposed,and the low-rank recovery of multi-subspaces is performed by using label-guided data.When there are only a few labeled samples,it is further studied that the low-rank restoration of the disturbed high-dimensional manifold data is performed by the low-rank restoration effect of the labeled nuclear norm model,and the low-rank completion of the unlabeled data is performed.A labeled robust re-gression model is proposed.The multi-subspace recovery capability of the proposed method is validated on synthetic bilunar manifold data.In the high-dimensional image data of faces and objects,the classification effect and low-rank recovery effect of the proposed algorithm are verified in the case of only a small amount of labeled data.