Low-rank Regularized Tensor Decomposition For Subspace Learning

With the advance of sensors,network and streaming technologies,large-scale multidimensional data observed from different perspectives or captured by different sensors has received wide attention from researchers.Data from multiple sources can form a multiplexed array,and tensors provide a natural representation of the data.Since raw visual data typically has a large size that is prone to dimensional catastrophe and over-fitting problems,it is desirable to find low-dimensional representations of raw data and assist learning algorithms by minimizing redundancy and noise.Subspace learning has proven to be an effective way to solve these problems.In this paper,the research on high-order data subspace learning is carried out.Firstly,the main methods of subspace learning,such as Principal Component Analysis(PCA),Linear Discriminant Analysis(LDA),Sparse Subspace Clustering(SSC),Manifold Learning etc,are briefly introduced and summarized.Then the feature extraction method based on tensor decomposition is sorted out.Then the key research of this paper is positioned on the subspace learning method.The supervision of tensor decomposition and the unsupervised subspace learning method are studied.For high-order data,especially for visual data,low rank regularization is introduced to eliminate sample redundancy,mining potential structural information,and a large number of experiments are conducted to verify the effectiveness of the proposed algorithm.The main contents and contributions of this article are mainly as follows:The subspace learning problem of high-order data is introduced.Through the in-depth study of the existing subspace learning algorithm,we find that vectorization of tensor data can not make use of the complete structural information,and it is promising to exploit the subspace learning algorithm based on tensor decomposition.Exploring the subspace learning algorithm based on tensor decomposition,introducing low rank regularization constraints,can not only use tensor structure to characterize multidimensional data,preserve the relationship between data,but also combine the idea of low-rank representation to remove data redundancy and discover the global structure information.Aiming at the proposed low-rank regularized tensor decomposition subspace learning method,the algorithm under supervised and unsupervised conditions is studied.The iterative solution process and specific steps of the algorithm implementation are described in detail,and the algorithm is verified on a large number of real data sets.Finally,the subspace learning idea combining low-rank representation and tensor decomposition is extended,and the potential of tensor decomposition in high dimensional data processing and analysis is prospected.