Research On Incremental Multi-attribute Singular Value Decomposition Algorithm Of Tensor

With the continuous integration of network information technology into all walks of life and more serving the production and life of human society,the integration of the real world and the virtual world has been strengthened,and the data is also developing towards high-dimensional.A large number of multi-dimensional and multi-attribute data have emerged in many scenes,such as industry,medical treatment,transportation,etc.The traditional way to express low-dimensional data can't fully meet the needs of analysing multi-attribute data for all walks of life currently.As high-order data,tensor is the promotion from low-order data to high-dimensional space,which can express the relationship between the attributes corresponding to different orders naturally.Tensor decomposition decomposes tensor data into several tensor factors with some special properties,which is an important tool for tensor analysis.The results obtained by traditional tensor decomposition methods are often related by single-mode multiplication.However,single-mode multiplication corresponds to a single attribute,and the connection between factors is single,which can not make full use of the multi-attribute characteristics of tensor.The tensor multi-attribute singular value decomposition studied in this thesis is a novel tensor decomposition method,which is different from the traditional tensor decomposition into the form of single-mode multiplication between factors.This method decomposes the tensor into the form of multiplication between factors through multimode multiplication,which is conducive to extracting the features of tensor from multiple modes.At the same time,it can effectively reduce the data size while retaining the main information of the data through interception.In many practical application scenarios,data will be generated continuously,so it is necessary to constantly update the tensor data.Simply merging historical data and incremental data for direct decomposition can not effectively use the existing decomposition results,which will cause a waste of computing resources.In order to improve the economy of the calculation process,this thesis studies the incremental method of multi-attribute singular value decomposition method.This thesis takes tensor as the core,and the research contents are summarized as follows: a multi-attribute singular value decomposition method of tensor is proposed.The decomposition results of classical tensor decomposition methods are mostly in the form of single-mode multiplication between factors.Single-mode multiplication only corresponds to one module,and multi-mode multiplication corresponds to multiple modules.Based on this,this thesis studies and proposes a multi-attribute singular value decomposition method of tensor.The result obtained by decomposing the tensor is in the form of multi-mode multiplication between factors.For the multi-attribute singular value decomposition in incremental scenarios,the merging rules under different growth orders are discussed,and the incremental method of tensor multi-attribute singular value method is given.The numerical experiments of multi-attribute singular value decomposition and its application in multi-attribute signal processing are carried out to verify the feasibility of multi-attribute singular value decomposition in feature extraction.