Tensor Train Big Data Fusion Mode Based On Lanczos Method

The world today has entered an era of rapid development of information technology.The scale of data has grown exponentially,and the value of big data has received increasing attention.With the deepening of networked applications,especially the development of technologies such as Internet+,big data,cloud computing,and Internet of Things,information and physical systems are further integrated,and networks and human society are seamlessly integrated to form a more complex system of people,machines,and information,that is,a Cyber-Physical-Social System(CPSS).In CPSS,massive data is generated,which has the characteristics of large volume,multiple types,high dimensionality,and low value density.So how to integrate these data into one to analyze and extract key features is an urgent problem to be solved.The past algorithms are difficult to apply to the existing big data scale.At present,the more effective method is to use tensors to represent big data,and then use tensor calculation,decomposition,modular multiplication and other methods to analyze and process big data.However,there may be different tensor decomposition methods for different local CPSS systems.At present,there is no unified method for unifying different tensor decomposition forms and processing them.Based on this,this thesis proposes a new tensor fusion mode.A variety of different tensor decompositions such as Tucker decomposition and CP decomposition can be uniformly converted into Tensor-Train(TT),and then the unified tensor can be analyzed and processed.The tensor chain is an emerging tensor representation,which uses a low-rank tensor core connection,which greatly reduces the tensor storage space.In this thesis,the internal optimization of TT decomposition is also carried out.The tensor chain decomposition TT-LSVD based on Lanczos method is proposed,which simplifies the singular value decomposition that is crucial in the TT decomposition process.This step mainly adopts the singular value decomposition based on Lanczos method.Then the simulation experiment is designed to verify the feasibility of the proposed algorithm,and the computational efficiency of the optimization algorithm and the traditional algorithm are compared.Finally,the whole model is applied to the recommendation system.The experimental results show that the proposed algorithm has better recommendation effect and higher computational efficiency.