The Eigentensor Based Multi-model Analysis And Research Of Big Data

With the rapid development of information and communication technologies,such as pervasive computing,Internet of Things,crowdsourcing and social networks,the data which describe and record human in Social space,Cyber space and Physical space are growing rapidly,the data scale is becoming larger and larger,and the data semantics are becoming richer and richer.CPSS(Cyber-Physical-Social Space)big data has been emerging.CPSS big data analysis is a very important research topic in the field of big data,which has attracted wide attention from academia and industry.In the era of CPSS big data,not only the magnitude and the structure of data have changed profoundly,but also the characteristics and rules embedded in data are related to multiple spaces'factors,which show multi-source,heterogeneous and multi-modal features.How to mine valuable,poten-tial,complex multi-modal features and semantic associations from massive,heterogeneous,high-dimensional and dynamic CPSS data has become a key and urgent problem,which requires new data models and mining algorithms.Therefore,it is of great theoretical and practical significance to establish the theory of multi-modal analysis,put forward the multi-modal processing model,and study the multi-modal processing algorithm for big data.This thesis focuses on the problem of big data multi-modal analysis,including large data multi-modal prediction,multi-modal dimensionality reduction,multi-modal knowledge discovery and so on.The main contributions of this thesis are summarized as follows:1.Proposing the eigentensor theory.The eigentensor is the expansion of eigenvector of matrix in modal.In space theory,it is the tensor basis,which is the generalization of vector basis in modal.Eigentensors make data features generalize from single modal space to multi-modal space,provide a theoretical basis for multi-model analysis and research of big data.2.To complete multi-modal prediction,the thesis proposed multi-modal prediction framework.A multivariate multi-step transition tensor(M~2T~2)model is proposed for multi-modal prediction.A novel algorithm to construct the corresponding transition tensor.Then,the thesis proposes a tensor based iterative algorithm to obtain the stationary probability(eigentensor),and prove the convergence of the algorithm.Also,the existence and unique-ness of the tensor stationary probability distribution is proved.Furthermore,the thesis ex-tends multi-modal prediction framework and combines multi-spaces random walk with tran-sition tensor to complete the multi-space prediction.Also,the proposed inter tensor power method(ITMP)'s convergence,the existence and uniqueness of the stationary probability distribution tensors are proved.3.Multi-modal Dimension Reduction for Big Data:A new tensor decomposition is proposed for dimension reduction for Big Data.Which decomposes a high order tensor into a core tensor and the orthogonal tensor basis(eigentensors).The proposed tensor decom-position is a multi-modal decomposition method and imposes the orthogonal constraints on the multi-models.In order to overcome high computational complexity problem in the or-thogonalization process,the high-order bidiagonal Lanczos method(HOBL)is developed.Furthermore,an incremental tensor decomposition method is proposed to update the orthog-onal tensor basis and core tensor for dynamic dimension reduction.4.Multi-modal Markov Decision Process(MMDP)model is proposed to model Multi-modal Reinforcement Learning(RL),the model consists of multi-modal state,multi-modal action,multi-modal transition tensor.To complete a tensor policy discovering,a tensor based method is developed to construct Action-aware Transition Tensor(ATT),which is used to fuse the heterogeneous data from the CPSS.In order to solve multi-modal knowledge discovery and multi-modal policy in CPSS space,a tensor Bellman equation is constructed with Action-aware Transition Tensor(ATT).Furthermore,a tensor based iterative optimization method is proposed to solve the multi-modal knowledge discovery and tensor optimal policy.