Improved Distributed Tensor Train Decomposition Based On Tensor Slicing

With the arrival of the Age of Big Data,traditional vector or matrix format for data representation methods are no longer sufficient to fully express the various attributes of the target.Tensor,as the extension of vectors or matrices in higher-order spaces,has attracted widespread attention as soon as it has been arisen.If each order of the tensor represents a certain attribute of the target,then the tensor could express each attribute of the target naturally and completely.The amount of data,however,will surge exponentially with the increase of the order,how to deal with huge tensor data,like storing,decomposition and compression,has become a problem.Tensor-train decomposition decomposes a high-order tensor into the products of low-order tensors in the chain form,achieving O(logN)dimensionality reduction,is an ideal solution to the problem of curse of dimensionality.Due to its remarkable superiority in dimensionality reduction,tensor train decomposition algorithm has been widely applied in many fields.Distributed tensor train decomposition method makes the iterative process into parallel,which significantly improves the effec-tiveness of algorithm.However,due to its unique reshaping methods,tensors cannot be divided along any orders which seriously restrict the promotion of distributed tensor train decompositon.In this thesis,based on tensor slicing and distributed tensor train decomposition based on algorithm parallel,two improved algorithms has been proposed which can solve the problems mentioned above and imrpove the scalablity and applicability.The summary of teh main research of this thesis is as follows.1.An improved tensor train decomposition method which divide the tensor along any order is proposed.By studing the discipline of tensor train decompositon reshaped matrix and the property of minimum block invariance,the relationship between the merged matrix of the sub-tensor by dividing along the first or last order and the direct expansion matrix of the original tensor is derived.The improved tensor train decomposition method which divide the tensor along first or last order is proposed.Then,based on it,a more applicable method called improved tensor train decomposition method which divide the tensor along any order is proposed.2.Multi-order distributed tensor train decomposition algorithm is proposed in this thesis.The feasibility of various cutting strategies has been deduced and verified.The algorithm for dividing tensors along a single order is further extended to multi-orders.At the same time,a distributed incremental tensor train decomposition algorithm is proposed to avoid the problem of repeating calculation of historical data when newly data is added.Finally,numerical experiments and CT application experiments were carried out on the Canadian Computing Center platform,which proved the effectiveness and superiority of the algorithm,and verified the feasibility of the algorithm in feature extraction.