The Application Of Tensor Decomposition On High Dimension Time Series

With the deepening of big data research,the role of tensor is becoming more promi-nent.Most deep learning frameworks use tensor as the basic data structure.Since the dimension of tensor is often high and the data occupies a lot of memory,the introduction of data compression method becomes very important.This paper chooses tensor decom-position as the main means of data compression.On the one hand,the high-dimensional data used in this paper has a sparse structure,tensor decomposition is particularly good at compressing such data,and the other reason is that tensor decomposition algorithms are more efficient than other data compression methods.In Chapter 4 and Chapter 5,Quantic Tensor Train(QTT)decomposition and Tensor Train(TT)decomposition are selected for the specific form of the data respectively.The results show that compress-ing data in this way can not only reduce memory consumption and improve calculation efficiency,but also optimize the accuracy of the model to a certain extent.The article mainly does the following three parts of work:1.Through theoretical analysis,it is proved that the quantic tensor train decom-position has core tensor invariability to time series data,which means in the modeling process,the data predicted by the coefficient tensor can be recovered by the time se-ries core tensor in a short period of time,which is also the basic guarantee for video prediction;2.The fourth chapter combines the quantic tensor train decomposition with the traditional time series model.By decomposing the video data to reduce the data dimen-sion,the meaning of the decomposed data are fully analyzed.Dividing data into QTT coefficient tensor and QTT core tensor and using the former as the data sets predicted by the model can not only further reduces the amount of data,but also is more effective to achieve parallel computing.Improvements have been made in both terms of space and time;3.By analyzing the current model for predicting high-dimensional time series through neural networks comprehensively,we divided the high-dimensional time series into space and time states.Effective information is extracted from these two states for se-quence prediction,and the network model is compressed through tensor train decom-position,which increases the model learning ability and memory utilization.