Research On Methods And Theory Of Tensor Learning For Complex High-dimensional Data

With the continuous development of the Internet,mobile Internet,Internet of Things and the rapid development of storage and communication technology,we can get more and more data which has great potential value.Data has become an important economic asset for the development of human society.Machine learning builds models or discovers knowledge from massive data sets,which provides algorithms and techniques for data analysis and data mining.Therefore,machine learning,as a key means to detect the value of data,plays an extremely important role in large data research In the real world,a number of data are presented in complex and high-dimensional form.Data contains many attributes or features,which is a great challenge to traditional machine learning.In this dissertation,the following aspects of research are specifically carried out:1.In this dissertation,support tensor description and kernel support tensor description are proposed and applied to anomaly detection of tensor-sensor data.The support vector description algorithm is extended to tensor space to form a support tensor description algorithm.It can deal with tensor data directly without expanding tensor data into vector data,so as to maintain the internal structure of original data and the relationship between data,and avoid the problem of"Curse of Dimensionality".Through CP decomposition and inner product of tensor,the kernel function tensor is solved.The kernel function replaces the tensor inner product to form the kernel support tensor data description.An algorithm is designed for anomaly detection of tensor data,which can effectively improve the detection performance.2.OCSTuM and GA-OCSTuM are proposed and applied to anomaly detection of sensor data.CP decomposition needs rank evaluation to approximate the original tensor.Tucker decomposition can obtain more accurate tensor decomposition,and reduce the dimension by adjusting the dimension of the core tensor.Therefore,Tucker decomposition is used to compress the attributes of each sample in large-scale data.OCSTuM is proposed by expanding one-class support vector machine from vector space to tensor space and applying Tucke decomposition.Aiming at the problem of large amount of redundant information in sensor data,GA-OCSTuM algorithm is constructed by using genetic algorithm to select data features and search optimal model parameters,which can effectively improve detection performance.3.Extreme tensor learning algorithm is proposed.Based on the theory of neural network,the weight matrix of extreme learning machine is transformed into a high-dimensional tensor representation.Tensor tensor-train is used to decompose low-rank approximation to the original tensor and construct tensor-train layer,which replaces the weight matrix of input layer to hidden layer in the neural network model.Extreme tensor learning algorithm can greatly compress network parameters and reduce storage while keeping performance unchanged or declining slightly.Based on tensor CP decomposition,Tucker decomposition,Tensor-Train decomposition,SVD,OCSVM and ELM,this dissertation proposes support tensor description algorithm,tensor Tucker learning machine and extreme tensor learning algorith,which improves the performance of the algorithms.