A Nonlinear One-class Support Higher-order Tensor Machine For Classification And Their Applications

With the rapid development of information technology and the reduction of data storage cost,people expect to extract more relevant relationships from the complex and disorderly mass data,and expand the prediction function of big data in the fields of macro-economy,fault diagnosis,machine learning.On the basise of the perfect theoretical principle and clear mathematical model,the traditional machine learning theory represented by support vector machine has attracted the attention of experts and scholars.However,with the explosion of data dimension,support vector machine shows serious fatal defects of over-fitting.In order to solve the curse of dimensionality and small sample size problems,support tensor machine emerged.Support tensor machine effectively maintains the structured information of the input data and fully exploits the correlation between the original data;furthermore,support tensor machine greatly reduces the number of variable parameters in the optimization problem,and avoids the common problems in the classifier model based on vector data.However,the research on classifiers based on tensor data is mostly concentrated on the field of multi-classification,and there are few studies about tensor theory on one-class classification problems.In reality,it is inevitable that we will encounter the situation of Friend-or-Foe identification and the heterogeneous extraction;therefore,it is necessary to carry out in-depth research on the one-class classification model based on tensor data.In this paper,the advantages and disadvantages of the tensor model are discussed in depth.A new one-class classification model based on tensor theory is proposed in this paper which is named as Nonlinear One-class Support Higher-order Tensor Machine(OCSHTM),and applied to face recognition and rolling bearing heterogeneous recognition.The main research contents of this paper are as follows:(1)The theory and characteristics of typical support tensor models are studied in detail,and then the paper emphatically disscusses the advantages and disadvantages of one-class support tensor machine.Aimed at the shortcomings that existing models are easy to fall into local optimum solution and model parameters are too many to cause over-fitting risk,OCSHTM is proposed.A variety of numerical experiments based on this model are carried out on public data sets,which shows the effectiveness and superiority of OCSHTM model.(2)OCSHTM model is applied to data processing and pattern recognition of face gray image.On the second-order tensor data set,OCSHTM model can effectively process high-dimensional small sample data,and has good model performance;at the same time,it establishes the optimal classification hyperplane to realize the identification of enemy and foe.(3)OCSHTM model is applied to fault diagnosis and heterogeneous recognition of rolling bearings,and one-class classification support tensor is applied to fault diagnosis of rotating machinery for the first time.OCSHTM algorithm can establish fault diagnosis model based on a small number of normal bearing vibration signals,and effectively accomplish the heterogeneous recognition of rolling bearings under the condition of guaranteeing the performance of the classifier.When the original signal is mixed with different degrees of environmental noise and abnormal vibration noise,the OCSHTM algorithm can still maintain a high recognition rate,which shows that the OCSHTM model has good robustness.