Research On Related Algorithms Of Support Vector Machine Based On Tensor

In the real world,a large amount of data is often expressed by tensor.For example,MRI images are made up of third-order tensors;each frame in video data is made up of third-order tensors.Tensor data contains a lot of nonlinear information,such as the structure information between data,and can reflect the real situation of samples more than vector data.As a classical algorithm in machine learning algorithm,support vector machine(SVM),it has many unique advantages in solving small sample,nonlinear and high-dimensional pattern recognition.Twin support vector machine(Twin-SVM)and one classification support vector machine(OC-SVM)are important extensions of SVM.Compared with the traditional SVM,the time complexity of Twin-SVM is reduced by three times,and OC-SVM is a new application of SVM in clustering task.However,both Twin-SVM and OC-SVM can only deal with vectorized data.It is no doubt that the accuracy of the model can be improved by directly using tensor data containing structural information.In this regard,this paper mainly studies the tensor based support vector machine algorithm theory,the main research content is as follows.Firstly,the Twin-SVM algorithm based tensor is studied,and propose the kernelized twin support tensor machine algorithm(KTw STM).Considering the nonlinear relationship between data,it is mapped to Hilbert space,and then the kernel CP decomposition is used to obtain the structure information of the tensor and input it into the objective function.The objective function is transformed into dual form by expression principle,and optimized by cross iteration method.Finally,two kinds of medical image data(f MRI)are collected.The experimental results show that the classification is compared with the traditional classification calculation Compared with the method,the nuclear twin support tensor machine performs better in f MRI data processing.Secondly,the paper studies the OC-SVM algorithm based on tensor,and proposes the kernelized one classification support tensor machine algorithm(KOC-STM).The nonlinear relationship between tensor data is preserved by using kernel CP decomposition technology.Then,the kernel function expression based on tensor is used to simplify the operation of tensor data in kernel space.Finally,an effective iterative algorithm is given for optimization problem.The experimental results show that compared with the classical clustering algorithm,the kernelized one classification support tensor machine has some advantages in processing outlier detection task based on tensor,and the accuracy has been improved obviously.