Wavelet Support Tensor Machine Model Based On Tucker Decomposition And Its Application

The rapid development of information technology has accelerated the production of data with higher dimensions,larger volumes and more complex structures,which urgently requires the emergence of corresponding data analysis and data mining technologies.Among them,tensor data with multiple dimensions is a typical representative,which is widely used in many research fields,such as image classification,medical aided diagnosis,financial prediction,remote sensing and fault diagnosis.The traditional processing method is to directly expand the tensor into a vector and process it with the vector-based method,which will undoubtedly destroy the data structure of the original tensor.The support tensor machine model studied in this paper is to complete data mining on the basis of preserving tensor structure information.In this paper,the theory and characteristics of support tensor machines are discussed in depth,and the current domestic and foreign theoretical research progress and the application of support tensor machines in many fields are analyzed.A novel tucker-wavelet supported tensor machine model is proposed for nonlinear classification problems in tensor space and applied to the diagnosis task of Alzheimer's disease based on functional magnetic resonance imaging(fMRI)data.The main research contents of this paper are as follows:(1)Aiming at the nonlinear classification problem of support tensor machines,the kernel function theory is studied in detail,and the performance of several current tensor kernel functions in maintaining the structural information of the original tensor is discussed.A new nonlinear support tensor machine algorithm is established based on the tucker decomposition of the tensor to preserve the structural information of the kernel function.In order to verify the classification performance of the new model on tensor data,two-dimensional and threedimensional data sets were established,and comparison experiments were carried out with multiple kernel functions and models.The experimental results show that the new model has advantages in tensor classification problems.(2)In order to further improve the performance of the model,according to the kernel function theory,a new form of wavelet kernel function based on tucker decomposition is proposed.Not only the applicability of the wavelet kernel function is theoretically demonstrated,but also the comparison experiments with multiple kernel functions are carried out on various types of data sets.The results show that the new kernel function performs better under the same conditions.(3)Applying the new support tensor machine model to the task of medical imaging diagnosis based on fMRI data.Four datasets representing different degrees of disease were first collected and built from the ADNI dataset,and then the fMRI data were preprocessed,followed by a sensitivity analysis of comparative trials and parameters.The experimental results show that the tucker-wavelet support tensor machine model proposed in this paper can be effectively applied in practical classification tasks and exhibits excellent classification performance.