Supervised Tensor Learning with Applications

In this thesis, a new supervised tensor learning (STL) approach with application to neuroimages has been studied and implemented. We applied our proposed polynomial kernel-based approach in order to analyze HIV infections based on fMRI and DTI brain images. The goal of this project was to achieve a more accurate prediction for HIV diagnosis using fMRI and DTI images of the brain. To achieve this goal we tried to improve the accuracy of the STL model by directly using tensor data as an input. Then, in order to solve STL problems, a structure-preserving feature mapping in addition to CP decomposed results has been defined to derive a Dual Structure-preserving Kernel (DuSK) in the tensor product feature space. Broadly, DuSK is a general framework to convert any vector-based kernel function to an equivalent tensorial representation. Different from traditional STL frameworks, that usually intend to use linear models, our approach was based on a nonlinear kernel method and tensor factorization techniques that can preserve the multi- way structures of tensorial data. We investigated the performance of DuSK together with Support Vector Machine (SVM) for HIV infection classification on tensorial fMRI and matricized DTI data sets. The experimental results are presented with details in evaluation chapter. According to our experiments, that DuSK with a nonlinear kernel can effectively boost classification performance in HIV data sets, and the choice of optimal kernel depends on the nature of the input data. Specifically, DuSK with an RBF kernel performs better on fMRI data, while DuSK with a polynomial kernel is better for DTI data.