Theoretical and Applied Contributions on Tensor Learning

Abstract

Tensor learning refers to a series of tools and techniques for modeling and understanding complex multidimensional datasets, in order to build efficient learning models. It is a fairly new area in machine learning, which blends, especially, with statistical learning and tensor models. Indeed, tensor learning has proven to be an alternative to conventional vector-based learning techniques that are well-known in the literature, such as the Support Tensor Machines (STM), which is a multilinear extension of the Support Vector Machines (SVM). This work proposes theoretical and applied contributions to tensor learning in the following way. First, a fully tensorial framework for seismic event classification is proposed, which performs feature extraction, dimensionality reduction and classification, with all these steps using tensor-based techniques. Next, a new dimensionality reduction technique called Low-Correlation Multilinear Dimensionality Reduction (LC-MDR), based on a new tensor decomposition, the Even-Order Nested PARAFAC Decomposition (EONPD), is proposed and validated, successfully reducing the correlation and dimensionality of seismic data, improving classification rates. And last, a multilinear sampling approach for tensor learning and data structuring is proposed, which is used in the modification of the SVM technique, joining the concept of multilinear sampling and tensor decompositions, more specificaly, the PARAFAC and Tucker, then, the proposed modifications, called Support Vector Machines with Multilinear PARAFAC Sampling (SVMMPS) and Support Vector Machines with Multilinear Tucker Sampling (SVM-MTS), are tested for photonic data classification. These three new proposed contributions to tensor learning showed better performance, in terms of accuracy, when compared to other techniques of the literature.