Support Vector Machines (SVM) and Logistic Regression (LR) are popular classification models used in machine learning. Their main drawback is that they can only accept vectors as inputs, which naturally calls for their extension to multidimensional data - tensors. Using the tensor algebra, we present some versions of these algorithms based on different tensor decompositions. Suport Tensor Machine and Rank-1 Logistic Regression represent the most basic extension of the above models, which already lead to better classification accuracy as they preserve spatial relationships using rank-1 tensors. However, there are more general methods based on different tensor decompositions that are more efficient. The aim of this thesis is to present the mathematical background of the tensor extensions of SVM and LR, their comparison and their suitability for a particular problem. We start with synthetic data representing basic geometric shapes and continue with traditional test data sets. In addition, this bachelor thesis covers the most recent achievements in the field of tensor classification.
|
