Multidimensional data classification with chordal distance based kernel and Support Vector Machines

In contemporary machine learning multidimensional rather than pure vector like data are frequently encountered. Traditionally, such multidimensional objects, such as color images or video sequences, are first transformed to a vector representation, and then processed by the classical learning algorithms operating with vectors. However, such multi-to-one dimension transformations usually lead to loss of important information. Thus, proposing novel methods for representing and learning with complex and multidimensional data is in focus of current machine learning research. In this paper, we propose a new method for efficient classification of multidimensional data based on a tensor-based kernel applied to the Support Vector Machines. We represent data as tensors, in order to preserve data dimensionality and to allow for processing of complex structures. To allow for an effective classification, we augment a Support Vector Machine (SVM) trained with Sequential Minimal Optimization (SMO) procedure with a chordal distance-based kernel for efficient classification of tensor-like objects. We also discuss different optimization methods for SVM, as well as present implementation details with computational time analysis. The proposed method is evaluated in both binary and multi-class classification problems. Comprehensive experimental analysis carried on a number of multidimensional benchmarks shows high usefulness of the proposed approach.