Tensor Kernel Functions Based on Core Tensors Applied to the Recognition of Hand Movements

Abstract

Kernel methods and Support Vector Machine (SVM) are widely used in machine learning. However, when multidimensional data are used, the classical vector-based kernel functions must vectorize the inputs, which breaks down the original tensor structure, leading to performance loss. To avoid this problem, tensor kernel functions can be used. In the present work, three novel tensor kernel functions are presented. The proposed methods are based on the core tensors of the Higher-Order Singular Value Decomposition (HOSVD) and Tensor-Train Decomposition (TTD). Two of the presented methods are fast kernel functions that ignore the factor matrices of these tensor decompositions, alleviating the time complexity burden. The presented techniques were evaluated in the classification of hand movements. A low-cost "smart glove" with accelerometers and gyroscopes was developed, generating tensor input samples with modes related to sensors, channels and features. The experiments showed a good performance of the proposed techniques when compared to state-of-the-art tensor kernel functions.