Efficient Structure-preserving Support Tensor Train Machine
Kirandeep Kour, Sergey Dolgov, Martin Stoll, Peter Benner; 24(4):1−22, 2023.
Abstract
With the increasing amount of collected data being high-dimensional multi-way arrays (tensors), it is crucial for efficient learning algorithms to make use of this tensorial structure as much as possible. The curse of dimensionality for high-dimensional data and the loss of structure when vectorizing the data highlight the need for specialized low-rank tensor classification methods. Kernel methods offer an attractive choice in the presence of limited training data, as they allow for a nonlinear decision boundary. In this study, we introduce the Tensor Train Multi-way Multi-level Kernel (TT-MMK), which combines the simplicity of the Canonical Polyadic decomposition, the classification power of the Dual Structure-preserving Support Vector Machine, and the reliability of the Tensor Train (TT) approximation. Experimental results demonstrate that the TT-MMK method is computationally reliable, less sensitive to tuning parameters, and achieves higher prediction accuracy in SVM classification compared to other state-of-the-art techniques.
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