Efficient Structure-preserving Support Tensor Train Machine

• URL: http://arxiv.org/abs/2002.05079v3
• Date: Tue, 3 Aug 2021 16:57:36 GMT
• Title: Efficient Structure-preserving Support Tensor Train Machine
• Authors: Kirandeep Kour, Sergey Dolgov, Martin Stoll and Peter Benner
• Abstract summary: Train Multi-way Multi-level Kernel (TT-MMK) We develop the Train Multi-way Multi-level Kernel (TT-MMK), which combines the simplicity of the Polyadic decomposition, the classification power of the Dual Structure-preserving Support Machine, and the reliability of the Train Vector approximation. We show by experiments that the TT-MMK method is usually more reliable, less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification when benchmarked against other state-of-the-art techniques.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor classification methods. In the presence of small amounts of training data, kernel methods offer an attractive choice as they provide the possibility for a nonlinear decision boundary. We develop 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. We show by experiments that the TT-MMK method is usually more reliable computationally, less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification when benchmarked against other state-of-the-art techniques.

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