Kernelized support tensor train machines

Kernelized support tensor train machines

Chen, Cong (The University of Hong Kong)
Batselier, K. (TU Delft Team Kim Batselier)
Yu, Wenjian (Tsinghua University)
Wong, Ngai (The University of Hong Kong)

2022

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we propose a tensor train (TT)-based kernel technique for the first time, and apply it to the conventional support vector machine (SVM) for high-dimensional image classification with very small number of training samples. Specifically, we propose a kernelized support tensor train machine that accepts tensorial input and preserves the intrinsic kernel property. The main contributions are threefold. First, we propose a TT-based feature mapping procedure that maintains the TT structure in the feature space. Second, we demonstrate two ways to construct the TT-based kernel function while considering consistency with the TT inner product and preservation of information. Third, we show that it is possible to apply different kernel functions on different data modes. In principle, our method tensorizes the standard SVM on its input structure and kernel mapping scheme. This reduces the storage and computation complexity of kernel matrix construction from exponential to polynomial. The validity proof and computation complexity of the proposed TT-based kernel functions are provided elaborately. Extensive experiments are performed on high-dimensional fMRI and color images datasets, which demonstrates the superiority of the proposed scheme compared with the state-of-the-art techniques.

Image classification
Support tensor machine
Tensor

http://resolver.tudelft.nl/uuid:2d64c8f9-56eb-48d9-a77b-1a8a35d7e249

https://doi.org/10.1016/j.patcog.2021.108337

2022-03-20

0031-3203

Pattern Recognition, 122

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2022 Cong Chen, K. Batselier, Wenjian Yu, Ngai Wong