Print Email Facebook Twitter Kernelized support tensor train machines Title Kernelized support tensor train machines Author 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) Date 2022 Abstract 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. Subject Image classificationSupport tensor machineTensor To reference this document use: http://resolver.tudelft.nl/uuid:2d64c8f9-56eb-48d9-a77b-1a8a35d7e249 DOI https://doi.org/10.1016/j.patcog.2021.108337 Embargo date 2022-03-20 ISSN 0031-3203 Source Pattern Recognition, 122 Bibliographical note 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. Part of collection Institutional Repository Document type journal article Rights © 2022 Cong Chen, K. Batselier, Wenjian Yu, Ngai Wong Files PDF 1_s2.0_S0031320321005173_main.pdf 964.39 KB Close viewer /islandora/object/uuid:2d64c8f9-56eb-48d9-a77b-1a8a35d7e249/datastream/OBJ/view