A Kernelized Support Tensor-Ring Machine for High-Dimensional Data Classification

Deng, Xinyang; Shi, Yuanquan; Yao, Dunhong; Tang, Xiyan; Mi, Chunqiao; Xiao, Jianhua; Zhou, Xian

doi:10.1109/iceitsa54226.2021.00039

Cited by 1 publication

(2 citation statements)

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“…In particular, the linear support higher-order tensor machine (SHTM) [40] is deemed as a special case of DuSK. The structural-preserving scheme in the CP-based DuSK was extended to that under TT and TR decompositions [26][27][28]. A summarization of the aforementioned works can be found in Table 1, where the "Loss" column presents the loss functions in STMs, "LRD" represents the low-rank decomposition type, "SST" is short for the sparsity of support tensors, and "DR" indicates data reduction.…”

Section: Related Workmentioning

confidence: 99%

“…However, this assumption is often violated in practical problems and the linear decision boundaries are not adequate to classify the data appropriately [23]. Inspired by the success of kernel tricks in the conventional SVM, it was witnessed in [24][25][26][27][28] that the classification accuracy can be greatly improved by combining tensor decompositions with kernel-based methods. For example, the dual structure-preserving kernel (DuSK) proposed by He et al [24] was constructed by feeding the factor vectors from the tensor CANDECOM/PARAFAC (CP) decomposition with the conventional Gaussian RBF kernel.…”

Section: Introductionmentioning

confidence: 99%

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Sparse Support Tensor Machine with Scaled Kernel Functions

Wang

Luo

2023

Mathematics

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As one of the supervised tensor learning methods, the support tensor machine (STM) for tensorial data classification is receiving increasing attention in machine learning and related applications, including remote sensing imaging, video processing, fault diagnosis, etc. Existing STM approaches lack consideration for support tensors in terms of data reduction. To address this deficiency, we built a novel sparse STM model to control the number of support tensors in the binary classification of tensorial data. The sparsity is imposed on the dual variables in the context of the feature space, which facilitates the nonlinear classification with kernel tricks, such as the widely used Gaussian RBF kernel. To alleviate the local risk associated with the constant width in the tensor Gaussian RBF kernel, we propose a two-stage classification approach; in the second stage, we advocate for a scaling strategy on the kernel function in a data-dependent way, using the information of the support tensors obtained from the first stage. The essential optimization models in both stages share the same type, which is non-convex and discontinuous, due to the sparsity constraint. To resolve the computational challenge, a subspace Newton method is tailored for the sparsity-constrained optimization for effective computation with local convergence. Numerical experiments were conducted on real datasets, and the numerical results demonstrate the effectiveness of our proposed two-stage sparse STM approach in terms of classification accuracy, compared with the state-of-the-art binary classification approaches.

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Section: Related Workmentioning

confidence: 99%