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Hauptverfasser: Du, Zhuolin, Song, Yisheng
Format: Preprint
Veröffentlicht: 2025
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Online-Zugang:https://arxiv.org/abs/2507.13012
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_version_ 1866918095852929024
author Du, Zhuolin
Song, Yisheng
author_facet Du, Zhuolin
Song, Yisheng
contents Based on the tensor-based large margin distribution and the nonparallel support tensor machine, we establish a novel classifier for binary classification problem in this paper, termed the Large Margin Distribution based NonParallel Support Tensor Machine (LDM-NPSTM). The proposed classifier has the following advantages: First, it utilizes tensor data as training samples, which helps to comprehensively preserve the inherent structural information of high-dimensional data, thereby improving classification accuracy. Second, this classifier not only considers traditional empirical risk and structural risk but also incorporates the marginal distribution information of the samples, further enhancing its classification performance. To solve this classifier, we use alternative projection algorithm. Specifically, building on the formulation where in the proposed LDM-NPSTM, the parameters defining the separating hyperplane form a tensor (tensorplane) constrained to be the sum of rank-one tensors, the corresponding optimization problem is solved iteratively using alternative projection algorithm. In each iteration, the parameters related to the projections along a single tensor mode are estimated by solving a typical Support Vector Machine-type optimization problem. Finally, the efficiency and performance of the proposed model and algorithm are verified through theoretical analysis and some numerical examples.
format Preprint
id arxiv_https___arxiv_org_abs_2507_13012
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Nonparallel Support Tensor Machine for Binary Classification based Large Margin Distribution and Iterative Optimization
Du, Zhuolin
Song, Yisheng
Optimization and Control
62H30, 15A63, 90C55
Based on the tensor-based large margin distribution and the nonparallel support tensor machine, we establish a novel classifier for binary classification problem in this paper, termed the Large Margin Distribution based NonParallel Support Tensor Machine (LDM-NPSTM). The proposed classifier has the following advantages: First, it utilizes tensor data as training samples, which helps to comprehensively preserve the inherent structural information of high-dimensional data, thereby improving classification accuracy. Second, this classifier not only considers traditional empirical risk and structural risk but also incorporates the marginal distribution information of the samples, further enhancing its classification performance. To solve this classifier, we use alternative projection algorithm. Specifically, building on the formulation where in the proposed LDM-NPSTM, the parameters defining the separating hyperplane form a tensor (tensorplane) constrained to be the sum of rank-one tensors, the corresponding optimization problem is solved iteratively using alternative projection algorithm. In each iteration, the parameters related to the projections along a single tensor mode are estimated by solving a typical Support Vector Machine-type optimization problem. Finally, the efficiency and performance of the proposed model and algorithm are verified through theoretical analysis and some numerical examples.
title A Nonparallel Support Tensor Machine for Binary Classification based Large Margin Distribution and Iterative Optimization
topic Optimization and Control
62H30, 15A63, 90C55
url https://arxiv.org/abs/2507.13012