NPrSVM: Nonparallel sparse projection support vector machine with efficient algorithm
NPrSVM: Nonparallel sparse projection support vector machine with efficient algorithm
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DOI：
10.1016/j.asoc.2020.106142
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Wei-Jie Chen;Y. Shao;Chunna Li;Yu-qing Wang;Ming-Zeng Liu;Zhen Wang
中科院分区：
文献类型：
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作者：
Wei-Jie Chen;Y. Shao;Chunna Li;Yu-qing Wang;Ming-Zeng Liu;Zhen Wang
最近提出的投影孪生支持向量机（PTSVM）是一种优秀的非并行分类器。然而，PTSVM采用最小二乘损失函数来度量其类内经验风险，导致了一些缺点，如决策的非稀疏性，对离群值的敏感性，昂贵的矩阵求逆，以及线性和非线性模型的不一致性。为了缓解这些问题，在本文中，我们提出了一种新的非并行稀疏投影支持向量机（NPrSVM）。与原始PTSVM将类内实例的投影值压缩到自己的类中心不同，NPrSVM的目标是在不敏感的管道内尽可能多地聚类它们。具体来说，我们的NPrSVM具有以下优点：（1）NPrSVM利用L1-范数对称的Hinge损失函数，不仅具有稀疏性，而且提高了对异常值的鲁棒性。(ii)NPrSVM中对偶问题的优雅公式不再涉及训练过程中的矩阵求逆。与PTSVM相比，这大大节省了计算时间。(iii)虽然PTSVM的非线性公式不是线性PTSVM的直接扩展，但我们的NPrSVM的线性和非线性版本是一致的。(iv)进一步设计了一种有效的双坐标下降算法，用于NPrSVM处理大规模分类。最后，通过在人工数据集和真实数据集上的大量实验，验证了NPrSVM的可行性和有效性。
The recently proposed projection twin support vector machine (PTSVM) is an excellent nonparallel classifier. However, PTSVM employs the least-squares loss function to measure its within-class empirical risk, resulting in several drawbacks, such as non-sparseness for decision, sensitivity to outliers, expensive matrix inversion, and inconsistency in the linear and nonlinear models. To alleviate these issues, in this paper, we propose a novel nonparallel sparse projection support vector machine (NPrSVM). Different from the original PTSVM that squeezes the projected values of within-class instances to its own class center, NPrSVM aims to cluster them as much as possible within an insensitive tube. Specifically, our NPrSVM owns the following attractive merits:(i) Benefiting from the L 1-norm symmetric Hinge loss function, NPrSVM not only enjoys sparseness for decision but also improves robustness to outliers.(ii) The elegant formulation of dual problems in NPrSVM no longer involves the matrix inversion during the training procedure. This greatly saves the computing time compared to PTSVM.(iii) While the nonlinear formulation of PTSVM is not the direct extension of linear PTSVM, the linear and nonlinear versions of our NPrSVM are consistent.(iv) An efficient dual coordinate descent algorithm is further designed for NPrSVM to handle large-scale classification. Finally, the feasibility and effectiveness of NPrSVM are validated by extensive experiments on both synthetic and real-world datasets.