An Online Two-Stage Classification Based on Projections

IF 1.8 3区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
Aimin Song, Yan Wang, Shengyang Luan
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Abstract

Kernel-based online classification algorithms, such as the Perceptron, NORMA, and passive-aggressive, are renowned for their computational efficiency but have been criticized for slow convergence. However, the parallel projection algorithm, within the adaptive projected subgradient method framework, exhibits accelerated convergence and enhanced noise resilience. Despite these advantages, a specific sparsification procedure for the parallel projection algorithm is currently absent. Additionally, existing online classification algorithms, including those mentioned earlier, heavily rely on the kernel width parameter, rendering them sensitive to its choices. In an effort to bolster the performance of these algorithms, we propose a two-stage classification algorithm within the Cartesian product space of reproducing kernel Hilbert spaces. In the initial stage, we introduce an online double-kernel classifier with parallel projection. This design aims not only to improve convergence but also to address the sensitivity to kernel width. In the subsequent stage, the component with a larger kernel width remains fixed, while the component with a smaller kernel width undergoes updates. To promote sparsity and mitigate model complexity, we incorporate the projection-along-subspace technique. Moreover, for enhanced computational efficiency, we integrate the set-membership technique into the updates, selectively exploiting informative vectors to improve the classifier. The monotone approximation of the proposed classifier, based on the designed \( \epsilon \)-insensitive function, is presented. Finally, we apply the proposed algorithm to equalize a nonlinear channel. Simulation results demonstrate that the proposed classifier achieves faster convergence and lower misclassification error with comparable model complexity.

Abstract Image

基于预测的在线两阶段分类法
基于核的在线分类算法,如 Perceptron、NORMA 和被动攻击算法,以计算效率高而著称,但因收敛速度慢而饱受诟病。然而,在自适应投影子梯度法框架内的并行投影算法却能加快收敛速度并增强抗噪声能力。尽管有这些优点,但目前还没有针对并行投影算法的特定稀疏化程序。此外,现有的在线分类算法,包括前面提到的那些,都严重依赖于核宽度参数,因此对其选择非常敏感。为了提高这些算法的性能,我们在再现核希尔伯特空间的笛卡尔乘积空间内提出了一种两阶段分类算法。在初始阶段,我们引入了并行投影的在线双核分类器。这种设计的目的不仅在于提高收敛性,还在于解决对核宽度的敏感性问题。在后续阶段,内核宽度较大的部分保持固定,而内核宽度较小的部分则进行更新。为了提高稀疏性和降低模型复杂度,我们采用了子空间投影技术。此外,为了提高计算效率,我们将集合成员技术整合到更新中,有选择性地利用信息向量来改进分类器。基于所设计的 \( \epsilon \)-不敏感函数,提出了分类器的单调近似值。最后,我们应用所提出的算法来均衡非线性信道。仿真结果表明,在模型复杂度相当的情况下,所提出的分类器收敛速度更快,误分类误差更低。
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来源期刊
Circuits, Systems and Signal Processing
Circuits, Systems and Signal Processing 工程技术-工程:电子与电气
CiteScore
4.80
自引率
13.00%
发文量
321
审稿时长
4.6 months
期刊介绍: Rapid developments in the analog and digital processing of signals for communication, control, and computer systems have made the theory of electrical circuits and signal processing a burgeoning area of research and design. The aim of Circuits, Systems, and Signal Processing (CSSP) is to help meet the needs of outlets for significant research papers and state-of-the-art review articles in the area. The scope of the journal is broad, ranging from mathematical foundations to practical engineering design. It encompasses, but is not limited to, such topics as linear and nonlinear networks, distributed circuits and systems, multi-dimensional signals and systems, analog filters and signal processing, digital filters and signal processing, statistical signal processing, multimedia, computer aided design, graph theory, neural systems, communication circuits and systems, and VLSI signal processing. The Editorial Board is international, and papers are welcome from throughout the world. The journal is devoted primarily to research papers, but survey, expository, and tutorial papers are also published. Circuits, Systems, and Signal Processing (CSSP) is published twelve times annually.
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