JZUS - Journal of Zhejiang University SCIENCE

Frontiers of Information Technology & Electronic Engineering 2020 Vol.21 No.4 P.587-603

An efficient parallel and distributed solution to nonconvex penalized linear SVMs

Author(s): Lei Guan, Tao Sun, Lin-bo Qiao, Zhi-hui Yang, Dong-sheng Li, Ke-shi Ge, Xi-cheng Lu
Affiliation(s): College of Computer, National University of Defense Technology, Changsha 410073, China; more
Corresponding email(s): guanleics@gmail.com, nudtsuntao@163.com, dsli@nudt.edu.cn
Key Words: Linear classification, Support vector machine (SVM), Nonconvex penalty, Alternating direction method of multipliers (ADMM), Parallel algorithm

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Abstract: Support vector machines (SVMs) have been recognized as a powerful tool to perform linear classification. When combined with the sparsity-inducing nonconvex penalty, SVMs can perform classification and variable selection simultaneously. However, the nonconvex penalized SVMs in general cannot be solved globally and efficiently due to their nondifferentiability, nonconvexity, and nonsmoothness. Existing solutions to the nonconvex penalized SVMs typically solve this problem in a serial fashion, which are unable to fully use the parallel computing power of modern multi-core machines. On the other hand, the fact that many real-world data are stored in a distributed manner urgently calls for a parallel and distributed solution to the nonconvex penalized SVMs. To circumvent this challenge, we propose an efficient alternating direction method of multipliers (ADMM) based algorithm that solves the nonconvex penalized SVMs in a parallel and distributed way. We design many useful techniques to decrease the computation and synchronization cost of the proposed parallel algorithm. The time complexity analysis demonstrates the low time complexity of the proposed parallel algorithm. Moreover, the convergence of the parallel algorithm is guaranteed. Experimental evaluations on four LIBSVM benchmark datasets demonstrate the efficiency of the proposed parallel algorithm.

一种有效求解非凸正则化线性支持向量机的并行与分布式方法

关磊¹，孙涛¹，乔林波¹，杨智慧^2,3，李东升¹，葛可适¹，卢锡城¹
¹国防科技大学计算机学院，中国长沙市，410073
²复旦大学计算机科学技术学院，中国上海市，201203
³上海市数据科学重点实验室，中国上海市，201203

摘要：支持向量机（SVM）被视为线性分类的有力工具。与可以产生稀疏效果的非凸惩罚项组合时，SVM能同时执行分类和变量选择。然而，由于其不可微、非凸和非平滑特性，非凸正则化SVM通常难以有效求得全局最优解。已有针对非凸正则化SVM的求解方案通常以串行方式求解，因而无法充分利用现代多核机器的并行处理能力。另一方面，现实世界中数据多以分布式方式存储，迫切需要一种并行与分布式方法求解非凸正则化SVM问题。为应对这一挑战，本文提出一种基于交替方向乘子法（ADMM）的并行算法高效求解非凸正则化SVM问题。采用有效技术降低并行算法的计算与同步开销。时间复杂度分析证明所提并行算法具有低复杂度。此外，该并行算法能保证收敛性。在LIBSVM数据集上的实验证明了所提并行算法的有效性。

关键词：线性分类；支持向量机；非凸惩罚项；交替方向乘子法（ADMM）；并行算法

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一种有效求解非凸正则化线性支持向量机的并行与分布式方法

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