发表机构
Laboratory of Parallel and Distributed Systems Institute for Computer Science and Control (SZTAKI); John von Neumann Faculty of Informatics Obuda University（并行与分布式系统实验室 计算机科学与控制研究所（匈牙利科学院计算机与自动化研究所）; 欧布达大学约翰·冯·诺依曼信息学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对计算最大间隔分离超平面问题，提出一种基于初始分离超平面的迭代几何方法，通过考虑局部信息解决凸二次优化问题，实验表明该方法在较大数据集上有竞争力，有时能超越现有直接求解方法。
AI 中文摘要
给定一个二分类线性可分数据集，目标是计算最大间隔分离超平面，即硬间隔支持向量机（SVM）分类器。本文研究若给定一个初始分离超平面，能否更高效地达到这个唯一最优解。我们提出一种几何方法，从初始分离超平面开始逐步改善超平面的对齐，在保持分离的同时不断增加间隔直至收敛到全局最优。每次迭代仅考虑局部信息即当前活跃集，根据该约简子集的最优分离超平面重新对齐超平面，将原始凸二次优化问题转化为一系列较小的子问题。文中详细介绍了算法、初步实验评估及一些理论发现。结果表明，当有初始分离超平面时，该方法在较大数据集上具有竞争力，某些情况下能优于直接求解优化问题的现有方法。
英文摘要
Given a binary-labeled linearly separable dataset, and the objective is to compute the maximum-margin separating hyperplane, also known as the hard-margin Support Vector Machine (SVM) classifier. This paper investigates whether, if given an initial separating hyperplane, can it be exploited to reach this unique optimum more efficiently. We present a geometric approach that gradually improves the alignment of the hyperplane, starting from an initial separating hyperplane, while preserving separation and continuously increasing its margin until convergence to the global optimum. At each iteration, the method considers only local information, namely the current active set, and aims to re-align the hyperplane according to the optimal separating hyperplane of this reduced subset. Consequently, the original convex quadratic optimization problem is addressed through a sequence of smaller subproblems. The paper presents the algorithm in detail, together with a preliminary experimental evaluation and several theoretical findings. The results suggest that, when an initial separating hyperplane is available, the proposed method can be competitive on larger datasets and, in some cases, can outperform state-of-the-art approaches that solve the optimization problem directly.
Comments15 pages, 1 figure
