带乘性间隔的多类线性感知机
Multiclass Linear Perceptrons with Multiplicative Margins
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中文总结 AI 辅助
本文提出带乘性间隔机制的多类线性感知机，推导其损失函数与错误界，实验显示其性能优于标准感知机及经典基线，可用于多种机器学习相关场景。
中文摘要 AI 辅助
本文提出了一类带乘性间隔机制（MMPerc）的多类线性感知机分类器，作为标准无间隔和加性间隔感知机的替代方案。乘性公式要求真实类别的得分超出竞争类别得分的指定比例，而非固定加性阈值，以此保证分类置信度，避免依赖数据和类别权重向量不同范数导致的得分幅值问题。本文提出了MMPerc的多种架构与算法变体，推导了线性可分与不可分数据下的关联损失函数和错误界，分析了关键设计考量，包括偏差、间隔阈值选择及训练模式。在合成与真实数据集上的大量实验表明，MMPerc分类器通常优于标准感知机，以及支持向量机、岭分类器等经典基线。因其简洁性、极简设计与计算效率，MMPerc分类器适用于常规机器学习任务、深度神经网络的线性评估、与超维计算/向量符号架构表示的集成，以及资源受限场景的部署。
英文摘要
This paper introduces a family of multiclass linear Perceptron classifiers with a multiplicative margin mechanism (MMPerc), as an alternative to standard margin-free and additive margin Perceptrons. The multiplicative formulation enforces classification confidence by requiring the true class score to exceed that of competing classes by a specified fraction of itself, rather than by a fixed additive threshold. This avoids dependence on score magnitudes arising from varied norms of data and class weight vectors. We propose several architectural and algorithmic variants of MMPerc, derive associated loss functions and mistake bounds for both linearly separable and non-separable data, and analyze key design considerations, including bias, margin threshold selection, and training modes. Extensive experiments on synthetic and real datasets show that MMPerc classifiers typically outperform the standard Perceptron, as well as classic baselines such as Support Vector Machines and Ridge classifiers. Owing to their simplicity, minimalistic design, and computational efficiency, MMPerc classifiers are promising candidates for conventional machine learning tasks, linear evaluation of Deep Neural Networks, integration with Hyperdimensional Computing / Vector Symbolic Architecture representations, and deployment in resource-constrained applications.
发表机构
- Luleå University of Technology（吕勒奥理工大学）
- Institute of Information Technologies and Systems（信息技术与系统研究所）
- La Trobe University（拉筹伯大学）
- Örebro University（厄勒布鲁大学）
- Research Institutes of Sweden（瑞典研究院）
机构由 AI 辅助整理，请以论文原文为准。
