用乘法边界提升多分类感知机的置信度,避免对数据尺度的依赖。
Multiclass Linear Perceptrons with Multiplicative Margins
- 通过分数倍数关系约束正确类得分,而非固定差值。
- 在真实和合成数据上优于标准感知机、SVM与岭分类器。
- 适合轻量级任务、深度模型线性评估及资源受限场景。
本文提出一类基于乘法边界的多分类线性感知机(MMPerc),作为传统无边界或加法边界感知机的替代方案。乘法机制要求正确类别得分需超过其他竞争类别得分的指定比例,而非固定增量,从而避免因数据与类别权重向量范数差异带来的得分幅度依赖。本文设计了多种架构与算法变体,推导出适用于线性可分与不可分数据的损失函数与误分类界,并分析了偏差、边界阈值选择与训练模式等关键设计因素。大量实验表明,MMPerc分类器在合成与真实数据集上普遍优于标准感知机,以及支持向量机与岭分类器等经典基线。由于其简洁性、极简设计与计算高效性,MMPerc是常规机器学习任务、深度神经网络线性评估、与超维度计算/向量符号架构融合,以及资源受限应用中的有力候选。
原文摘要 · Abstract (English)
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.
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