Multiclass Linear Perceptrons with Multiplicative Margins

2026-08-30

AI Summary

本文提出了一种具有乘性边界机制的多类线性感知器分类器（MMPerc），通过要求真实类别分数超过其他竞争类别的特定比例来增强分类信心，解决了标准感知器依赖得分幅度的问题。

Abstract

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.

Problem

• Multiplicative Margin
• Perceptron Classifiers
• Classification Confidence
• Score Magnitudes
• Data Norms

Innovation

• Multiplicative Margin
• Multiclass Linear Perceptron
• Classification Confidence