用几何图方法构建无需调参的多类分类器，提升边界平滑性与计算效率。
Multiclass Graph-Based Large Margin Classifiers: Unified Approach for Support Vectors and Neural Networks
- 基于加布里埃尔图构造无超参、免优化的分类框架
- 提出新激活函数与中心神经元结构，实现更平滑的分类边界
- 兼容反向传播与线性方程求解，适合追求高效与稳定性的研究者
大型边缘分类器最初源于优化框架，但支持向量可通过几何方法获得。本文推进了加布里埃尔图（GG）在二分类与多分类问题中的应用。针对芯片类（Chipclass），提出一种无超参数、无需优化的基于GG的二分类器，探讨激活函数与支持边（SE）中心神经元对分类的影响，引入更平滑的函数和结构支持向量（SSV）中心神经元，以实现低概率边缘与更平滑的分类轮廓。扩展神经网络架构，可使用softmax与交叉熵损失进行反向传播训练，或通过求解线性方程组完成。提出新的基于子图/距离的成员函数用于图正则化，并设计了一种比标准方法更高效的GG重计算算法。实验结果通过弗里德曼检验表明，该方法优于以往基于GG的分类器，且与树基模型统计等效。
原文摘要 · Abstract (English)
While large margin classifiers are originally an outcome of an optimization framework, support vectors (SVs) can be obtained from geometric approaches. This article presents advances in the use of Gabriel graphs (GGs) in binary and multiclass classification problems. For Chipclass, a hyperparameter-less and optimization-less GG-based binary classifier, we discuss how activation functions and support edge (SE)-centered neurons affect the classification, proposing smoother functions and structural SV (SSV)-centered neurons to achieve margins with low probabilities and smoother classification contours. We extend the neural network architecture, which can be trained with backpropagation with a softmax function and a cross-entropy loss, or by solving a system of linear equations. A new subgraph-/distance-based membership function for graph regularization is also proposed, along with a new GG recomputation algorithm that is less computationally expensive than the standard approach. Experimental results with the Friedman test show that our method was better than previous GG-based classifiers and statistically equivalent to tree-based models.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。