arXiv:2511.04873stat.MLcs.LG2025-11

用拓扑结构选原型,让模型更稳定、更贴近数据本质。

Prototype Selection Using Topological Data Analysis

  • 基于拓扑数据分析的双阶段与单阶段原型选择方法
  • 在15个数据集上表现优于7种基线,尤其在边界保留上领先
  • 无需标签信息即可保持类别比例,适合小样本和鲁棒性场景

原型选择方法可压缩训练集,但现有分类(如聚类、优化、混合等)未涵盖对数据多尺度拓扑结构的操作。本文提出两种基于持续性的原型选择器:拓扑原型选择器(TPS)和边界感知拓扑原型选择器(BoundaryTPS)。TPS通过两个连续的Rips滤波保留边界相关点与内部典型点;BoundaryTPS采用顶点加权滤波,聚焦于决策边界附近。在15个真实数据集上与7种经典基线对比,拓扑方法占据设计空间中独特位置。BoundaryTPS在H₁持久图保留上的平均弗里德曼排名最低,显著优于5种基线(Nemenyi检验,α=0.05);TPS排名第三。两者在折叠扰动下均比链式决策选择器更稳定,且无需标签机制即保持原始类别比例。总体G-Mean表现具有竞争力,但非最优,跨折叠组合中排名第一频率分别为11.3%(TPS)和9.9%(BoundaryTPS)。实验表明,两者在样本量增长时呈亚二次方级扩展。

原文摘要 · Abstract (English)

Prototype selection methods compress a training set, but the existing taxonomy of condensation, edition, hybrid, competence-based, optimization-based, and clustering-based families does not include methods that operate on the multi-scale topological structure of the data. This paper introduces two different persistence-based prototype selector variants, Topological Prototype Selector (TPS) and Boundary-Conscious Topological Prototype Selector (BoundaryTPS). TPS uses two sequential Rips filtrations to retain boundary-relevant and interior-typical points. BoundaryTPS is a single-stage variant whose vertex-weighted filtration concentrates retention near the decision boundary. We evaluate both methods against seven classical baselines on fifteen real datasets and find that the topological methods occupy a different operating point in the prototype-selection design space than existing methods. BoundaryTPS achieves the lowest mean Friedman rank on $H_1$ persistence-diagram preservation and is significantly better than five of the seven baselines (Nemenyi, $α= 0.05$). TPS ranks third on the same endpoint. Both methods are more stable under fold perturbation than any chained-decision selector tested, and both inherit the source set's class proportions without label-aware machinery. On aggregate G-Mean both methods are competitive but not leading, with rank-1 frequencies of $11.3\%$ (TPS) and $9.9\%$ (BoundaryTPS) across fold combinations. Empirically, both methods scale sub-quadratically in sample size.

原型选择拓扑数据分析稳定性无监督

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。