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arXiv 2503.03418cs.LGcs.AI

单纯形 SMOTE:针对不平衡学习问题的过采样解决方案

Simplicial SMOTE: Oversampling Solution to the Imbalanced Learning Problem

Sber AI Lab(Sber AI实验室);HSE University(高等经济大学)

Oleg Kachan, Andrey Savchenko, Gleb Gusev

AI总结:

本文提出 Simplicial SMOTE,通过从几何邻域单纯复形的单纯形而非图中边进行采样,生成更贴合数据分布的少数类合成点,实验证明其及扩展算法优于现有几何采样方法。

摘要:

SMOTE(合成少数类过采样技术)是随机过采样以在不平衡学习问题中平衡类别的成熟几何方法,随后衍生出许多扩展。其思想是引入少数类的合成数据点,每个新点是现有数据点与其 k 近邻之一的凸组合。本文通过将 SMOTE 视为从几何邻域图的边上进行采样,并借鉴拓扑数据分析工具,提出了一种新技术 Simplicial SMOTE,它从几何邻域单纯复形的单纯形中采样。新合成点由相对于由任意数量足够接近的数据点所张成的单纯形的重心坐标定义,而非仅由一对数据点定义。这种几何数据模型的替换,相比现有几何采样方法,能更好地覆盖底层数据分布,并允许生成更接近决策边界上多数类的少数类合成点。我们通过实验证明,Simplicial SMOTE 优于包括原始 SMOTE 在内的几种流行几何采样方法。此外,我们展示了单纯形采样可轻松集成到现有 SMOTE 扩展中。我们泛化并评估了经典 Borderline SMOTE、Safe-level SMOTE 和 ADASYN 算法的单纯形扩展,它们的性能均优于其基于图的对应版本。

英文摘要:

SMOTE (Synthetic Minority Oversampling Technique) is the established geometric approach to random oversampling to balance classes in the imbalanced learning problem, followed by many extensions. Its idea is to introduce synthetic data points of the minor class, with each new point being the convex combination of an existing data point and one of its k-nearest neighbors. In this paper, by viewing SMOTE as sampling from the edges of a geometric neighborhood graph and borrowing tools from the topological data analysis, we propose a novel technique, Simplicial SMOTE, that samples from the simplices of a geometric neighborhood simplicial complex. A new synthetic point is defined by the barycentric coordinates w.r.t. a simplex spanned by an arbitrary number of data points being sufficiently close rather than a pair. Such a replacement of the geometric data model results in better coverage of the underlying data distribution compared to existing geometric sampling methods and allows the generation of synthetic points of the minority class closer to the majority class on the decision boundary. We experimentally demonstrate that our Simplicial SMOTE outperforms several popular geometric sampling methods, including the original SMOTE. Moreover, we show that simplicial sampling can be easily integrated into existing SMOTE extensions. We generalize and evaluate simplicial extensions of the classic Borderline SMOTE, Safe-level SMOTE, and ADASYN algorithms, all of which outperform their graph-based counterparts.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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