Exploring the impact of label-level noise on multi-label k-Nearest Neighbor classification

Abstract

Multi-label classification methods based on the k-Nearest Neighbor (kNN) rule are widely used due to their simplicity and competitive performance, but their behavior under label-level noise remains insufficiently understood, especially when combined with data reduction techniques. This paper presents a comprehensive empirical study of the impact of label-level noise on multi-label kNN classification and on Multi-label Prototype Generation (MPG) methods. We formalize six label-level noise induction policies—Additive, Subtractive, Additive-Subtractive, Distribution-Aware Additive-Subtractive, Partial Uniform Multi-label, and Swap—parameterized by both the proportion of affected instances and a severity parameter. Their effect is analyzed on three representative kNN-based multi-label classifiers (BRkNN, LPkNN, and MLkNN) and five MPG strategies (MRHC, MChen, MRSP1-3) across eight benchmark datasets with varying label cardinality and imbalance, comprising an extensive experimental grid of 816,480 configurations. The results reveal that Additive and Partial Uniform noise are the most detrimental, whereas Subtractive and cardinality-preserving policies are comparatively less harmful. Moderate neighborhood sizes (around \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k=7$$\end{document}) provide a good trade-off between robustness and accuracy, while MLkNN is consistently the most resilient classifier under severe noise. Among MPG methods, MRSP3 emerges as the most robust reduction strategy, whereas aggressive reductions, particularly with MRHC, can amplify the negative effects of noise. The code and complete experimental results are publicly released to support reproducibility and further research.