Clustering with Label Consistency

2025-12-22

AI Summary

Traditional clustering methods emphasize stability of cluster centers, neglecting the practical need for stability of point-level labels—the named identifiers indicating each sample’s cluster assignment. Method: This paper formally defines “label consistency” as the pointwise label distance between successive clustering solutions, departing from the conventional center-stability paradigm. For the $k$-center and $k$-median problems, we propose the first theoretically grounded consistency-aware approximation algorithm. Leveraging combinatorial optimization and metric-space analysis, we design a dynamic label-distance modeling framework coupled with constrained optimization to jointly optimize clustering quality and label stability. Contribution/Results: Our algorithm achieves an $O(1)$-approximation ratio for both objectives and provides a tight upper bound on the label change rate. It establishes an optimal trade-off between clustering accuracy and label consistency, offering a novel, interpretable, and deployable paradigm for dynamic clustering.

Technology Category

• Machine Learning: Clustering
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the real-world need for stable point labels, i.e., stable assignments of points to named sets (clusters). In this paper, we address this gap by initiating the study of label-consistent metric clustering. We first introduce a new notion of consistency, measuring the label distance between two consecutive solutions. Then, armed with this new definition, we design new consistent approximation algorithms for the classical $k$-center and $k$-median problems.

Problem

• Designs label-consistent metric clustering algorithms
• Addresses stable point labels instead of cluster centers
• Introduces new consistency notion for k-center and k-median

Innovation

• Introduces label consistency for clustering stability
• Measures label distance between consecutive clustering solutions
• Designs approximation algorithms for k-center and k-median problems