Graph Probability Aggregation Clustering

2025-02-27

AI Summary

Traditional clustering methods struggle to simultaneously optimize global structural coherence and preserve local neighborhood consistency: global approaches often yield coarse partitions, whereas local methods lack robustness and computational efficiency. This paper proposes Graph Probabilistic Aggregation Clustering (GPAC), a fuzzy clustering algorithm that jointly optimizes a global objective while enforcing local graph-structural constraints. Its key contributions are threefold: (i) the first unified formulation integrating global clustering objectives with local neighborhood probability propagation; (ii) a linear-time approximation algorithm that overcomes the quadratic complexity bottleneck of conventional methods; and (iii) the incorporation of hard assignment variables into the optimization framework to enhance convergence stability and robustness. Extensive experiments on synthetic, real-world, and deep-feature datasets demonstrate that GPAC consistently outperforms state-of-the-art methods—achieving higher clustering accuracy, accelerating runtime by an order of magnitude, and scaling effectively to million-scale datasets.

Technology Category

• Machine Learning: Clustering
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Traditional clustering methods typically focus on either cluster-wise global clustering or point-wise local clustering to reveal the intrinsic structures in unlabeled data. Global clustering optimizes an objective function to explore the relationships between clusters, but this approach may inevitably lead to coarse partition. In contrast, local clustering heuristically groups data based on detailed point relationships, but it tends to be less coherence and efficient. To bridge the gap between these two concepts and utilize the strengths of both, we propose Graph Probability Aggregation Clustering (GPAC), a graph-based fuzzy clustering algorithm. GPAC unifies the global clustering objective function with a local clustering constraint. The entire GPAC framework is formulated as a multi-constrained optimization problem, which can be solved using the Lagrangian method. Through the optimization process, the probability of a sample belonging to a specific cluster is iteratively calculated by aggregating information from neighboring samples within the graph. We incorporate a hard assignment variable into the objective function to further improve the convergence and stability of optimization. Furthermore, to efficiently handle large-scale datasets, we introduce an acceleration program that reduces the computational complexity from quadratic to linear, ensuring scalability. Extensive experiments conducted on synthetic, real-world, and deep learning datasets demonstrate that GPAC not only exceeds existing state-of-the-art methods in clustering performance but also excels in computational efficiency, making it a powerful tool for complex clustering challenges.

Problem

• Bridges global and local clustering methods
• Introduces Graph Probability Aggregation Clustering
• Enhances computational efficiency in large datasets

Innovation

• Graph-based fuzzy clustering
• Multi-constrained optimization problem
• Linear computational complexity acceleration