Potential-based Hierarchical Agglomerative (PHA) clustering

Potential-based Hierarchical Agglomerative (PHA) clustering implements a hierarchical agglomerative clustering approach that leverages a constructed potential field together with pairwise distances to capture global and local data distribution for improved cluster identification.

Key Features:

• Potential Field Construction: Constructs a potential field for all data points related to nonparametric estimation of the global probability density function.
• Similarity Metric: Defines a similarity metric that integrates the potential field and the distance matrix to combine global and local distribution information.
• Edge-Weighted Tree Representation: Provides an equivalent similarity formulation based on an edge-weighted tree encompassing all data points.
• Computational Complexity: Implements a fast agglomerative clustering algorithm with reported time complexity O(N-2).
• Empirical Evaluation: Has been evaluated against six other typical agglomerative clustering methods on four synthetic datasets and two real-world datasets, showing faster runtimes and more satisfactory clustering outcomes in most scenarios.
• Versatility: Demonstrates robustness across different types of datasets.

Scientific Applications:

• Benchmarking and method comparison: Used to compare clustering performance against other agglomerative methods on synthetic and real-world datasets.
• General cluster analysis: Applied to diverse dataset types to identify cluster structures by integrating global probability density information and local distances.

Methodology:

Constructs a potential field related to nonparametric estimation of the global probability density function; computes a similarity metric combining the potential field and the distance matrix; derives an equivalent similarity via an edge-weighted tree; applies a fast agglomerative clustering algorithm with time complexity O(N-2).