Clustering by Local Gravitation.

Area of Science:

• Data Science
• Machine Learning
• Computational Statistics

Background:

• Cluster analysis aims to group data points using distance metrics.
• Existing methods may not fully capture nuanced relationships within data clusters.
• Understanding local data point interactions is crucial for effective clustering.

Purpose of the Study:

• To propose a novel clustering model based on local gravitation among data points.
• To introduce new local measures, centrality and coordination, to capture differences in data point forces.
• To develop and validate new clustering algorithms: local gravitation clustering and communication with local agents.

Main Methods:

• A local gravitation model where data points exert forces on neighbors.
• Definition and investigation of centrality and coordination measures.
• Development of two new clustering algorithms: local gravitation clustering and communication with local agents.
• Empirical validation using synthetic and real-world datasets.

Main Results:

• Distinct differences in local resultant forces (LRF) exist between cluster centers and boundaries.
• Centrality and coordination measures effectively capture these LRF differences.
• Both proposed clustering methods demonstrate good performance across diverse datasets.
• The local gravitation approach offers a new perspective on data partitioning.

Conclusions:

• The local gravitation clustering and communication with local agents methods are effective for data partitioning.
• The proposed local measures (centrality and coordination) enhance the understanding of cluster structures.
• This work provides a novel framework for cluster analysis leveraging local interactions.