Topology description for data distributions using a topology graph with divide-and-combine learning strategy

Area of Science:

• Data Science
• Topology
• Machine Learning

Background:

• Understanding data distribution topologies is crucial for effective data description.
• General distributions often lack intuitive topological descriptions.
• Existing methods struggle to provide clear insights into data topology.

Purpose of the Study:

• To propose a novel concept, the topology graph, for describing the principal topology of data distributions.
• To establish a one-to-one correspondence between data topology features and graph structures.
• To develop a method for learning and generating these topology graphs.

Main Methods:

• A novel concept of a 'topology graph' is introduced.
• A divide-and-combine learning strategy is developed for general data distributions.
• A cluster growing algorithm is implemented based on the learning strategy.

Main Results:

• The topology graph effectively represents the skeleton of data distributions.
• Annularity features correspond to graph loops, and divarication features correspond to graph branches.
• Experimental results demonstrate good performance on artificial and real-world datasets.

Conclusions:

• Topology graphs provide an intuitive understanding of data distribution topologies.
• The proposed learning strategy and cluster growing algorithm are effective in generating topology graphs.
• The method shows promise for various data analysis applications.