Global collaboration through local interaction in competitive learning

Area of Science:

• Computational topology
• Machine learning algorithms
• Data visualization

Background:

• Self-organizing maps (SOMs) are vital for preserving data topology.
• Previous methods required global agent interactions for SOMs.
• The necessity of global interaction for SOMs was an open question.

Purpose of the Study:

• To investigate if global topology can be uncovered using only local interactions in self-organizing agents.
• To develop a simplified and potentially distributed SOM algorithm.
• To assess the performance and scalability of the new approach on challenging datasets.

Main Methods:

• Developed a novel algorithm enforcing uniform map quality across agents.
• Utilized strictly local interactions between agents for map formation.
• Tested the algorithm on diverse and large-scale point cloud datasets.

Main Results:

• Demonstrated that global topology can be uncovered through local interactions alone.
• The algorithm successfully mapped the topology of challenging datasets.
• A linear relationship between training time and dataset size was observed for large point clouds.

Conclusions:

• Global interaction is not necessary for self-organizing maps to preserve global topology.
• The new approach reduces algorithmic complexity and is scalable.
• This work is a foundational step towards distributed self-organizing maps.