# Global Collaboration through Local Interaction in Competitive Learning

## TL;DR

This paper demonstrates that global data topology can be learned through local interactions alone, enabling scalable, distributed self-organizing maps with reduced complexity.

## Contribution

It introduces a novel algorithm that uncovers global topology via local interactions, challenging the assumption that global communication is necessary.

## Key findings

- The algorithm reliably uncovers global topology across diverse datasets.
- Map training time scales linearly with dataset size.
- The approach reduces algorithmic complexity and supports distributed implementation.

## Abstract

Feature maps, that preserve the global topology of arbitrary datasets, can be formed by self-organizing competing agents. So far, it has been presumed that global interaction of agents is necessary for this process. We establish that this is not the case, and that global topology can be uncovered through strictly local interactions. Enforcing uniformity of map quality across all agents, results in an algorithm that is able to consistently uncover the global topology of diversely challenging datasets.The applicability and scalability of this approach is further tested on a large point cloud dataset, revealing a linear relation between map training time and size. The presented work not only reduces algorithmic complexity but also constitutes first step towards a distributed self organizing map.