SOM of SOMs.

Area of Science:

• Computational intelligence
• Machine learning
• Topology

Background:

• Self-organizing maps (SOMs) are unsupervised learning algorithms for dimensionality reduction and data visualization.
• Existing SOM architectures may struggle with organizing complex, multi-layered data distributions.
• Hierarchical data structures are prevalent in various scientific domains.

Purpose of the Study:

• To propose and describe a novel hierarchical extension of the Self-Organizing Map (SOM) called SOM(2).
• To introduce a "SOM of SOMs" architecture capable of organizing product manifolds.
• To generalize this hierarchical concept to other neural network families like Neural Gas (NG).

Main Methods:

• Development of the SOM(2) architecture, featuring a parent SOM and multiple child SOMs.
• Training child SOMs to represent data class distributions on manifolds.
• Training the parent SOM to map the group of manifolds represented by child SOMs.
• Generalization to SOM(n) and combinations with other SOM families (e.g., Neural Gas).

Main Results:

• The SOM(2) architecture successfully organizes a product manifold, analogous to a fiber bundle in topology.
• Algorithms for SOM(2) and its variations are presented.
• Simulation results demonstrating the efficacy of the proposed hierarchical SOM approach are reported.

Conclusions:

• The SOM(2) provides a powerful hierarchical framework for organizing complex data distributions.
• This extension offers flexibility by allowing combinations with other SOM families and generalization to higher dimensions (SOM(n)).
• The proposed architecture has potential applications in domains requiring the analysis of structured and multi-level data.