Randomized Self-Organizing Map.

Area of Science:

• Computational neuroscience
• Machine learning
• Topology

Background:

• Self-organizing maps (SOMs) are unsupervised learning algorithms for dimensionality reduction and visualization.
• Traditional SOMs often use regular grid structures, which can limit flexibility with complex data.
• High-dimensional datasets pose challenges for standard SOM topology and organization.

Purpose of the Study:

• To propose a novel variation of the self-organizing map algorithm.
• To introduce random neuron placement on a 2D manifold using blue noise distribution.
• To enable more flexible self-organization, particularly for high-dimensional data.

Main Methods:

• Developed a randomized self-organizing map (RSOM) algorithm.
• Utilized blue noise distribution for initial neuron placement, creating controllable discontinuities.
• Tested the algorithm on 1D, 2D, and 3D tasks, including the MNIST dataset.
• Validated results using spectral analysis and topological data analysis (TDA).

Main Results:

• The RSOM demonstrated effective self-organization across various dimensionalities.
• Controllable discontinuities in topology improved flexibility with high-dimensional data.
• The algorithm showed robustness, successfully reorganizing after simulated neural lesion and neurogenesis.
• Validation confirmed the topological properties and organizational capabilities of the RSOM.

Conclusions:

• The randomized self-organizing map offers enhanced flexibility and adaptability for complex datasets.
• Blue noise-based topology provides a robust framework for unsupervised learning.
• The RSOM's ability to handle neural plasticity demonstrates potential for brain-inspired computing.