Ordering process of self-organizing maps improved by asymmetric neighborhood function

Area of Science:

• Artificial Intelligence
• Computational Neuroscience
• Machine Learning

Background:

• Self-Organizing Maps (SOMs) are unsupervised neural network algorithms.
• SOMs can enter undesirable multi-stable states, leading to topological defects and performance degradation.

Purpose of the Study:

• To address topological defects in SOMs.
• To enhance the ordering process and performance of SOMs.

Main Methods:

• Introduction of an asymmetric neighborhood function into the SOM algorithm.
• Comparison with conventional symmetric neighborhood functions.
• Development of an improved asymmetric neighborhood function to mitigate map distortion.

Main Results:

• The asymmetric neighborhood function accelerates the ordering process, even with defects.
• For 1D SOMs, the ordering steps are reduced from O(N^3) to O(N^2).
• The proposed method addresses ordering issues in twisted states of 2D SOMs, which are problematic for symmetric functions.

Conclusions:

• Asymmetric neighborhood functions offer a significant improvement for SOM training.
• The enhanced SOM algorithm demonstrates increased efficiency and robustness against topological defects.
• This approach is effective for both 1D and 2D SOMs, including complex configurations.