Magnification control in self-organizing maps and neural gas

Area of Science:

• Machine Learning
• Artificial Neural Networks
• Data Science

Background:

• Vector quantization methods have historically explored magnification control.
• Self-organizing maps (SOM) and neural gas (NG) are unsupervised learning algorithms.
• Controlling magnification is crucial for adapting these algorithms to data structures.

Purpose of the Study:

• To investigate and compare magnification control strategies for SOM and NG.
• To adapt and extend existing magnification control methods to both algorithms.
• To analyze the impact of these control mechanisms on algorithm behavior across different data dimensions.

Main Methods:

• Application of three structurally similar learning approaches: localized learning, concave-convex learning, and winner-relaxing learning.
• Extension of concave-convex learning for SOM to a more generalized framework.
• Introduction of concave-convex learning as a novel approach for NG.

Main Results:

• The three investigated control mechanisms demonstrate applicability to both SOM and NG.
• Concave-convex learning for NG is presented as a new method.
• Generally, control mechanisms yield only minor behavioral differences between SOM and NG.

Conclusions:

• The proposed magnification control methods are effective for both SOM and NG.
• Neural gas (NG) demonstrates robustness across all data dimensions for these methods.
• Self-organizing maps (SOM) show dimension-specific limitations, with results primarily valid for one-dimensional data.