A Rigorous Link Between Self-Organizing Maps and Gaussian Mixture Models

• URL: http://arxiv.org/abs/2009.11710v1
• Date: Thu, 24 Sep 2020 14:09:04 GMT
• Title: A Rigorous Link Between Self-Organizing Maps and Gaussian Mixture Models
• Authors: Alexander Gepperth, Benedikt Pf\"ulb
• Abstract summary: This work presents a mathematical treatment of the relation between Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs) We show that energy-based SOM models can be interpreted as performing gradient descent. This link allows to treat SOMs as generative probabilistic models, giving a formal justification for using SOMs to detect outliers, or for sampling.
• Score: 78.6363825307044
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work presents a mathematical treatment of the relation between Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs). We show that energy-based SOM models can be interpreted as performing gradient descent, minimizing an approximation to the GMM log-likelihood that is particularly valid for high data dimensionalities. The SOM-like decrease of the neighborhood radius can be understood as an annealing procedure ensuring that gradient descent does not get stuck in undesirable local minima. This link allows to treat SOMs as generative probabilistic models, giving a formal justification for using SOMs, e.g., to detect outliers, or for sampling.

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