A Rigorous Link Between Self-Organizing Maps and Gaussian Mixture Models
| Autor: | Alexander Gepperth, Benedikt Pfülb |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Self-organizing map
Computer science Computer Science::Neural and Evolutionary Computation Probabilistic logic Sampling (statistics) 02 engineering and technology 010501 environmental sciences Mixture model 01 natural sciences Maxima and minima Stochastic gradient descent Outlier 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Gradient descent Algorithm 0105 earth and related environmental sciences |
| Zdroj: | Artificial Neural Networks and Machine Learning – ICANN 2020 ISBN: 9783030616151 ICANN (2) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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