Commitment and typicality measures for the Self-Organizing Map

Abstract

Soft classification using Kohonen's Self-Organizing Map (SOM) has not been explored as thoroughly as the Multi-Layer-Perceptron (MLP) neural network. In this paper, we propose two non-parametric algorithms for the SOM to provide soft classification outputs. These algorithms, which are labelling-frequency-based, are called SOM Commitment (SOM-C) and SOM Typicality (SOM-T), expressing in the first case the degree of commitment the classifier has for each class for a specific pixel and in the second case, how typical that pixel's reflectances are of those upon which the classifier was trained. To evaluate the two proposed algorithms, soft classifications of a Satellite Pour l'Observation de la Terre (SPOT) High Resolution Visible (HRV) image and an Airborne Visible Infrared Imaging Spectrometer (AVIRIS) image were undertaken. Both traditional soft classifiers, i.e. Bayesian posterior probability and Mahalanobis typicality classifier, and the most frequently used non-parametric neural network model, i.e. MLP, were used as a comparison. Principal-components analysis (PCA) was used to explore the relationship between these measures. Results indicate that great similarities exist between the SOM-C, MLP and the Bayesian posterior probability classifiers, while the SOM-T corresponds closely with Mahalanobis typicality probabilities. However, as implemented, they have the advantage of being non-parametric. The proposed measures significantly outperformed Bayesian and Mahalanobis classifiers when using the hyperspectral AVIRIS image.

Acknowledgements

The support of the University Consortium of Geographic Information Science (UCGIS) and Clark Labs are gratefully acknowledged. The procedures covered in this paper have been implemented in the IDRISI GIS and Image Processing System.