Supervised Batch Neural Gas

Recently, two extensions of neural gas have been proposed: a fast batch version of neural gas for data given in advance, and extensions of neural gas to learn a (possibly fuzzy) supervised classification. Here we propose a batch version for supervised neural gas training which allows to efficiently learn a prototype-based classification, provided training data are given beforehand. The method relies on a simpler cost function than online supervised neural gas and leads to simpler update formulas. We prove convergence of the algorithm in a general framework, which also incorporates supervised k-means and supervised batch-SOM, and which opens the way towards metric adaptation as well as application to proximity data not embedded in a real-vector space.