Neural Gas Clustering for Dissimilarity Data with Continuous Prototypes

Prototype based neural clustering or data mining methods such as the self-organizing map or neural gas constitute intuitive and powerful machine learning tools for a variety of application areas. However, the classical methods are restricted to data embedded in a real vector space and have only limited applicability to noneuclidean data as occurs in, for example, biomedical or symbolic fields. Recently, extensions of unsupervised neural prototype based clustering to dissimilarity data, i.e. data characterized in terms of a dissimilarity matrix only, have been proposed substituting the mean by the so-called generalized median. Thereby, the location of prototypes is chosen within the discrete input space which constitutes a severe limitation in particular for sparse data sets since the prototype flexibility is restricted. Here we present a generalization of median neural gas such that prototypes can be interpreted as mixtures of discrete input locations. We derive a batch optimization scheme based on a corresponding cost function.