Interval data clustering using self-organizing maps based on adaptive Mahalanobis distances

The self-organizing map is a kind of artificial neural network used to map high dimensional data into a low dimensional space. This paper presents a self-organizing map for interval-valued data based on adaptive Mahalanobis distances in order to do clustering of interval data with topology preservation. Two methods based on the batch training algorithm for the self-organizing maps are proposed. The first method uses a common Mahalanobis distance for all clusters. In the second method, the algorithm starts with a common Mahalanobis distance per cluster and then switches to use a different distance per cluster. This process allows a more adapted clustering for the given data set. The performances of the proposed methods are compared and discussed using artificial and real interval data sets.