Batch SOM algorithms for interval-valued data with automatic weighting of the variables
Résumé
Interval-valued data is most utilized to represent either the uncertainty related to a single measurement, or the variability of the information inherent to a group rather than an individual. In this paper, we focus on Kohonen self-organizing maps (SOMs) for interval-valued data, and design a new Batch SOM algorithm that optimizes an explicit objective function. This algorithm can handle, respectively, suitable City-Block, Euclidean and Hausdorff distances with the purpose to compare interval-valued data during the training of the SOM. Moreover, most often conventional batch SOM algorithms consider that all variables are equally important in the training of the SOM. However, in real situations, some variables may be more or less important or even irrelevant for this task. Thanks to a parameterized definition of the above-mentioned distances, we propose also an adaptive version of the new algorithm that tackles this problem with an additional step where a relevance weight is automatically learned for each interval-valued variable. Several examples with synthetic and real interval-valued data sets illustrate the usefulness of the two novel batch SOM algorithms.