From variable weighting to cluster characterization in topographic unsupervised learning

We introduce a new learning approach, which provides simultaneously self-organizing map (SOM) and local weight vector for each cluster. The proposed approach is computationally simple, and learns a different features vector weights for each cell (relevance vector). Based on the self-organizing map approach, we present two new simultaneously clustering and weighting algorithms: local weighting observation lwo-SOM and local weighting distance lwd-SOM. Both algorithms achieve the same goal by minimizing different cost functions. After learning phase, a selection method with weight vectors is used to prune the irrelevant variables and thus we can characterize the clusters. We illustrate the performance of the proposed approach using different data sets. A number of synthetic and real data are experimented on to show the benefits of the proposed local weighting using self-organizing models.