Smoothed data density histogram on self-organizing map and its application to cluster analysis

This paper proposes an automatic clustering method using self-organizing feature maps (SOM). There are a lot of studies on the automatic clustering. Among them, SOM-based clustering methods are attracted in terms of visual understandabilities. In general SOM, each weight vector after learning covers a subspace in input space. In the SOM-based clustering, a histogram, i.e. a density distribution of data, is constructed from the frequency of data existing in each subspace. In most situations, the histogram obtained from the learnt SOM involves more excessive peaks and valleys than we envisioned by the true number of clusters. Therefore, it is difficult to assign the data to clusters from the visual inspections of histogram. In this study, to eliminate the unnecessary extremums from histogram and make cluster analyses easier, a method to smooth the histogram is proposed. In the proposed method, the histogram is edited by considering learnt weight vectors and neighborhood characteristics. As a result, the edited histogram is enough smoothed to understand the relationships between the agglomeration of data and clusters. In addition, an automatic clustering scheme is proposed on the basis of the edited histogram. The effectiveness and the validity of the proposed method for the automatic clustering are examined for several artificially generated data.