Performance evaluation of FMIG clustering using fuzzy validity indexes

The clustering of high-dimensional data presents a critical computational problem. Therefore, it is convenient to arrange the cluster centres on a grid with a small dimensional space that reduces computational cost and can be easily visualized. Moreover, in real applications there is no sharp boundary between classes, real datasets are naturally defined in a fuzzy context. Therefore, fuzzy clustering fits better for complex real datasets to determine the best distribution. Self-organizing map (SOM) technique is appropriate for clustering and vector quantization of high-dimensional data. In this paper we present a new fuzzy learning approach called FMIG (fuzzy multilevel interior growing self-organizing maps). The proposed algorithm is a fuzzy version of MIGSOM (multilevel interior growing self-organizing maps). The main contribution of FMIG is to define a fuzzy process of data mapping and to take into account the fuzzy aspect of high-dimensional real datasets. This new algorithm is able to auto-organize the map accordingly to the fuzzy training property of the nodes. In the second step, the introduced scheme for FMIG is clustered by means of fuzzy C-means (FCM) to discover the interior class distribution of the learned data. The validation of FCM partitions is directed by applying six validity indexes. Superiority of the new method is demonstrated by comparing it with crisp MIGSOM, GSOM (growing SOM) and FKCN (fuzzy Kohonen clustering network) techniques. Thus, our new method shows improvement in term of quantization error, topology preservation and clustering ability.