Learning the Number of Clusters in Self Organizing Map

Abstract

The Self-Organizing Map (SOM: Kohonen (1984, 2001)) is a neuro-computational algorithm to map high-dimensional data to a two-dimensional space through a competitive and unsupervised learning process. Self-Organizing Maps differ from other artificial neural networks in the sense that they use a neighborhood function to preserve the topological properties of the input space. This unsupervised learning algorithm is a popular nonlinear technique for dimensionality reduction and data visualization. The SOM is often used as a first phase for unsupervised classification (i.e. clustering). Clustering methods are able to perform an automatic detection of relevant sub-groups or clusters in unlabeled data sets, when one does not have prior knowledge about the hidden structure of these data. Patterns in the same cluster should be similar to each other, while patterns in different clusters should not (internal homogeneity and the external separation). Clustering plays an indispensable role for understanding various phenomena described by data sets. A clustering problem can be defined as the task of partitioning a set of objects into a collection of mutually disjoint subsets. Clustering is a segmentation problem which is considered as one of the most challenging problems in unsupervised learning. Various approaches have been proposed to solve the problem (Jain & Dubes, 1988). An efficient method to grouping problems is based on the learning of a Self-Organizing Map. In the first phase of the process, the standard SOM approach is used to compute a set of reference vectors (prototypes) representing local means of the data. In the second phase, the obtained prototypes are grouped to form the final partitioning using a traditional clustering method (e.g. K-means or hierarchical methods). Such an approach is called a twolevel clustering method. In this work, we focus particular attention on two-level clustering algorithms. One of the most crucial questions in many real-world cluster applications is how to determine a suitable number of clusters K, also known as the model selection problem. Without a priori knowledge there is no simple way of knowing that number. The purpose of our work is to provide a simultaneous two-level clustering approach using SOM, by learning at the same time the structure of the data and its segmentation, using both distance and density information. This new clustering algorithm assumes that a cluster is a dense region of objects surrounded by a region of low density (Yue et al., 2004; Ultsch, 2005; Ocsa et al., 2007; Pamudurthy et al., 2007). This approach is very effective when the clusters are 2