Chapter 5

Detection of the Number of Clusters through Non-Parametric Clustering Algorithms

5.1. Introduction

As described in Chapter 1, the identification of the optimum number of clusters in a dataset is one of the fundamental open problems in unsupervised learning. One solution to this problem is (implicitly) provided by the pole-based clustering (PoBOC) algorithm proposed by Guillaume Cleizou [CLE 04a]. Among the different clustering approaches described in Chapter 1, the PoBOC algorithm is the only method that does not require the specification of any kind of a priori information from the user. The algorithm is an overlapping, graph-based approach that iteratively identifies a set of initial cluster prototypes and builds the clusters around these objects based on their neighborhoods.

However, one limitation of the PoBOC algorithm is related to the global formulation of neighborhood applied to extract the final clusters. The neighborhood of one object is defined in terms of its average distance to all other objects in the dataset (see section 2.1). This global parameter may be suitable for discovering uniformly spread clusters on the data space. However, the algorithm may fail to identify all existing clusters if the input data are organized in a hierarchy of classes, in such a way that two or more subclasses are closer to each other than the average class distance.

To overcome this limitation, a new hierarchical strategy based on PoBOC has been developed called “hierarchical ...

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