Sequential Cluster Estimation: A Generalized Model for Finding Large Numbers of Clusters in Data

Abstract

Clustering is an unsupervised learning method that partitions a set of objects into groups (clusters) of similar objects, where similarity is often computed from numerical object feature vectors (also called data points). An early (and still very popular) clustering algorithm, called k-means, finds clusters by minimizing the sum of the squared distances between data points and associated cluster centers. The k-means algorithm (like many other so-called hard clustering algorithms) assigns each object to one and only one of the considered clusters. In practice, however, cluster assignments may often be ambiguous. Objects may partially belong to several clusters or fit to none of these clusters. Such kinds of ambiguity can be mathematically handled by what is termed fuzzy set theory . A fuzzy variant of k -means called fuzzy c-means (FCM) has emerged to become one of the most popular fuzzy clustering methods, with hundreds of thousands of scientific publications. For a survey. Fuzzy clustering is often used to generate membership functions for fuzzy rule-based systems. Alternating cluster estimation (ACE)is an extension of FCM for arbitrary membership function shapes. This article introduces sequential cluster estimation (SCE), a variant of ACE that finds clusters sequentially and outperforms nonsequential clustering for data with many clusters.