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Partitive clustering (K‐means family)

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Abstract Partitional clustering is an important part of cluster analysis. Cluster analysis can be considered as one of the the most important approaches to unsupervised learning. The goal of clustering is to find clusters from unlabeled data, which means that data belonging to the same cluster are as similar as possible, whereas data belonging to different clusters are as dissimilar as possible. Partitional clustering is categorized as a prototype‐based model, i.e., each cluster can be represented by a prototype, leading to a concise description of the original data set. According to different definitions of prototypes, such as data point, hyperplane, and hypersphere, the clustering methods can be categorized into different types of clustering algorithms with various prototypes. Besides organizing these partitional clustering methods into such a unified framework, relations between some commonly used nonpartitional clustering methods and partitional clustering methods are also discussed here. We give a brief overview of clustering, summarize well‐known partitional clustering methods, and discuss the major challenges and key issues of these methods. Simple numerical experiments using toy data sets are carried out to enhance the description of various clustering methods. © 2012 Wiley Periodicals, Inc. This article is categorized under: Algorithmic Development > Structure Discovery Fundamental Concepts of Data and Knowledge > Knowledge Representation Technologies > Structure Discovery and Clustering

Example of clustering. (a) The three clusters denoted by three different colors differ in shape and size. (b) Three different clusters for the USPS digit number ‘0’, ‘8’,‘9’.

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Clustering result of spectral clustering algorithm: (a) input data, (b) similarity matrix, (c) clustering result of the new data in the new feature space, and (d) clustering results of data set shown in (a).

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Complex data sets and clustering result. (a) Data set with three intermediate points. (b) Clustering result for (a) by K means.

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Clustering results of different clustering algorithms: (a) input data, (b) K‐means clustering, (c) K‐medoids clustering, and (d) affinity propagation algorithm.

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Clustering result of K‐means algorithm. (a) Input data. (b) Clustering result. The gained cluster centers (prototypes) are denoted by circles where they are not real data points in the original data set in (a).

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Different clustering results based on different similarity measures.

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