K-Means and Related Clustering Methods

• Published in: Core Concepts in Data Analysis pp. 221 - 281
• Main Author: Mirkin, Boris
• Format: Book Chapter
• Language: English
• Published: United Kingdom Springer London, Limited 2011; Springer London
• Series: Undergraduate Topics in Computer Science
• Subjects: Artificial intelligence; Cluster Centroid; Company Data; Data Scatter; Discrete mathematics; Fuzzy Cluster; Gravity Center; Maths for computer scientists
• ISBN: 0857292862; 9780857292865
• ISSN: 1863-7310
• DOI: 10.1007/978-0-85729-287-2_6

K-Means is arguably the most popular data analysis method. The method outputs a partition of the entity set into clusters and centroids representing them. It is very intuitive and usually requires just a few pages to get presented. This text includes a number of less popular subjects that are important when using K-Means for real-world data analysis: Data standardization, especially, at mixed scales Innate tools for interpretation of clusters Analysis of examples of K-Means working and its failures Initialization – the choice of the number of clusters and location of centroids sVersions of K-Means such as incremental K-Means, nature inspired K-Means, and entity-centroid “medoid” methods are presented. Three modifications of K-Means onto different cluster structures are given:. Fuzzy K-Means for finding fuzzy clusters, Expectation-Maximization (EM) for finding probabilistic clusters, and Kohonen self-organizing maps (SOM) that tie up the sought clusters to a visually convenient two-dimensional grid. Equivalent reformulations of K-Means criterion are described – they can yield different algorithms for K-Means. One of these is explained at length: K-Means extends Principal component analysis to the case of binary scoring factors, which yields the so-called Anomalous cluster method, a key to an intelligent version of K-Means with automated choice of the number of clusters and their initialization.