This paper synthesizes the results, methodology, and research conducted concerning the K-means clustering method over the last fifty years. The K-means method is first introduced, various formulations of the minimum variance loss function and alternative loss functions within the same class are outlined, and different methods of choosing the number of clusters and initialization, variable preprocessing, and data reduction schemes are discussed. Theoretic statistical results are provided and various extensions of K-means using different metrics or modifications of the original algorithm are given, leading to a unifying treatment of K-means and some of its extensions. Finally, several future studies are outlined that could enhance the understanding of numerous subtleties affecting the performance of the K-means method.

K‐means clustering: A half‐century synthesis

This paper proposes a k-means type clustering algorithm that can automatically calculate variable weights. A new step is introduced to the k-means clustering process to iteratively update variable weights based on the current partition of data and a formula for weight calculation is proposed. The convergency theorem of the new clustering process is given. The variable weights produced by the algorithm measure the importance of variables in clustering and can be used in variable selection in data mining applications where large and complex real data are often involved. Experimental results on both synthetic and real data have shown that the new algorithm outperformed the standard k-means type algorithms in recovering clusters in data.

Automated variable weighting in k-means type clustering

This textbook explores the different aspects of data mining from the fundamentals to the complex data types and their applications, capturing the wide diversity of problem domains for data mining issues. It goes beyond the traditional focus on data mining problems to introduce advanced data types such as text, time series, discrete sequences, spatial data, graph data, and social networks. Until now, no single book has addressed all these topics in a comprehensive and integrated way. The chapters of this book fall into one of three categories: Fundamental chapters: Data mining has four main problems, which correspond to clustering, classification, association pattern mining, and outlier analysis. These chapters comprehensively discuss a wide variety of methods for these problems. Domain chapters: These chapters discuss the specific methods used for different domains of data such as text data, time-series data, sequence data, graph data, and spatial data. Application chapters: These chapters study important applications such as stream mining, Web mining, ranking, recommendations, social networks, and privacy preservation. The domain chapters also have an applied flavor. Appropriate for both introductory and advanced data mining courses, Data Mining: The Textbook balances mathematical details and intuition. It contains the necessary mathematical details for professors and researchers, but it is presented in a simple and intuitive style to improve accessibility for students and industrial practitioners (including those with a limited mathematical background). Numerous illustrations, examples, and exercises are included, with an emphasis on semantically interpretable examples. Praise for Data Mining: The Textbook - As I read through this book, I have already decided to use it in my classes. This is a book written by an outstanding researcher who has made fundamental contributions to data mining, in a way that is both accessible and up to date. The book is complete with theory and practical use cases. Its a must-have for students and professors alike!" -- Qiang Yang, Chair of Computer Science and Engineering at Hong Kong University of Science and Technology"This is the most amazing and comprehensive text book on data mining. It covers not only the fundamental problems, such as clustering, classification, outliers and frequent patterns, and different data types, including text, time series, sequences, spatial data and graphs, but also various applications, such as recommenders, Web, social network and privacy. It is a great book for graduate students and researchers as well as practitioners." -- Philip S. Yu, UIC Distinguished Professor and Wexler Chair in Information Technology at University of Illinois at Chicago

Data Mining: The Textbook

Use of traditional k-mean type algorithm is limited to numeric data. This paper presents a clustering algorithm based on k-mean paradigm that works well for data with mixed numeric and categorical features. We propose new cost function and distance measure based on co-occurrence of values. The measures also take into account the significance of an attribute towards the clustering process. We present a modified description of cluster center to overcome the numeric data only limitation of k-mean algorithm and provide a better characterization of clusters. The performance of this algorithm has been studied on real world data sets. Comparisons with other clustering algorithms illustrate the effectiveness of this approach.

A k-mean clustering algorithm for mixed numeric and categorical data

With the technology development in cyber physical systems and big data, there are huge potential to apply them to achieve personalization and improve resource efficiency in Industry 4.0. As Industr...

Big data for cyber physical systems in industry 4.0: a survey

This correspondence describes extensions to the fuzzy k-means algorithm for clustering categorical data. By using a simple matching dissimilarity measure for categorical objects and modes instead of means for clusters, a new approach is developed, which allows the use of the k-means paradigm to efficiently cluster large categorical data sets. A fuzzy k-modes algorithm is presented and the effectiveness of the algorithm is demonstrated with experimental results.

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A fuzzy k-modes algorithm for clustering categorical data

Recently, Chaturvedi, Green and Carroll (2001) presented a nonparametric approach to deriving clusters from categorical data using a new clustering procedure called K-modes. Huang (1998) proposed the K-modes clustering algorithm. In this note, we demonstrate the equivalence of the two K-modes procedures.

A Note on K-modes Clustering

In this paper we present some initial results of a project which uses data-mining techniques to search for evidence of massive compact halo objects (MACHOs) from very large time series database. MACHOs are the proposed materials that probably make the “dark matter” surrounding our own and other galaxies. It was suggested that MACHOs may be detected through the gravitational microlensing effect which can be identified from the light curves of background stars. The objective of this project is two-fold, namely, (i) identification of new classes of variable stars and (ii) detection of microlensing events. In this paper, we present the major characteristics of the time series astronomical data, data preprocessing techniques to process these time series, and some domain-specific techniques to separate candidate variable stars from the nonvariant ones. We discuss the use of the Fourier model to represent the time series and the k -means based clustering method to classify variable stars.

Zhexue Huang

Papers

A fuzzy k-modes algorithm for clustering categorical data

A Note on K-modes Clustering

Data-mining massive time series astronomical data: challenges, problems and solutions