The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

Time-series clustering - A decade review

With modern technologies such as microarray, deep sequencing, and liquid chromatography-mass spectrometry (LC-MS), it is possible to measure the expression levels of thousands of genes/proteins simultaneously to unravel important biological processes. A very first step towards elucidating hidden patterns and understanding the massive data is the application of clustering techniques. Nonlinear relations, which were mostly unutilized in contrast to linear correlations, are prevalent in high-throughput data. In many cases, nonlinear relations can model the biological relationship more precisely and reflect critical patterns in the biological systems. Using the general dependency measure, Distance Based on Conditional Ordered List (DCOL) that we introduced before, we designed the nonlinear K-profiles clustering method, which can be seen as the nonlinear counterpart of the K-means clustering algorithm. The method has a built-in statistical testing procedure that ensures genes not belonging to any cluster do not impact the estimation of cluster profiles. Results from extensive simulation studies showed that K-profiles clustering not only outperformed traditional linear K-means algorithm, but also presented significantly better performance over our previous General Dependency Hierarchical Clustering (GDHC) algorithm. We further analyzed a gene expression dataset, on which K-profile clustering generated biologically meaningful results.

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K-Profiles: A Nonlinear Clustering Method for Pattern Detection in High Dimensional Data.

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally, we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm. This review adds to the earlier version, Murtagh F, Contreras P. Algorithms for hierarchical clustering: an overview, Wiley Interdiscip Rev: Data Mining Knowl Discov 2012, 2, 86–97. WIREs Data Mining Knowl Discov 2017, 7:e1219. doi: 10.1002/widm.1219

This article is categorized under: 

Algorithmic Development > Hierarchies and Trees
Technologies > Classification
Technologies > Structure Discovery and Clustering

Algorithms for hierarchical clustering: an overview

Preface Part I. Clustering, Data and Similarity Measures: 1. Data clustering 2. DataTypes 3. Scale conversion 4. Data standardization and transformation 5. Data visualization 6. Similarity and dissimilarity measures Part II. Clustering Algorithms: 7. Hierarchical clustering techniques 8. Fuzzy clustering algorithms 9. Center Based Clustering Algorithms 10. Search based clustering algorithms 11. Graph based clustering algorithms 12. Grid based clustering algorithms 13. Density based clustering algorithms 14. Model based clustering algorithms 15. Subspace clustering 16. Miscellaneous algorithms 17. Evaluation of clustering algorithms Part III. Applications of Clustering: 18. Clustering gene expression data Part IV. Matlab and C++ for Clustering: 19. Data clustering in Matlab 20. Clustering in C/C++ A. Some clustering algorithms B. Thekd-tree data structure C. Matlab Codes D. C++ Codes Subject index Author index.

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Chaoqun Ma

Papers

Data Clustering: Theory, Algorithms, and Applications

Data Clustering: Theory, Algorithms, and Applications (ASA-SIAM Series on Statistics and Applied Probability)

1. Data Clustering

19. Data Clustering in MATLAB

9. Center-Based Clustering Algorithms