Cluster analysis and applications

With the development of Big Data platforms for managing massive amount of data and wide availability of tools for processing these data, the biggest limitation is the lack of trained experts who are qualified to process and interpret the results. This textbook is intended for graduate students and experts using methods of cluster analysis and applications in various fields. With clear explanations of ideas and precise definitions of notions, accompanied by numerous examples and exercises together with Mathematica programs and modules, Cluster Analysis and Applications is meant for students and researchers in various disciplines, working in data analysis or data science.

1 -- Introduction. 2 Representatives -- 2.1 Representative of data sets with one feature. 2.1.1. Best LS-representative -- 2.1.2 Best `1-representative -- 2.1.3 Best representative of weighted data -- 2.1.4 Bregman divergences -- 2.2 Representative of data sets with two features -- 2.2.1 Fermat orricelli weber problem -- 2.2.2 Centroid of a set in the plane -- 2.2.3 Median of a set in the plane -- 2.2.4 Geometric median of a set in the plane -- 2.3 Representative of data sets with several features -- 2.3.1 Representative of weighted data -- 2.4 Representative of periodic data -- 2.4.1 Representative of data on the unit circle -- 2.4.2 Burn diagram -- 3 Data clustering -- 3.1 Optimal k-partition -- 3.1.1 Minimal distance principle and Voronoi diagram -- 3.1.2 k-means algorithm -- 3.2 Clustering data with one feature -- 3.2.1 Application of the LS-distance-like function -- 3.2.2 The dual problem -- 3.2.3 Least absolute deviation principle -- 3.2.4 Clustering weighted data -- 3.3 Clustering data with two or several features -- 3.3.1 Least squares principle -- 3.3.2 The dual problem -- 3.3.3 Least absolute deviation principle -- 3.4 Objective function F(c1 ..., ck) = Pm i=1 min 1d"d" …