The Cluster Analysis in Big Data Mining

Abstract

The purpose of this chapter is the consideration of modern methods of the cluster analysis, crisp methods and fuzzy methods, robust probabilistic and possibilistic clustering methods, their properties and application. The problem of cluster analysis is formulated, main criteria and metrics are considered and discussed. Classification of cluster analysis methods is presented, several crisp methods are considered, in particular, hard C-means method and Ward’s method. Fuzzy clustering methods are considered and analyzed: fuzzy C-means method and its generalization Gustavsson-Kessel’s method of cluster analysis which is used when metrics of distance differs from Euclidian. The methods of initial location of cluster centers are considered: peak and differential grouping and their properties analyzed. Adaptive robust clustering algorithms are presented and analyzed which are used when initial data is distorted by high level of noise, or by outliers. In the Sect. 1.7 robust probabilistic algorithms of fuzzy clustering are considered and investigated for batch processing mode and on-line mode which may be used for clustering in BD bases. Experimental investigations of the considered clustering methods are presented, including clustering of UNO countries by indicators of sustainable development.