Clustering -- Basic concepts and methods

We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task? And how can clustering results be validated? Connectivity-based versus prototype-based approaches are reflected in the context of several popular methods: single-linkage, spectral embedding, k-means, and Gaussian mixtures are discussed as well as the density-based protocols (H)DBSCAN, Jarvis-Patrick, CommonNN, and density-peaks.