Clustering is an unsupervised machine learning and pattern recognition method. In general, in addition to revealing hidden groups of similar observations and clusters, their number needs to be determined. Internal clustering validation indices estimate this number without any external information. The purpose of this article is to evaluate, empirically, characteristics of a representative set of internal clustering validation indices with many datasets. The prototype-based clustering framework includes multiple, classical and robust, statistical estimates of cluster location so that the overall setting of the paper is novel. General observations on the quality of validation indices and on the behavior of different variants of clustering algorithms will be given.

Hybrid metal nanoparticles, consisting of a nano-crystalline metal core and a protecting shell of organic ligand molecules, have applications in diverse areas such as biolabeling, catalysis, nanomedicine, and solar energy. Despite a rapidly growing database of experimentally determined atom-precise nanoparticle structures and their properties, there has been no successful, systematic way to predict the atomistic structure of the metal-ligand interface. Here, we devise and validate a general method to predict the structure of the metal-ligand interface of ligand-stabilized gold and silver nanoparticles, based on information about local chemical environments of atoms in experimental data. In addition to predicting realistic interface structures, our method is useful for investigations on the steric effects at the metal-ligand interface, as well as for predicting isomers and intermediate structures induced by thermal dynamics or interactions with the environment. Our method is applicable to other hybrid nanomaterials once a suitable set of reference structures is available.

Two new initialization methods for K-means clustering are proposed. Both proposals are based on applying a divide-and-conquer approach for the K-means‖ type of an initialization strategy. The second proposal also uses multiple lower-dimensional subspaces produced by the random projection method for the initialization. The proposed methods are scalable and can be run in parallel, which make them suitable for initializing large-scale problems. In the experiments, comparison of the proposed methods to the K-means++ and K-means‖ methods is conducted using an extensive set of reference and synthetic large-scale datasets. Concerning the latter, a novel high-dimensional clustering data generation algorithm is given. The experiments show that the proposed methods compare favorably to the state-of-the-art by improving clustering accuracy and the speed of convergence. We also observe that the currently most popular K-means++ initialization behaves like the random one in the very high-dimensional cases.