A mini-review of clustering algorithms and their theoretical properties, with applications to molecular science
Résumé
Clustering is a fundamental task, in particular to analyse potential and free energy landscapes in molecular science. In this survey, I review the key properties of three remarkable clustering algorithms (k-means ++, persistence-based clustering, and spectral clustering) with a double perspective. The first one is the specification of the main mathematical and algorithmic properties of the algorithms; the second one is the relevance of these methods for structural, thermodynamic, and kinetic analysis. Doing
so provides a unique opportunity to mention important connexions between optimization, graph theory, geometry, and theoretical biophysics.
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