A survey of clustering methods via optimization methodology

. Clustering is one of fundamental tasks in unsupervised learning and plays a very important role in various application areas. This paper aims to present a survey of five types of clustering methods in the perspective of optimization methodology, including center-based methods, convex clustering, spectral clustering, subspace clustering, and optimal transport based clustering. The connection between optimization methodology and clustering algorithms is not only helpful to advance the understanding of the principle and theory of existing clustering algorithms, but also useful to inspire new ideas of efficient clustering algorithms. Preliminary numerical experiments of various clustering algorithms for datasets of various shapes are provided to show the preference and specificity of each algorithm.