Distance Geometry and Data Science

DOI10.1007/S11750-020-00563-0arXiv1909.08544MaRDI QIDQ6325565

Publication date: 18 September 2019

Abstract: Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in vectorial form. In this survey we discuss the fundamental problem of mapping graphs to vectors, and its relation with mathematical programming. We discuss applications, solution methods, dimensional reduction techniques and some of their limits. We then present an application of some of these ideas to neural networks, showing that distance geometry techniques can give competitive performance with respect to more traditional graph-to-vector mappings.

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Artificial neural networks and deep learning (68T07) Semidefinite programming (90C22) Nonconvex programming, global optimization (90C26) General theory of distance geometry (51K05) Randomized algorithms (68W20) Statistical aspects of big data and data science (62R07) Metric embeddings as related to computational problems and algorithms (68R12)

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