Distance geometry and data science

Leo Liberti ()
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Leo Liberti: LIX CNRS, Ecole Polytechnique, Institut Polytechnique de Paris

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2020, vol. 28, issue 2, No 1, 339 pages

Abstract: 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.

Keywords: Euclidean distance; Isometric embedding; Random projection; Mathematical programming; Machine learning; Artificial neural networks; 51Kxx; 90Cxx; 68Pxx (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11750-020-00563-0

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