Distance geometry and data science

By Leo Liberti. 2019

35 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

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Citations in the corpus

Mathematical optimization in classification and regression trees (2021, background): “(2020), Liberti (2020) for surveys reviewing the use of Mathematical Optimization in Machine Learning, and Carrizosa and Romero Morales (2013), Duarte Silva (2017), Palagi (2019), and Piccialli and Sciandrone (2018) for surveys focusing on specific methodologies.”