Distance Geometry and Data Science

TL;DR

This paper surveys the problem of converting graph-structured data into vector form, exploring mathematical programming, applications, and limitations, and demonstrates the effectiveness of distance geometry techniques in neural network tasks.

Contribution

It provides a comprehensive overview of graph-to-vector mapping methods, highlighting the role of distance geometry and presenting a novel neural network application.

Findings

Distance geometry techniques can achieve competitive neural network performance.

Graph-to-vector mappings are crucial for many data science tasks.

Limitations exist in current dimensional reduction methods.

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.