Effective representations and analyses of symbolic data, such as lexical data (words) and networks (graphs), have become of great interest in recent years, due both to advancements in data collection in Natural Language Processing (NLP), and the ubiquity of social networks. Such data often has no natural numerical representation, and is typically described in terms relational expressions or as pairwise similarities. It turns out that finding numerical representations of such data in “Hyperbolic” spaces—rather than into the more familiar Euclidean spaces—is a more effective way to preserve valuable relational information.

An important unexplored question is how can one enhance hyperbolic numerical representations that improves upon the downstream prediction tasks (eg classification and regression on symbolic data). The goal of this project is to take a data-driven approach to address this key question.

By analyzing social network and lexical data, we want to learn an effective notion of distance (or a metric) on the hyperbolic space that helps in classification tasks. This metric learning problem in hyperbolic space can be viewed as a generalization of the Mahalanobis distance metric learning problem in Euclidean spaces. We will design and implement our metric learning algorithm and using social network data as a real-world case study, evaluate the effectiveness of such learned representations.

This project is NOT accpeting application.

Faculty Advisor

  • Professor Nakul Verma
  • Department/School: CS/SEAS
  • Location: Morningside Campus

Project timeline

  • Earliest starting date: 03/01/2019
  • End date: 05/31/2019
  • Number of hours per week of research expected during Spring 2019: ~10

Candidate requirements

  • Skill sets: Machine Learning, Convex Optimization, Strong ML programming skills in a scientific language such as Matlab or Python.
  • Student eligibility (as of Spring 2019): freshman, sophomore, junior, senior, master’s
  • International students on F1 or J1 visa: eligible
  • Additional comments: Basic familiarity with Metric Learning and Differential Geometry is a plus.