2012 AISTATS AISTATS 2012

On a Connection between Maximum Variance Unfolding, Shortest Path Problems and IsoMap

Abstract

We present an equivalent formulation of the Maximum Variance Unfolding (MVU) problem in terms of distance matrices. This yields a novel interpretation of the MVU problem as a regularized version of the shortest path problem on a graph. This interpretation enables us to establish an asymptotic convergence result for the case that the underlying data are drawn from a Riemannian manifold which is isometric to a convex subset of Euclidean space.

🌉 Interdisciplinary Bridge — Machine Learning and Mathematics & Optimization
🧭 Keyword Pioneer — shortest path problem
🐣 Hot Topic Early Bird — dimensionality reduction
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Security & Privacy, Speech & Audio