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.
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Interdisciplinary Bridge
— Machine Learning and Mathematics & Optimization
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Keyword Pioneer
— shortest path problem
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Hot Topic Early Bird
— dimensionality reduction
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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