2008
NIPS
NeurIPS 2008
Diffeomorphic Dimensionality Reduction
Abstract
This paper introduces a new approach to constructing meaningful lower dimensional representations of sets of data points. We argue that constraining the mapping between the high and low dimensional spaces to be a diffeomorphism is a natural way of ensuring that pairwise distances are approximately preserved. Accordingly we develop an algorithm which diffeomorphically maps the data near to a lower dimensional subspace and then projects onto that subspace. The problem of solving for the mapping is transformed into one of solving for an Eulerian flow field which we compute using ideas from kernel methods. We demonstrate the efficacy of our approach on various real world data sets.
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Authors
Topics
Machine Learning > Core Methods > Representation Learning
Machine Learning > Core Methods > Embedding Learning
Machine Learning > Optimization & Theory > Theory
Deep Learning > Architectures > Neural Networks
Mathematics & Optimization > Mathematics > Geometry
Machine Learning > Core Methods > Dimensionality Reduction
Machine Learning > Core Methods > Feature Learning
Mathematics & Optimization > Optimization > Kernel Methods