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NIPS
2001

Global Coordination of Local Linear Models

9 years 3 months ago
Global Coordination of Local Linear Models
High dimensional data that lies on or near a low dimensional manifold can be described by a collection of local linear models. Such a description, however, does not provide a global parameterization of the manifold--arguably an important goal of unsupervised learning. In this paper, we show how to learn a collection of local linear models that solves this more difficult problem. Our local linear models are represented by a mixture of factor analyzers, and the "global coordination" of these models is achieved by adding a regularizing term to the standard maximum likelihood objective function. The regularizer breaks a degeneracy in the mixture model's parameter space, favoring models whose internal coordinate systems are aligned in a consistent way. As a result, the internal coordinates change smoothly and continuously as one traverses a connected path on the manifold--even when the path crosses the domains of many different local models. The regularizer takes the form of...
Sam T. Roweis, Lawrence K. Saul, Geoffrey E. Hinto
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2001
Where NIPS
Authors Sam T. Roweis, Lawrence K. Saul, Geoffrey E. Hinton
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