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IJCAI
2003

Continuous nonlinear dimensionality reduction by kernel Eigenmaps

11 years 29 days ago
Continuous nonlinear dimensionality reduction by kernel Eigenmaps
We equate nonlinear dimensionality reduction (NLDR) to graph embedding with side information about the vertices, and derive a solution to either problem in the form of a kernel-based mixture of affine maps from the ambient space to the target space. Unlike most spectral NLDR methods, the central eigenproblem can be made relatively small, and the result is a continuous mapping defined over the entire space, not just the datapoints. A demon­ stration is made to visualizing the distribution of word usages (as a proxy to word meanings) in a sample of the machine learning literature. 1 Background: Graph embcddings Consider a connected graph with weighted undirected edges specified by edge matrix W. Let be the posi­ tive edge weight between connected vertices i and j zero otherwise. Let D = diag(Wl) be a diagonal matrix where the cumulative edge weights into vertex /. The following points are well known or easily derived in spectral graph theory [Fiedler, 1975; Chung, 1997]:
Matthew Brand
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2003
Where IJCAI
Authors Matthew Brand
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