TR2003-21

Continuous nonlinear dimensionality reduction by kernel eigenmaps


    •  Brand, M.E., "Continuous Nonlinear Dimensionality Reduction by Kernel Eigenmaps", International Joint Conference on Artificial Intelligence (IJCAI), August 2003.
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      • @inproceedings{Brand2003aug,
      • author = {Brand, M.E.},
      • title = {Continuous Nonlinear Dimensionality Reduction by Kernel Eigenmaps},
      • booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)},
      • year = 2003,
      • month = aug,
      • url = {http://www.merl.com/publications/TR2003-21}
      • }
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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 demonstration is made to visualizing the distribution of word usages (as a proxy to word meanings) in a sample of the machine learning literature.