Continuous nonlinear dimensionality reduction by kernel Eigenmaps

Brand, Matthew

Continuous nonlinear dimensionality reduction by kernel Eigenmaps

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Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence. Pages 547-553.

Abstract

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.

Matthew Brand. 2003. Continuous nonlinear dimensionality reduction by kernel Eigenmaps. In Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, IJCAI-03. IJCAI, 547–553. https://ijcai.org/proceedings/2003/81

@inproceedings{ijcai2003p81,
  title     = {Continuous nonlinear dimensionality reduction by kernel Eigenmaps},
  author    = {Brand, Matthew},
  booktitle = {Proceedings of the Eighteenth International Joint Conference on
               Artificial Intelligence, {IJCAI-03}},
  publisher = {International Joint Conferences on Artificial Intelligence},
  editor    = {Georg Gottlob},
  pages     = {547--553},
  year      = {2003},
  url       = {https://ijcai.org/proceedings/2003/81},
}

TY  - CPAPER
TI  - Continuous nonlinear dimensionality reduction by kernel Eigenmaps
AU  - Brand, Matthew
T2  - Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, IJCAI-03
PB  - International Joint Conferences on Artificial Intelligence
PY  - 2003
SP  - 547
EP  - 553
UR  - https://ijcai.org/proceedings/2003/81
ER  -