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Semi-Supervised Laplacian Regularization of Kernel Canonical Correlation Analysis

2008

Conference Paper

ei


Kernel canonical correlation analysis (KCCA) is a dimensionality reduction technique for paired data. By finding directions that maximize correlation, KCCA learns representations that are more closely tied to the underlying semantics of the data rather than noise. However, meaningful directions are not only those that have high correlation to another modality, but also those that capture the manifold structure of the data. We propose a method that is simultaneously able to find highly correlated directions that are also located on high variance directions along the data manifold. This is achieved by the use of semi-supervised Laplacian regularization of KCCA. We show experimentally that Laplacian regularized training improves class separation over KCCA with only Tikhonov regularization, while causing no degradation in the correlation between modalities. We propose a model selection criterion based on the Hilbert-Schmidt norm of the semi-supervised Laplacian regularized cross-covariance operator, which we compute in closed form.

Author(s): Blaschko, MB. and Lampert, CH. and Gretton, A.
Book Title: ECML PKDD 2008
Journal: Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2008
Pages: 133-145
Year: 2008
Month: August
Day: 0
Editors: Daelemans, W. , B. Goethals, K. Morik
Publisher: Springer

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Address: Berlin, Germany
Digital: 0
DOI: 10.1007/978-3-540-87479-9_27
Event Name: 19th European Conference on Machine Learning
Event Place: Antwerpen, Belgium
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5248,
  title = {Semi-Supervised Laplacian Regularization of Kernel Canonical Correlation Analysis},
  author = {Blaschko, MB. and Lampert, CH. and Gretton, A.},
  journal = {Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2008},
  booktitle = {ECML PKDD 2008},
  pages = {133-145},
  editors = {Daelemans, W. , B. Goethals, K. Morik},
  publisher = {Springer},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Berlin, Germany},
  month = aug,
  year = {2008},
  month_numeric = {8}
}