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Fast Kernel ICA using an Approximate Newton Method

2007

Conference Paper

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Recent approaches to independent component analysis (ICA) have used kernel independence measures to obtain very good performance, particularly where classical methods experience difficulty (for instance, sources with near-zero kurtosis). We present Fast Kernel ICA (FastKICA), a novel optimisation technique for one such kernel independence measure, the Hilbert-Schmidt independence criterion (HSIC). Our search procedure uses an approximate Newton method on the special orthogonal group, where we estimate the Hessian locally about independence. We employ incomplete Cholesky decomposition to efficiently compute the gradient and approximate Hessian. FastKICA results in more accurate solutions at a given cost compared with gradient descent, and is relatively insensitive to local minima when initialised far from independence. These properties allow kernel approaches to be extended to problems with larger numbers of sources and observations. Our method is competitive with other modern and classical ICA approaches in both speed and accuracy.

Author(s): Shen, H. and Jegelka, S. and Gretton, A.
Book Title: JMLR Workshop and Conference Proceedings Volume 2: AISTATS 2007
Journal: Proceedings of the 11th International Conference on Artificial Intelligence and Statistics (AISTATS 2007)
Pages: 476-483
Year: 2007
Month: March
Day: 0
Editors: Meila, M. , X. Shen
Publisher: MIT Press

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

Event Name: 11th International Conference on Artificial Intelligence and Statistics
Event Place: San Juan, Puerto Rico

Address: Cambridge, MA, USA
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF
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BibTex

@inproceedings{4295,
  title = {Fast Kernel ICA using an Approximate Newton Method},
  author = {Shen, H. and Jegelka, S. and Gretton, A.},
  journal = {Proceedings of the 11th International Conference on Artificial Intelligence and Statistics (AISTATS  2007)},
  booktitle = {JMLR Workshop and Conference Proceedings Volume 2: AISTATS 2007},
  pages = {476-483},
  editors = {Meila, M. , X. Shen},
  publisher = {MIT Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Cambridge, MA, USA},
  month = mar,
  year = {2007},
  month_numeric = {3}
}