Efficiently updating and tracking the dominant kernel principal components

The dominant set of eigenvectors of the symmetrical kernel Gram matrix is used in many important kernel methods (like e.g. kernel Principal Component Analysis, feature approximation, denoising, compression, prediction) in the machine learning area. Yet in the case of dynamic and/or large-scale data,...

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Bibliographic Details
Published in:Neural networks 2007-03, Vol.20 (2), p.220-229
Main Authors: Hoegaerts, L., De Lathauwer, L., Goethals, I., Suykens, J.A.K., Vandewalle, J., De Moor, B.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Computer science
control theory
systems
Detection, estimation, filtering, equalization, prediction
Dominant eigenspace
Eigenvalues
Exact sciences and technology
Humans
Information Storage and Retrieval
Information, signal and communications theory
Kernel Gram matrix
Large scale data
Learning and adaptive systems
Logical Observation Identifiers Names and Codes
Neural Networks (Computer)
Pattern recognition
Pattern Recognition, Automated
Pattern recognition. Digital image processing. Computational geometry
Principal Component Analysis
Prinicipal components
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Tracking
Updating
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Summary:The dominant set of eigenvectors of the symmetrical kernel Gram matrix is used in many important kernel methods (like e.g. kernel Principal Component Analysis, feature approximation, denoising, compression, prediction) in the machine learning area. Yet in the case of dynamic and/or large-scale data, the batch calculation nature and computational demands of the eigenvector decomposition limit these methods in numerous applications. In this paper we present an efficient incremental approach for fast calculation of the dominant kernel eigenbasis, which allows us to track the kernel eigenspace dynamically. Experiments show that our updating scheme delivers a numerically stable and accurate approximation for eigenvalues and eigenvectors at every iteration in comparison to the batch algorithm.
ISSN:0893-6080
1879-2782
DOI:10.1016/j.neunet.2006.09.012