Abstract
To deal with the computational and storage problem for the large-scale data set, an improved Kernel Principal Component Analysis based on 1-order and 2-order statistical quantity, is proposed. By dividing the large scale data set into small subsets, we could treat 1-order and 2-order statistical quantity (mean and autocorrelation matrix) of each subset as the special computational unit. A novel polynomial-matrix kernel function is also adopted to compute the similarity between the data matrices in place of vectors. The proposed method can greatly reduce the size of kernel matrix, which makes its computation possible. Its effectiveness is demonstrated by the experimental results on the artificial and real data set.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Scholkopf, B., Smola, A., Muller, K.R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10, 1299–1319 (1998)
Fukunaga, K.: Introduction to Statistical Pattern Recognition. Academic Press, London (1990)
Shawe-Taylor, J., Scholkopf, B.: Kernel Methods for Pattern Analysis, 3rd edn. Cambridge University Press, Cambridge (2004)
Zheng, W.M., Zou, C.R., Zhao, L.: An Improved Algorithm for Kernel Principal Components Analysis. Neural Processing Letters 22, 49–56 (2005)
France, V., Hlavac, V.: Greedy Algorithm for a Training Set Reduction in the Kernel Methods. In: Petkov, N., Westenberg, M.A. (eds.) CAIP 2003. LNCS, vol. 2756, pp. 426–433. Springer, Heidelberg (2003)
Achlioptas, D., McSherry, M., Scholkopf, B.: Sampling techniques for kernel methods. In: Advances in Neural Information Processing Systems (2002)
Smola, A., Cristianini, N.: Sparse Greefy Matrix Approximation for Machine Learning. In: International Conference on Machine Learning (2000)
Kim, K.I., Franz, M.O., Scholkopf, B.: Iterative Kernel Principal Component Analysis for image modeling. IEEE Trans. Pattern Anal. Mach. Intell. 27(9), 1351–1366 (2005)
Shi, W.Y., Guo, Y.F., Xue, X.Y.: Matrix-based Kernel Principal Component Analysis for Large-scale Data Set. In: International Joint Conference on Neural Networks, USA
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shi, W., Zhang, D. (2010). An Improved Kernel Principal Component Analysis for Large-Scale Data Set. In: Zhang, L., Lu, BL., Kwok, J. (eds) Advances in Neural Networks - ISNN 2010. ISNN 2010. Lecture Notes in Computer Science, vol 6064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13318-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-13318-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13317-6
Online ISBN: 978-3-642-13318-3
eBook Packages: Computer ScienceComputer Science (R0)