Abstract
Recently Multiple Kernel Learning (MKL) has gained increasing attention in constructing a combinational kernel from a number of basis kernels. In this paper, we proposed a novel approach of multiple kernel learning for clustering based on the kernel k-means algorithm. Rather than using a convex combination of multiple kernels over the whole input space, our method associates to each cluster a localized kernel. We assign to each cluster a weight vector for feature selection and combine it with a Gaussian kernel to form a unique kernel for the corresponding cluster. A locally adaptive strategy is used to localize the kernel for each cluster with the aim of minimizing the within-cluster variance of the corresponding cluster. We experimentally compared our methods to kernel k-means and spectral clustering on several data sets. Empirical results demonstrate the effectiveness of our method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Schölkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press (2002)
Filippone, M., Camastra, F., Masulli, F., Rovetta, S.: A Survey of Kernel and Spectral Methods for Clustering. Pattern Recognition 41(1), 176–190 (2008)
Wu, Z.D., Xie, W.X., Yu, J.P.: Fuzzy C-means Clustering Algorithm Based on Kernel Method. In: Proceedings of the International Conference on Computational Intelligence and Multimedia Applications, pp. 49–54 (2003)
Yu, K., Ji, L., Zhang, X.: Kernel Nearest-Neighbor Algorithm. Neural Processing Letters 15(2), 147–156 (2002)
Zhang, D.Q., Chen, S.C.: Kernel Based Fuzzy and Possibilistic C-means Clustering. In: Proceedings of the International Conference Artificial Neural Network, Turkey, pp. 122–125 (2003)
Schölkopf, B., Smola, A.J., Müller, K.R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10, 1299–1319 (1998)
Inokuchi, R., Miyamoto, S.: LVQ Clustering and SOM Using a Kernel Function. In: Proceedings of IEEE International Conference on Fuzzy Systems, vol. 3, pp. 1497–1500 (2004)
Qinand, A.K., Suganthan, P.N.: Kernel Neural Gas Algorithms with Application to Cluster Analysis. In: 17th International Conference on Pattern Recognition (ICPR 2004), vol. 4, pp. 617–620 (2004)
Xu, L., Neufeld, J., Larson, B., Schuurmans, D.: Maximum Margin Clustering. In: Advances in Neural Information Processing Systems, vol. 17, pp. 1537–1544 (2005)
Camastra, F., Verri, A.: A Novel Kernel Method for Clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(5), 801–804 (2005)
Hur, A.B., Horn, D., Siegelmann, H.T., Vapnik, V.: Support vector clustering. Journal of Machine Learning Research 2, 125–137 (2001)
Dhillon, I.S., Guan, Y., Kulis, B.: A Unified View of Kernel K-means. Spectral Clustering and Graph Cuts. Computational Complexity, 1–20 (2005)
Lanckriet, G., Cristianini, N., Ghaoui, L., Bartlett, P., Jordan, M.: Learning the Kernel Matrix with Semidefinite Programming. Journal of Machine Learning Research 5, 27–72 (2004)
Sonnenburg, S., Rätsch, G., Schäfer, C., Schölkopf, B.: Large Scale Multiple Kernel Learning. Journal of Machine Learning Research 7, 1531–1565 (2006)
Bach, F., Lanckriet, G., Jordan, M.: Multiple Kernel Learning, Conic Duality, and the SMO Algorithm. In: Proceedings of the 21th International Conference on Machine Learning, pp. 6–13 (2004)
Gehler, P.V., Nowozin, S.: Infinite Kernel Learning. Technical Report No. TR-178, Max Planck Institute for Biological Cybernetics (2008)
Rakotomamonjy, A., Bach, F., Canu, S., Grandvalet, Y.: Simple MKL. Journal of Machine Learning Research 9, 2491–2521 (2008)
Kloft, M., Brefeld, U., Sonnenburg, S., Laskov, P., Müller, K.R., Zien, A.: Efficient and Accurate l p-norm Multiple Kernel Learning. In: Advances in Neural Information Processing Systems, vol. 22, pp. 997–1005 (2009)
Jin, R., Hoi, S.C.H., Yang, T.: Online Multiple Kernel Learning: Algorithms and Mistake Bounds. In: Hutter, M., Stephan, F., Vovk, V., Zeugmann, T. (eds.) ALT 2010. LNCS, vol. 6331, pp. 390–404. Springer, Heidelberg (2010)
Zhao, B., Kwok, J.T., Zhang, C.: Multiple Kernel Clustering. In: Proceedings of the 9th SIAM International Conference on Data Mining (SDM 2009), pp. 638–649 (2009)
Lewis, D.P., Jebara, T., Noble, W.S.: Nonstationary Kernel Combination. In: Proceedings of the 23th International Conference on Machine Learning, pp. 553–560 (2006)
Gönen, M., Alpaydin, E.: Localized multiple kernel learning. In: Proceedings of the 25th International Conference on Machine Learning, pp. 352–359 (2008)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On Spectral Clustering: Analysis and an Algorithm. In: Advances in Neural Information Processing Systems, vol. 14, pp. 849–856 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, L., Hu, X. (2012). A Novel Multiple Kernel Clustering Method. In: Huang, DS., Gupta, P., Zhang, X., Premaratne, P. (eds) Emerging Intelligent Computing Technology and Applications. ICIC 2012. Communications in Computer and Information Science, vol 304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31837-5_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-31837-5_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31836-8
Online ISBN: 978-3-642-31837-5
eBook Packages: Computer ScienceComputer Science (R0)