Abstract
Motivated by the local reconstruction approach to discovering low dimensional structure in high dimensional data, we propose a novel clustering algorithm that effectively utilizes local reconstruction information. We obtain the local reconstruction weights by minimizing the reconstruction error between each data point and the reconstruction from its neighbors. An entropy regularization term is incorporated into the reconstruction objective function so that the smoothness of the reconstruction weights can be explicitly controlled. The reconstruction weights are then used to obtain the clustering result by employing spectral clustering techniques. Experimental results on a number of datasets demonstrate that our algorithm performs well relative to other approaches, which validate the effectiveness of our approach for clustering.
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
Bach, F.R., Jordan, M.I.: Learning Spectral Clustering, with Application To Speech Separation. Journal of Machine Learning Research 7, 1963–2001 (2006)
Boyd, S., Vandenberghe, V.: Convex Optimization. Cambridge University Press, Cambridge (2004)
Brito, M., Chavez, E., Quiroz, A., Yukich, J.: Connectivity of the Mutual K-nearest-neighbor Graph in Clustering and Outlier Detection. Statistics and Probability Letters 35(1), 33–42 (1997)
Chan, P.K., Schlag, M.D.F., Zien, J.Y.: Spectral K-way Ratio-cut Partitioning and Clustering. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 13(9), 1088–1096 (1994)
Fokkema, D.R., Sleijpen, G.L.G., van der Vorst, H.A.: Jacobi–Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils. SIAM Journal on Scientific Computing 20(1), 94–125 (1998)
Lewis, D.D.: Reuters-21578 text categorization test collection
Luo, P., Zhan, G., He, Q., Shi, Z., Lü, K.: On defining partition entropy by inequalities. IEEE Transactions on Information Theory 53(9), 3233–3239 (2007)
Roweis, S., Saul, L.: Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290(5500), 2323–2326 (2000)
Saul, L., Roweis, S.: Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifold. Journal of Machine Learning Research 4, 119–155 (2003)
Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)
Shi, J., Malik, J.: Normalized Cuts and Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)
Strehl, A., Ghosh, J.: Cluster Ensembles — A Knowledge Reuse Framework for Combining Multiple Partitions. Journal of Machine Learning Research 3, 583–617 (2002)
Sun, J., Shen, Z., Li, H., Shen, Y.: Clustering via Local Regression. In: Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (2008)
TREC: Text REtrieval Conference, http://trec.nist.gov
Wang, F., Zhang, C.: Label Propagation through Linear Neighborhoods. IEEE Transactions on Knowledge and Data Engineering 20(1), 55–67 (2008)
Wu, M., Schölkopf, B.: A Local Learning Approach for Clustering. Advances in Neural Information Processing Systems 19 (2006)
Yu, S.X., Shi, J.: Multiclass Spectral Clustering. In: Proceedings of the 9th International Conference on Computer Vision (2003)
Zha, H., He, X., Ding, C., Gu, M., Simon, H.D.: Spectral Relaxation for K-means Clustering. Advances in Neural Information Processing Systems 14 (2001)
Zhao, Y., Karypis, G.: Empirical and Theoretical Comparisons of Selected Criterion Functions for Document Clustering. Machine Learning 55, 311–331 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sun, J., Shen, Z., Su, B., Shen, Y. (2009). Regularized Local Reconstruction for Clustering. In: Theeramunkong, T., Kijsirikul, B., Cercone, N., Ho, TB. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2009. Lecture Notes in Computer Science(), vol 5476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01307-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-01307-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01306-5
Online ISBN: 978-3-642-01307-2
eBook Packages: Computer ScienceComputer Science (R0)