Abstract
Clustering algorithms are intensively used in the image analysis field in compression, segmentation, recognition and other tasks. In this work we present a new approach in clustering vector datasets by finding a good order in the set, and then applying an optimal segmentation algorithm. The algorithm heuristically prolongs the optimal scalar quantization technique to vector space. The data set is sequenced using one-dimensional projection spaces. We show that the principal axis is too rigid to preserve the adjacency of the points. We present a way to refine the order using the minimum weight Hamiltonian path in the data graph. Next we propose to use the principal curve to better model the non-linearity of the data and find a good sequence in the data. The experimental results show that the principal curve based clustering method can be successfully used in cluster analysis.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Slagle, J.L., Chang, C.L., Heller, S.L.: A Clustering and Data-Reorganization Algorithm. IEEE Transactions on Systems, Man and Cybernetics 5, 121–128 (1975)
Wu, X.: Optimal Quantization by Matrix Searching. Journal of Algorithms 12, 663–673 (1991)
Soong, F.K., Juang, B.H.: Optimal Quantization of LSP Parameters. IEEE Transactions on Speech and Audio Processing 1, 15–24 (1993)
Jain, A.K., Murty, M.N., Flynn, P.J.: Data Clustering: A review. ACM Computing Surveys 31 (1999)
MacQueen, J.: Some Methods for Classification and Analysis of Multivariate Observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–296 (1967)
Zahn, C.T.: Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters. IEEE Transactions on Computers, 68–86 (1971)
Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice-Hall, New Jersey (1988)
Bezdek, J.C., Ehrlich, R., Full, W.: FCM: the Fuzzy c-Means Clustering Algorithm. Computers and Geosciences 10, 191–203 (1984)
Kohonen, T.: Self-Organizing Maps. Springer, Berlin (1995)
Fränti, P.: Genetic Algorithm with Deterministic Crossover for Vector Quantization. Pattern Recognition Letters 21, 61–68 (2000)
Gordon, A.D.: Classification. Chapman and Hall, London (1980)
Wu, X.: Color Quantization by Dynamic Programming and Principal Analysis. ACM Transactions on Graphics 11, 348–372 (1992)
Aggarwal, A., Schieber, B., Tokuyama, T.: Finding a Minimum Weight K-link Path in Graphs with Monge Property and Applications. In: Proceedings of the 9th Annual Symposium on Computational Geometry, pp. 189–197 (1993)
Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis. Prentice-Hall, New Jersey (1988)
Garey, M., Johnson, D.: Computers and Intractability: A Guide to NP_Completeness. W.H. Freeman, New York (1979)
Hastie, T., Stuetzle, W.: Principal Curves. Journal of the American Statistical Association 84, 502–516 (1989)
Banfield, J.D., Raftery, A.E.: Ice Floe Identification in Satellite Images Using Mathematical Morphology and Clustering about Principal Curves. Journal of the American Statistical Association 87, 7–16 (1992)
Chang, K., Ghosh, J.: Principal Curves for Non-Linear Feature Extraction and Classification. In: Proceedings SPIE, pp. 120–129 (1998)
Kegl, B., Krzyzak, A., Linder, T., Zeger, K.: Learning and Design of Principal Curves. IEEE Transactions on Pattern Analysis and Machine Intelligence 22, 281–297 (2000)
Verbeek, J.J., Vlassis, N., Krose, B.: A k-Segments Algorithm for Finding Principal Curves. Pattern Recognition Letters 23, 1009–1017 (2002)
Sandilya, S., Kulkarni, S.R.: Principal Curves with Bounded Turn. IEEE Transactions on Information Theory 48, 2789–2793 (2002)
Mulier, F., Cherkassky, V.: Self-organization as an Iterative Kernel Smoothing Process. Neural Computation 7, 1165–1177 (1995)
Fränti, P., Kivijäri, J.: Randomized Local Search Algorithm for the Clustering Problem. Pattern Analysis and Applications 3, 358–369 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cleju, I., Fränti, P., Wu, X. (2005). Clustering Based on Principal Curve. In: Kalviainen, H., Parkkinen, J., Kaarna, A. (eds) Image Analysis. SCIA 2005. Lecture Notes in Computer Science, vol 3540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499145_88
Download citation
DOI: https://doi.org/10.1007/11499145_88
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26320-3
Online ISBN: 978-3-540-31566-7
eBook Packages: Computer ScienceComputer Science (R0)