Abstract
We study clustering problem within quantum mechanical framework by utilizing the Schroedinger equation written for the lowest energy state. We extend the analysis of Horn and Gottlieb [1] by providing an explicit discussion of probability distribution within full quantum mechanical context and examine the clustering performances for various probability distribution functions with numerical experiments.
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Keywords
- Cluster Center
- Probability Distribution Function
- Cluster Performance
- Quantum Potential
- Explicit Discussion
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References
Horn, D., Gottlieb, A.: Algorithm for Data Clustering in Pattern Recognition Problems Based on Quantum Mechanics. Phys.Rev. Lett. 88 (2002)
Roberts, S.J.: Non-parametric unsupervised cluster analysis. Pattern Recognition 30(2), 261–272 (1997)
Hinneburg, A., Keim, D.A.: An Efficient Approach to Clustering in Multimedia Databases with Noise. In: Proc. 4th Int. Conf. on Knowledge Discovery and Data Mining. AAAI Press, New York (1998)
Gasiorowicz, S.: Quantum Physics, 3rd edn. John Wiley and Sons, Chichester (2003)
Merzbacher, E.: Quantum Mechanics, 3rd edn. John Wiley and Sons, Chichester (1998)
Ripley, B.D.: Ftp Archive, Department of Statistics, Univ. of Oxford, http://www.stats.ox.ac.uk/pub/PRNN/
Morrison, D.F.: Multivariate Statistical Methods, 2nd edn. McGraw-Hill, New York (1976)
Holland, P.R.: The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics. Cambridge U. Press, Cambridge (1993)
Penrose, R.: Shadows of the Mind. Oxford University Press, Oxford (1994)
Perus, M., Dey, S.K.: Quantum systems can realize content-addressable associative memory; Applied Math. Letters 13(8), 31–36 (2000)
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© 2005 Springer-Verlag Berlin Heidelberg
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Demir, G.K. (2005). Clustering Within Quantum Mechanical Framework. In: Pal, S.K., Bandyopadhyay, S., Biswas, S. (eds) Pattern Recognition and Machine Intelligence. PReMI 2005. Lecture Notes in Computer Science, vol 3776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11590316_23
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DOI: https://doi.org/10.1007/11590316_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30506-4
Online ISBN: 978-3-540-32420-1
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