Abstract
Non-parametric data representation can be done by means of a potential function. This paper introduces a methodology for finding modes of the potential function. Two different methods are considered for the potential function representation: by using summations of Gaussian kernels, and by employing quantum clustering. In the second case each data sample is associated with a quantum physics particle that has a radial energy field around its location. Both methods use a scaling parameter (bandwidth) to model the strength of the influence around each data sample. We estimate the scaling parameter as the mean of the Gamma distribution that models the variances of K-nearest data samples to any given data. The local Hessian is used afterwards to find the modes of the resulting potential function. Each mode is associated with a cluster. We apply the proposed algorithm for blind signal separation and for the topographic segmentation of radar images of terrain.
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References
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, Chichester (2000)
Parzen, E.: On estimation of a probability density function and mode. Annals Mathematical Statistics 33, 1065–1076 (1962)
Roberts, S.J.: Parametric and non-parametric unsupervised cluster analysis. Pattern Recognition 30(2), 261–272 (1997)
Schraudolph, N.N.: Gradient-based manipulation of nonparametric entropy estimates. IEEE Trans. on Neural Networks 15(4), 828–837 (2004)
Sheather, S.J.: Density estimation. Stat. Science 19(4), 588–597 (2004)
Silverman, B.W.: Density estimation for statistics and data analysis. Chapman and Hall, Boca Raton (1986)
Gasiorowicz, S.: Quantum Physics. Wiley, Chichester (1996)
Horn, D., Gottlieb, A.: The method of quantum clustering. In: Proc. of Advances in Neural Infor. Proc. Systems (NIPS), vol. 14, pp. 769–776 (2001)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman & Hall, Boca Raton (1995)
Nasios, N., Bors, A.G.: Blind source separation using variational expectation-maximization algorithm. In: Petkov, N., Westenberg, M.A. (eds.) CAIP 2003. LNCS, vol. 2756, pp. 442–450. Springer, Heidelberg (2003)
Bors, A.G., Hancock, E.R., Wilson, R.C.: Terrain analysis using radar shape-from-shading. IEEE Trans. on Pattern Analysis and Machine Intelligence 25(8), 974–992 (2003)
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Nasios, N., Bors, A.G. (2005). Finding the Number of Clusters for Nonparametric Segmentation. In: Gagalowicz, A., Philips, W. (eds) Computer Analysis of Images and Patterns. CAIP 2005. Lecture Notes in Computer Science, vol 3691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556121_27
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DOI: https://doi.org/10.1007/11556121_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28969-2
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