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Pattern Recognition with Non-Euclidean Similarities

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Man-Machine Interactions 3

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 242))

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Abstract

Pairwise dissimilarity representations are frequently used as an alternative to feature vectors in pattern recognition.One of the problems encountered in the analysis of such data, is that the dissimilarities are rarely Euclidean, while statistical learning algorithms often rely on Euclidean distances. Such non-Euclidean dissimilarities are often corrected or imposed geometry via embedding. This talk reviews and and extends the field of analysing non-Euclidean dissimilarity data.

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References

  1. Biederman, I.: Recognition-by-components: A theory of human image understanding. Psychological Review 94(2), 115–147 (1987)

    Article  Google Scholar 

  2. Bishop, C.M.: Neural networks for pattern recognition. Oxford University Press, USA (1995)

    Google Scholar 

  3. Bunke, H., Sanfeliu, A.: Syntactic and Structural Pattern Recognition: Theory and Applications. World Scientific (1990)

    Google Scholar 

  4. Chow, B., Luo, F.: Combinatorial ricci flows on surfaces. Journal of Differential Geometry 63(1), 97–129 (2003)

    MathSciNet  MATH  Google Scholar 

  5. Dubuisson, M.P., Jain, A.K.: A modified Hausdorff distance for object matching. In: Proceedings of the 12th IAPR International Conference on Pattern Recognition, vol. 1, pp. 566–568. IEEE (1994)

    Google Scholar 

  6. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern classification, 2nd edn. Wiley, New York (2001)

    MATH  Google Scholar 

  7. Duin, R.P.W., Pękalska, E.: Non-Euclidean dissimilarities: causes and informativeness. In: Hancock, E.R., Wilson, R.C., Windeatt, T., Ulusoy, I., Escolano, F. (eds.) SSPR&SPR 2010. LNCS, vol. 6218, pp. 324–333. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Duin, R.P.W., Pękalska, E., Harol, A., Lee, W.-J., Bunke, H.: On Euclidean corrections for Non-Euclidean dissimilarities. In: da Vitoria Lobo, N., Kasparis, T., Roli, F., Kwok, J.T., Georgiopoulos, M., Anagnostopoulos, G.C., Loog, M. (eds.) S+SSPR 2008. LNCS, vol. 5342, pp. 551–561. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Gower, J.C.: Properties of euclidean and non-euclidean distance matrices. Linear Algebra and its Applications 67, 81–97 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gower, J.C., Legendre, P.: Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification 3(1), 5–48 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gu, X., He, Y., Jin, M., Luo, F., Qin, H., Yau, S.T.: Manifold splines with a single extraordinary point. Computer-Aided Design 40(6), 676–690 (2008)

    Article  MATH  Google Scholar 

  12. Haasdonk, B., Pękalska, E.: Indefinite kernel fisher discriminant. In: Proceedings of the International Conference on Pattern Recognition, ICPR 2008 (2008)

    Google Scholar 

  13. Hamilton, R.S.: Three-manifolds with positive Ricci curvature. Journal of Differential Geometry 17(2), 255–306 (1982)

    MathSciNet  MATH  Google Scholar 

  14. Hamilton, R.S.: The Ricci flow on surfaces. Contemporary Mathematics 71, 237–262 (1988)

    Article  Google Scholar 

  15. Jiang, R., Gu, X.: Multiscale, curvature-based shape representation for surfaces. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV 2011), pp. 1887–1894 (2011)

    Google Scholar 

  16. Jin, M., Kim, J., Gu, X.: Discrete surface ricci flow: Theory and applications. In: Martin, R., Sabin, M.A., Winkler, J.R. (eds.) Mathematics of Surfaces 2007. LNCS, vol. 4647, pp. 209–232. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Jin, M., Luo, F., Gu, X.: Computing surface hyperbolic structure and real projective structure. In: Proceedings of the ACM Symposium on Solid and Physical Modeling (SPM 2006), pp. 105–116. ACM (2006)

    Google Scholar 

  18. Laub, J.: Non-metric pairwise proximity data. Ph.D. thesis, Berlin Institute of Technology (2004)

    Google Scholar 

  19. Laub, J., Roth, V., Buhmann, J.M., Müller, K.R.: On the information and representation of Non-Euclidean pairwise data. Pattern Recognition 39(10), 1815–1826 (2006)

    Article  MATH  Google Scholar 

  20. Mitchell, T.M.: Machine learning. McGraw-Hill (1997)

    Google Scholar 

  21. Pękalska, E., Duin, R.P.W.: The Dissimilarity Representation for Pattern Recognition. Foundations and Applications. World Scientific Publishing Company (2005)

    Google Scholar 

  22. Pękalska, E., Duin, R.P.W.: Beyond traditional kernels: classification in two dissimilarity-based representation spaces. IEEE Transactions on Systems, Man and Cybernetics – Part C 38(6) (2008)

    Google Scholar 

  23. Pękalska, E., Duin, R.P.W., Günter, S., Bunke, H.: On not making dissimilarities Euclidean. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 1145–1154. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  24. Pękalska, E.z., Harol, A., Duin, R.P.W., Spillmann, B., Bunke, H.: Non-Euclidean or non-metric measures can be informative. In: Yeung, D.-Y., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR 2006 and SPR 2006. LNCS, vol. 4109, pp. 871–880. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  25. Pękalska, E., Paclik, P., Duin, R.P.W.: A generalized kernel approach to dissimilarity-based classification. The Journal of Machine Learning Research 2, 175–211 (2001)

    Google Scholar 

  26. Perelman, G.: Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. Public Library of Science Biology 4(5), 1–7 (2006)

    Google Scholar 

  27. Poole, D.: Linear algebra: a modern introduction, 2nd edn. Cengage Learning (2006)

    Google Scholar 

  28. Roth, V., Laub, J., Buhmann, J.M., Müller, K.R.: Going metric: Denoising pairwise data. In: Advances in Neural Information Processing Systems 15, pp. 817–824 (2002)

    Google Scholar 

  29. Sanfeliu, A., Fu, K.S.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics 13(3), 353–362 (1983)

    Article  MATH  Google Scholar 

  30. Sarkar, R., Yin, X., Gao, J., Luo, F., Gu, X.D.: Greedy routing with guaranteed delivery using ricci flows. In: Proceedings of the International Conference on Information Processing in Sensor Networks (IPSN 2009), pp. 121–132. IEEE (2009)

    Google Scholar 

  31. Saucan, E., Appleboim, E., Wolansky, G., Zeevi, Y.Y.: Combinatorial ricci curvature and Laplacians for image processing. In: Proceedings of the 2nd International Congress on Image and Signal Processing (CISP 2009), pp. 1–6. IEEE (2009)

    Google Scholar 

  32. Shapiro, L.G., Haralick, R.M.: A metric for comparing relational descriptions. IEEE Transactions on Pattern Analysis and Machine Intelligence 7(1), 90–94 (1985)

    Article  Google Scholar 

  33. Tao, T.: Ricci flow. Tech. rep., Department of Mathematics, University of California, Los Angeles (2008)

    Google Scholar 

  34. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)

    Article  Google Scholar 

  35. Zeng, W., Samaras, D., Gu, D.: Ricci flow for 3D shape analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(4), 662–677 (2010)

    Article  Google Scholar 

  36. Zeng, W., Yin, X., Zeng, Y., Lai, Y., Gu, X., Samaras, D.: 3D face matching and registration based on hyperbolic Ricci flow. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPRW 2008), pp. 1–8. IEEE (2008)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of York, York, United Kingdom

    Edwin R. Hancock, Eliza Xu & Richard C. Wilson

Authors
  1. Edwin R. Hancock
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  2. Eliza Xu
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  3. Richard C. Wilson
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Corresponding author

Correspondence to Edwin R. Hancock .

Editor information

Editors and Affiliations

  1. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Dr. Aleksandra Gruca

  2. Polish Academy of Sciences and Silesian University of Technology, Gliwice, Poland

    Tadeusz Czachórski

  3. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Stanisław Kozielski

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Hancock, E.R., Xu, E., Wilson, R.C. (2014). Pattern Recognition with Non-Euclidean Similarities. In: Gruca, D., Czachórski, T., Kozielski, S. (eds) Man-Machine Interactions 3. Advances in Intelligent Systems and Computing, vol 242. Springer, Cham. https://doi.org/10.1007/978-3-319-02309-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-02309-0_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02308-3

  • Online ISBN: 978-3-319-02309-0

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