Advertisement

k-Means Clustering with Hölder Divergences

  • Frank NielsenEmail author
  • Ke Sun
  • Stéphane Marchand-Maillet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10589)

Abstract

We introduced two novel classes of Hölder divergences and Hölder pseudo-divergences that are both invariant to rescaling, and that both encapsulate the Cauchy-Schwarz divergence and the skew Bhattacharyya divergences. We review the elementary concepts of those parametric divergences, and perform a clustering analysis on two synthetic datasets. It is shown experimentally that the symmetrized Hölder divergences consistently outperform significantly the Cauchy-Schwarz divergence in clustering tasks.

References

  1. Mitrinovic, D.S., Pecaric, J., Fink, A.M.: Classical and New Inequalities in Analysis, vol. 61. Springer Science & Business Media, New York (2013)zbMATHGoogle Scholar
  2. Kanamori, T., Fujisawa, H.: Affine invariant divergences associated with proper composite scoring rules and their applications. Bernoulli 20, 2278–2304 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  3. Kanamori, T.: Scale-invariant divergences for density functions. Entropy 16, 2611–2628 (2014)CrossRefMathSciNetGoogle Scholar
  4. Arthur, D., Vassilvitskii, S.: \(k\)-means++: the advantages of careful seeding. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 1027–1035 (2007)Google Scholar
  5. Nielsen, F., Sun, K., Marchand-Maillet, S.: On Hölder projective divergences. Entropy 19, 122 (2017)CrossRefGoogle Scholar
  6. Holder, O.L.: Über einen Mittelwertssatz. Nachr. Akad. Wiss. Gottingen Math. Phys. Kl. 44, 38–47 (1889)Google Scholar
  7. Nielsen, F., Boltz, S.: The Burbea-Rao and Bhattacharyya centroids. IEEE Trans. Inf. Theory 57, 5455–5466 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  8. Nielsen, F., Nock, R.: Total Jensen divergences: definition, properties and clustering. In: Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, Queensland, Australia, 19–24 April 2015, pp. 2016–2020 (2015)Google Scholar
  9. Hasanbelliu, E., Giraldo, L.S., Principe, J.C.: Information theoretic shape matching. IEEE Trans. Pattern Anal. Mach. Intell. 36, 2436–2451 (2014)CrossRefGoogle Scholar
  10. Rami, H., Belmerhnia, L., Drissi El Maliani, A., El Hassouni, M.: Texture retrieval using mixtures of generalized gaussian distribution and cauchy-schwarz divergence in wavelet domain. Image Commun. 42, 45–58 (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Frank Nielsen
    • 1
    • 2
    Email author
  • Ke Sun
    • 3
  • Stéphane Marchand-Maillet
    • 4
  1. 1.École PolytechniquePalaiseauFrance
  2. 2.Sony Computer Science Laboratories Inc.TokyoJapan
  3. 3.King Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia
  4. 4.University of GenevaGenevaSwitzerland

Personalised recommendations