k-Means Clustering with Hölder Divergences
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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.
- Arthur, D., Vassilvitskii, S.: \(k\)-means++: the advantages of careful seeding. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 1027–1035 (2007)Google Scholar
- Holder, O.L.: Über einen Mittelwertssatz. Nachr. Akad. Wiss. Gottingen Math. Phys. Kl. 44, 38–47 (1889)Google Scholar
- 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
- 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