1732-3916 Uniform Cross-entropy Clustering Brzeski Maciej author Spurek Przemysław author TensorCell Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland Correspondence to: Maciej Brzeski maciej.brzeski@doctoral.uj.edu.pl Correspondence to: Przemysław Spurek przemyslaw.spurek@uj.edu.pl 24 03 2017 Volume 25 2016 117 126 Copyright © 2017 2017 <p style="text-align: left;"><span style="text-align: justify;">Robust mixture models approaches, which use non-normal distributions have recently been upgraded to accommodate data with fixed bounds. In this article we propose a new method based on uniform distributions and Cross-Entropy Clustering (CEC). We combine a simple density model with a clustering method which allows to treat groups separately and estimate parameters in each cluster individually. Consequently, we introduce an effective clustering algorithm which deals with non-normal data.</span></p> 1 [1] Jain A., Data clustering: 50 years beyond K-means. Pattern Recognition Letters, 2010, 31 (8), pp. 651–666. 2 [2] Levin M.S., Combinatorial clustering: Literature review, methods, examples. Journal of Communications Technology and Electronics, 2015, 60 (12), pp. 1403–1428. 3 [3] McLachlan G., Krishnan T., The EM algorithm and extensions. vol. 382. John Wiley &amp; Sons, 2007. 4 [4] McLachlan G., Peel D., Finite mixture models. John Wiley &amp; Sons, 2004. 5 [5] Tabor J., Misztal K., Detection of elliptical shapes via cross-entropy clustering. In: Pattern Recognition and Image Analysis. vol. 7887, Jun 2013, pp. 656–663. 6 [6] Elguebaly T., Bouguila N., Background subtraction using finite mixtures of asymmetric gaussian distributions and shadow detection. Machine Vision and Applications, 2014, 25 (5), pp. 1145–1162. 7 [7] Spurek P., General split gaussian cross–entropy clustering. Expert Systems with Applications, 2017, 68, pp. 58–68. 8 [8] Lee S.X., McLachlan G.J., Finite mixtures of canonical fundamental skew t-distributions. Statistics and Computing, 2015, pp. 1–17. 9 [9] Lin T.I., Ho H.J., Lee C.R., Flexible mixture modelling using the multivariate skew-t-normal distribution. Statistics and Computing, 2014, 24 (4), pp. 531–546. 10 [10] Vrbik I., McNicholas P., Analytic calculations for the em algorithm for multivariate skew-t mixture models. Statistics &amp; Probability Letters, 2012, 82 (6), pp. 1169–1174. 11 [11] Browne R.P., McNicholas P.D., A mixture of generalized hyperbolic distributions. Canadian Journal of Statistics, 2015. 12 [12] ´Smieja M., Wiercioch M., Constrained clustering with a complex cluster structure. Advances in Data Analysis and Classification, pp. 1–26. 13 [13] Spurek P., Tabor J., Byrski K., Active function cross-entropy clustering. Expert Systems with Applications, 2017, 72, pp. 49–66. 14 [14] Banfield J.D., Raftery A.E., Model-based gaussian and non-gaussian clustering. Biometrics, 1993, pp. 803–821. 15 [15] Jirsa L., Pavelkov´a L., Estimation of uniform static regression model with abruptly varying parameters. In: Informatics in Control, Automation and Robotics (ICINCO), 2015 12th International Conference on. 1, IEEE, 2015, pp. 603–607. 16 [16] Pavelkov´a L., K´arn`y M., State and parameter estimation of state-space model with entry-wise correlated uniform noise. International Journal of Adaptive Control and Signal Processing, 2014, 28 (11), pp. 1189–1205. 17 [17] Nagy I., Suzdaleva E., Mlyn´arov´a, T., Mixture-based clustering non-gaussian data with fixed bounds. In: Proceedings of the IEEE International conference Intelligent systems IS. 16, 2016, pp. 4–6. 18 [18] Tabor J., Spurek P., Cross-entropy clustering. Pattern Recognition, 2014, 47(9), pp. 3046–3059. 19 [19] Casella G., Berger R.L., Statistical inference. 2. Duxbury Pacific Grove, CA, 2002. 20 [20] Hartigan, J.A., Clustering algorithms, 1975. 21 [21] ´Smieja M., Tabor J., Spherical wards clustering and generalized voronoi diagrams. In: Data Science and Advanced Analytics (DSAA), 2015. 36678 2015. IEEE International Conference on, IEEE, 2015, pp. 1–10. 22 [22] Telgarsky M., Vattani A., Hartigan’s method: k-means clustering without voronoi. In: AISTATS, 2010, pp. 820–827. 23 [23] Bentley J.L., Multidimensional binary search trees used for associative searching. Communications of the ACM, 1975, 18 (9), pp. 509–517.