Center-based l₁–clustering method

Angulo, J. and Serra, J. (2007). Modelling and segmentation of colour images in polar representations, Image and VisionComputing 25(4): 475-495.10.1016/j.imavis.2006.07.018Search in Google Scholar

Äyrämö, S. (2006). Knowledge Mining Using Robust Clustering, Ph.D. thesis, University of Jyväskylä, Jyväskylä.Search in Google Scholar

Bagirov, A.M. and Ugon, J. (2005). An algorithm for minimizing clustering functions, Optimization54(4-5): 351-368.10.1080/02331930500096155Search in Google Scholar

Bagirov, A.M., Ugon, J. and Webb, D. (2011). Fast modified global k-means algorithm for incremental cluster construction, Pattern Recognition 44(4): 886-876.10.1016/j.patcog.2010.10.018Search in Google Scholar

Bezdek, J.C. (1981). Pattern Recognition with Fuzzy ObjectiveFunction Algorithms, Kluwer Academic Publishers, Norwell, MA.10.1007/978-1-4757-0450-1Search in Google Scholar

Boyd, D.L. and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press, Cambridge.10.1017/CBO9780511804441Search in Google Scholar

Chaovalitwongse, W.A., Butenko, S. and Pardalos, P.M., (Eds.) (2009). Clustering Challenges in Biological Networks, World Scientific, London.Search in Google Scholar

Choulakian, V. (2001). Robust q-mode principal component analysis in L1, Computational Statistics & Data Analysis, 37(2): 135-150.10.1016/S0167-9473(01)00005-6Search in Google Scholar

Clarke, F. H., (1990). Optimization and Nonsmooth Analysis, SIAM, Philadelphia, PA.10.1137/1.9781611971309Search in Google Scholar

Cominetti, R. and Michelot, C. (1997 ). Sufficient conditions for coincidence in l1-minisum multifacility location problems, Operations Research Letters 20(4): 179-185.10.1016/S0167-6377(96)00051-XSearch in Google Scholar

Cord, A., Ambroise, C. and Cocquerez, J.-P. (2006 ). Feature selection in robust clustering based on Laplace mixture, Pattern Recognition Letters 27(6): 627-635.10.1016/j.patrec.2005.09.028Search in Google Scholar

Cupec, R., Grbi´c, R., Sabo, K. and Scitovski, R. (2009). Three points method for searching the best least absolute deviations plane, Applied Mathematics and Computation215(3): 983-994.10.1016/j.amc.2009.06.023Search in Google Scholar

Duda, R., Hart, P. and Stork, D. (2001). Pattern Classification, Wiley, New York, NY.Search in Google Scholar

Finkel, D.E. and Kelley, C.T. (2006). Additive scaling and the DIRECT algorithm, Journal of Global Optimization36(4): 597-608.10.1007/s10898-006-9029-9Search in Google Scholar

Floudas, C.A. and Gounaris, C.E. (2009). A review of recent advances in global optimization, Journal of Global Optimization45(4): 3-38.10.1007/s10898-008-9332-8Search in Google Scholar

Frąckiewicz, M. and Palus, H. (2011). KHM clustering techique as a segmentation method for endoscopic colour images, International Journal of Applied Mathematicsand Computer Science 21(1): 203-209, DOI: 10.2478/v10006-011-0015-0.10.2478/v10006-011-0015-0Search in Google Scholar

Gan, G., Ma, C. and Wu, J. (2007). Data Clustering: Theory,Algorithms, and Applications, SIAM, Philadelphia, PA.10.1137/1.9780898718348Search in Google Scholar

Grbić, R., Nyarko, E.K. and Scitovski, R. (2012). A modification of the direct method for Lipschitz global optimization for a symmetric function, Journal of Global Optimization, 57(4): 1193-1212, DOI: 10.1007/s10898-012-0020-3.10.1007/s10898-012-0020-3Search in Google Scholar

Grbić , R., Scitovski, K., Sabo, K. and Scitovski, R. (2013). Approximating surfaces by the moving least absolute deviations method, Applied Mathematics and Computation219(9): 4387-4399.10.1016/j.amc.2012.10.041Search in Google Scholar

Gurwitz, C. (1990). Weighted median algorithms for l1 approximation, BIT 30(2): 301-310.10.1007/BF02017350Search in Google Scholar

Hathaway, R.J. and Bezdek, J.C. (2001). Fuzzy c-means clustering of incomplete data, IEEE Transactions onSystems, Man, and Cybernetics, Part B: Cybernetics31(5): 735-744.10.1109/3477.95603518244838Search in Google Scholar

Hubert, L. and Arabie, P. (1985). Comparing partitions, Journalof Classification 2(1): 193-218.10.1007/BF01908075Search in Google Scholar

Jain, A. (2010). 50 years beyond k-means, Pattern RecognitionLetters 31(8): 651-666.10.1016/j.patrec.2009.09.011Search in Google Scholar

Jajuga, K. (1987). A clustering method based on the L1-norm, Computational Statistics & Data Analysis 5(4): 357-371.10.1016/0167-9473(87)90058-2Search in Google Scholar

Jajuga, K. (1991). L1-norm based fuzzy clustering, Fuzzy Setsand Systems 39(1): 43-50.10.1016/0165-0114(91)90064-WSearch in Google Scholar

Iyigun, C. (2007). Probabilistic Distance Clustering, Ph.D. thesis, Graduate School, Rutgers, New Brunswick, NJ.Search in Google Scholar

Jones, D.R., Perttunen, C.D. and Stuckman, B.E. (1993).Search in Google Scholar

Lipschitzian optimization without the Lipschitz constant, Journal of Optimization Theory and Applications79(1): 157-181. 10.1007/BF00941892Search in Google Scholar

Jörnsten, R. (2004). Clustering and classification based on the L1 data depth, Journal of Multivariate Analysis90(1): 67-89.10.1016/j.jmva.2004.02.013Search in Google Scholar

Kogan, J. (2007). Introduction to Clustering Large andHigh-Dimensional Data, Cambridge University Press, Cambridge.Search in Google Scholar

Leisch, F. (2006). A toolbox for k-centroids cluster analysis, Computational Statistics & Data Analysis 51(2): 526-544.10.1016/j.csda.2005.10.006Search in Google Scholar

Li, X. Hu, W., Wang, H. and Zhang, Z. (2010). Linear discriminant analysis using rotational invariant L1 norm, Neurocomputing 73(13-15): 2571-2579.10.1016/j.neucom.2010.05.016Search in Google Scholar

Scitovski, R. and Scitovski, S. (2013). A fast partitioning algorithm and its application to earthquake investigation, Computers and Geosciences 59(1): 124-131.10.1016/j.cageo.2013.06.010Search in Google Scholar

Simiński, K. (2012). Neuro-rough-fuzzy approach for regression modelling from missing data, International Journal of AppliedMathematics and Computer Science 22(2): 461-476, DOI: 10.2478/v10006-012-0035-4.10.2478/v10006-012-0035-4Search in Google Scholar

Späth, H. (1976). L1-cluster analysis, Computing16(4): 379-387.10.1007/BF02252086Search in Google Scholar

Späth, H. (1987). Using the L1-norm within cluster analysis, in Y. Dodge (Ed.), Proceedings of the First InternationalConference on Statistical Data Analysis Based on theL1-Norm and Related Methods, University of Neuchatel/Switzerland, August 31-September 04, 1987, Elsevier, Amsterdam, pp. 427-434.Search in Google Scholar

Malinen, M.I. and Fränti, P. (2012). Clustering by analytic functions, Information Sciences 217(1): 31-38.10.1016/j.ins.2012.06.018Search in Google Scholar

Meng, D., Zhao, Q and Xu, Z. (2012). Improve robustness of sparse PCA by L1-norm maximization, Pattern Recognition45(1): 487-497.10.1016/j.patcog.2011.07.009Search in Google Scholar

Pintér, J.D. (1996). Global Optimization in Action (Continuousand Lipschitz Optimization: Algorithms, Implementationsand Applications), Kluwer Academic Publishers, Dordrecht.Search in Google Scholar

Ruszczynski, A (2006). Nonlinear Optimization, Princeton University Press, Princeton/Oxford, NJ. Search in Google Scholar

Sabo, K. and Scitovski, R. (2008). The best least absolute deviations line-properties and two efficient methods, ANZIAMJournal 50(2): 185-198.10.1017/S1446181108000345Search in Google Scholar

Sabo, K., Scitovski, R. and Vazler, I. (2011). Searching for a best LAD-solution of an overdetermined system of linear equations motivated by searching for a best LAD-hyperplane on the basis of given data, Journal ofOptimization Theory and Applications 149(2): 293-314.10.1007/s10957-010-9791-1Search in Google Scholar

Sabo, K., Scitovski, R. and Vazler, I. (2012). One-dimensional center-based l1-clustering method, Optimization Letters7(1): 5-2210.1007/s11590-011-0389-9Search in Google Scholar

Sabo, K., Scitovski, R., Vazler, I. and Zeki´c-Sušac, M. (2011). Mathematical models of natural gas consumption, EnergyConversion and Management 52(3): 1721-1727.10.1016/j.enconman.2010.10.037Search in Google Scholar

Teboulle, M. (2007). A unified continuous optimization framework for center-based clustering methods, Journal ofMachine Learning Research 8(1): 65-102.Search in Google Scholar

Vardi, Y., Zhang, C. H. (2000). The multivariate L1-median and associated data depth, Proceedings of the NationalAcademy of Sciences, United States of America97(4): 1423-1426.10.1073/pnas.97.4.14232644910677477Search in Google Scholar

Vazler, I., Sabo, K. and Scitovski, R. (2012). Weighted median of the data in solving least absolute deviations problems, Communications in Statistics-Theory and Methods41(8): 1455-1465.10.1080/03610926.2010.539750Search in Google Scholar

Zhang, J., Peng, L., Zhao, X. and Kuruoglu E.E. (2012 ). Robust data clustering by learning multi-metric lq-norm distances, Expert Systems with Applications 39(1): 335-349.10.1016/j.eswa.2011.07.023Search in Google Scholar