SOFT CLUSTERING ALGORITHM BASED ON SEPARATING HYPERSURFACES
DOI:
https://doi.org/10.18372/1990-5548.52.11860Keywords:
Clustering, artificial neural networks, soft clustering, nonlinear optimization.Abstract
A new “soft” clustering algorithm is proposed based on the use of artificial neural networks as models of hypersurfaces that separate clusters. The algorithm allows to solve the problem of soft clusterization as a problem of smooth nonlinear function optimization and, therefore, to apply the entire mathematical apparatus of nonlinear optimization, which has evolved significantly in recent years.References
Geoffrey Hinton, and Terrence J. Sejnowski, Unsupervised Learning: Foundations of Neural Computation. MIT Press, 1999.
Ken Bailey, Numerical Taxonomy and Cluster Analysis. Typologies and Taxonomies, 1994, 34 p.
D. Aloise, A. Deshpande, P. Hansen, and P. Popat, NP-hardness of Euclidean sum-of-squares clustering, 2009.
M. Mahajan, P. Nimbhorkar, and K. Varadarajan, The Planar k-Means Problem is NP-Hard, 2009.
E. W. Forgy, Cluster Analysis of Multivariate Data: Efficiency Versus Interpretability of Classifications. Biometrics. 1965, 21: 768–769.
Joe H. Ward, Hierarchical Grouping to Optimize an Objective Function. Journal of the American Statistical Association. 2009, 58 (301): 236–244.
Teuvo Kohonen, Self-Organized Formation of Topologically Correct Feature Maps. Biological Cybernetics. 1982, 43 (1): 59–69.
Warren McCulloch, and Walter Pitts, A Logical Calculus of Ideas Immanent in Nervous Activity. Bulletin of Mathematical Biophysics. 1943, 5 (4): 115–133.
James C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. 1981.
Christopher M. Bishop, Pattern Recognition and Machine Learning. Springer. 2006.
Downloads
Issue
Section
License
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).