Competitive clustering algorithms based on ultrametric properties |
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| Affiliation: | 1. University of Paris 8, France;2. Ecole Pratique des Hautes Etudes, France;3. University of Versailles Saint-Quentin-en-Yvelines, France;1. Department of Pediatrics, Medical University of South Carolina College of Medicine, Medical University of South Carolina College of Medicine, Charleston, SC;2. Department of Healthcare Leadership and Management, Medical University of South Carolina College of Health Professions, Charleston, SC;1. Respiratory Department, Hospital Universitari Arnau de Vilanova and Santa Maria, IRBLleida, Lleida, Spain;2. Centro de Investigación Biomédica en Red de Enfermedades Respiratorias (CIBERES), Madrid, Spain;1. Respiratory Center, Pediatric Hospital of Córdoba, Cordoba, Argentina;2. CIMER (Respiratory Medicine Investigation Center of Medicine Faculty), Catholic University of Córdoba, Cordoba, Argentina;3. Eastern Regional Clinic, San Francisco, Córdoba, Argentina;4. Chairman of Medicine at Catholic University of Cordoba and National University of Cordoba, Argentina;5. Chairman of Epidemiology of Medicine at Catholic University of Cordoba, Cordoba, Argentina;6. Cardiologic Model Institute, Cordoba, Argentina;7. Division of Allergy, Clinical Immunology and Rheumatology, Dept of Pediatrics, Federal University of São PauloEscola Paulista de Medicina, São Paulo, Brazil |
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| Abstract: | We propose in this paper two new competitive unsupervised clustering algorithms: the first algorithm deals with ultrametric data, it has a computational cost of O(n). The second algorithm has two strong features: it is fast and flexible on the processed data type as well as in terms of precision. The second algorithm has a computational cost, in the worst case, of O(n2), and in the average case, of O(n). These complexities are due to exploitation of ultrametric distance properties. In the first method, we use the order induced by an ultrametric in a given space to demonstrate how we can explore quickly data proximity. In the second method, we create an ultrametric space from a sample data, chosen uniformly at random, in order to obtain a global view of proximities in the data set according to the similarity criterion. Then, we use this proximity profile to cluster the global set. We present an example of our algorithms and compare their results with those of a classic clustering method. |
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