A Fractal Fuzzy Approach To Clustering Tendency Analysis

A hybrid system WELS implemented with the combination of Fractal Dimension Theory and Fuzzy Approximate Reasoning, in order to analyze datasets. In this paper, we describe its application in the initial phase of clustering methodology: the clustering tendency analysis. The Box-Counting Algorithm is carried out on a dataset, and with its resultant curve one obtains numeric indications related to the features of the dataset. Then, a fuzzy inference system acts upon these indications and produces information which enable the analysis mentioned above. © Springer-Verlag 2004.3171395404Barnsley, M., (1988) Fractals Everywhere, , Academic Press Inc, San Diego, California, USABlake, C.L., Merz, C.J., (1998) UCI Repository of Machine Learning DatabasesCan, F., Altingovde, Demir, E.I.S., Efficiency and effectiveness of query processing in cluster-based retrieval Information Systems, 2003, , to appearCastro, L.N., Voz Zuben, F.J., (2001) Data Mining: A Heuristic Approach, pp. 231-259. , chapter aiNet: an artificial immune network for data analysis, Idea Group Publishing, USAFeeny, B.F., Fast multifractal analysis by recursive box covering (2000) International Journal of Bifurcation and Chaos, 10 (9), pp. 2277-2287Jain, K.J., Dubes, R.C., (1988) Algorithms for Clustering Data, , Prentice-Hall, Inc., New Jersey, USAKlir, G.J., Yuan, B., (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications, , Prentice-HallKruger, A., Implementation of a fast box-counting algorithm (1996) Computer Physics Communications, 98, pp. 224-234Massey, L., (2003) Using ART1 Neural Networks to Determine Clustering Tendency, , chapter Applications and Science in Soft Computing. Springer-VerlagPeitgen, H.O., Jurgens, H., Saupe, D., (1992) Chaos and Fractals: New Frontiers of Science, , Springer-Verlag New York Inc., New York, USAPeres, S.M., Netto, M.L.A., Using fractal dimension to fuzzy pre-processing of n-dimensional datasets (2003) ICSE 2003 - Sixteenth International Conference Art System Engineering, , Conventry, United Kingdom, Accepted toPeres, S.M., Netto, M.L.A., Fractal fuzzy decision making: What is the adequate dimension for self-organizing maps (2004) NAFI PS 2004 - North American Fuzzy Information Processing Society, , Banff, Canada, to appearPeres, S.M., Netto, M.L.A., Um sistema hibrido para analise heuristica de dados utilizando teoria de fractais e raciocinio aproximado (2004) Technical Report, , Universidade Estadual de Campinas, Campinas, Sao Paulo, BrasilTraina Jr., C., Traina, A., Wu, L., Faloutsos, C., Fast feature selection using fractal dimension (2002) XV Brazilian Database Symposium, pp. 158-171. , João Pessoa, PA, Brazi