Abstract: One of the most important issues regarding the analysis of raw data is the adequate identification of groups within such data. There have been many attempts to define a measure of what is “adequate” clustering. In all published cases, however, the adequateness of a cluster depends on a measure of distance chosen a priori. A metric or distance function is a function which defines a distance between elements of a set (for instance, one of the Ln family or Mahalanobis’ distances have been utilized). Once a metric has been defined it remains to prove that the resulting clusters do, indeed, correspond to a proper classification. An obvious disadvantage of this methodology is, however, that in the space of the metric all clusters are hyperspherical. The shortcoming is that this fact immediately invalidates the attempt to find irregular shapes in such N-dimensional space. A metric induces a topology on a set but not all topologies can be generated by a metric. Topological unmetrisable spaces correspond, in this case, to a family of formulas developed originally by Gielis which he called a “superformula” (S). By replacing a metric by the elements of the hull defined by S we allow the search for more general shapes for our clusters. We report on the application of Vasconcelos Genetic Algorithm to find the parameters of S whose hulls encompass a large number of observations and the application of this method to data mining.

Brief biography of the speaker:
Angel Fernando Kuri-Morales is an Engineer in Electronics by the Universidad Anahuac in Mexico City. He got a M.Sc. degree from the University of Illinois and a Ph.D. from Kennedy-Western University. He is the author of two text books and more than 70 articles published in international magazines and conferences. He is a member of the National System of Researchers (SNI). He won an international prize for the best solution to the "Iterated Prisoner's Dilemma" during the International Congress on Evolutionary Computation in 2000. He has been included in “Who is Who in the World” in 1988, 1998, 2000, 2002, 2003 and 2007. He received the best paper award during the 7th Industrial Conference in Data Mining, Leipzig, Germany. He has been president of several International Congresses, and invited speaker in many national and international scientific events. He belongs to the Evaluating Committee in the Area of Computer Science of CONACYT (the National Council for Science and Technology in Mexico). He was founder partner of Micromex, Inc. and IDET, Inc. and Director of Applied Research in the Center for Research in Computation of the National Polytechnic Institute. He is a Distinguished Lecturer of the Association for Computing Machinery (ACM) and member of the Scientific Committee of the World Scientific and Engineering Academy and Society (WSEAS). Currently he is the member of the Board of IBERAMIA, President of the Mexican Society for Artificial Intelligence and Professor in the Autonomous Technological Institute of Mexico (ITAM).