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Advanced Mathemmatical Methods Of Early Warnıng Systems And Quality Control By New Methods Of Data Mining Stochastics And Optimization With Aplications İn Finance,ındustry And The Enviroment.

Weber, Gerhard Wilhelm
Our research project aims at further mathematical advances in the field of Data Mining, continuing the achievements made at Institute of Applied Mathematics (IAM) of METU during the last years. We aim at new contributions in theory, methods and applications. In fact, in 2009, the TÜBİTAK project on “Utilization and Development of Data Mining Methods in Quality Analysis and Improve- ment in Manufacturing” ended, and in 2009, the BAP project on “Advanced Mathematical Methods of Quality Analysis and Improvement by New Methods of Computational Statistics and Optimization with Applications in Manufacturing and Finance” ended. Both projects were hosted at METU and we from IAM contributed, especially, by the new mathematical methods in Regression Theory: these are, namely, Additive Models, Generalized Additive Models, our new GAM & CQP, CMARS, moreover: GLM & CQP, GPLM & CQP, and we are still working on improvements of CMARS by preprocessing via Clustering Theory and on Robust CMARS which became our new “product”. These tools are also applicable in Classification Theory, where we created the new Infinite Kernel Learning, and in analysis and optimization of Desirability Functions. All these achievements and ongoing projects are united by their need and utilization of Modern Continuous Optimization Methods, namely, Conic Programming, Robust Optimization, Multi- Objective Programming and Nonsmooth Optimization, of the Theory of Inverse Problems, e.g., Tikhonov Regularization, and of preparatory Clustering Techniques, including the use of state- of-the-art Statistics. While our theoretical and practical results of the last years showed how competitive our new methods are in the field of manufacturing, but also in the financial bank sector of the credit business, we went on with even more refined and mixed (hybrid) kinds of models, with the inclusion of new Smoothing techniques and, most importantly, of Uncertainty into our models (of both polyhedral and ellipsoidal form). In fact uncertainty comes from a lack of knowledge or information, from noise and perturbation; when we regard uncertainty as the existence of a (probability) space of possible scenarios, then we have entered the domain of probability theory and stochastics, especially, since our research will be on time-dependent paths, of stochastic processes. Therefore, we shall further extend our successful research of the last years into the presence of high random fluctuations, of time-dependence and of mixed continuous-discrete, especially, impulsive or hybrid, kinds of dynamical system. Our most recent research area in this respect is concerned with financial “bubbles”: with their identification, prediction and their optimal control.