Prof. Zhenyuan Wang
University of Nebraska at Omaha, USA
Speech Title: New Models for Data Analysis Based on Nonlinear Integrals
Biography: Professor Zhenyuan Wang graduated from Department of Mathematics, Fudan University in 1962. He received his Ph.D. from the Department of Systems Science, State University of New York at Binghamton in 1991. He taught various mathematical courses in Hebei University for many years since 1962, supervised graduate students from 1978, and served as the Chair of the Mathematics Department there from 1985 to 1990. He was a visiting scholar, visiting professor, or research fellow in University Paris VI, Binghamton University (SUNY), Chinese University of Hong Kong, New Mexico State University, and University of Texas at El Paso during the period from 1979 to 2009. Currently, he is a tenured full professor in the Department of Mathematics, University of Nebraska at Omaha. He received a number of honors and awards including the title of “National expert” from the Chinese National Scientific and Technological Commission in 1986 and the “Citation Classic Award” from the Institute for Scientific Information (USA) in 2000. His research interests are nonadditive measures, nonlinear integrals, probability and statistics, optimization, soft computing, and data science. He is the author or a co-author of more than 160 research papers and three monographs: “Fuzzy Measure Theory” (1992), “Generalized Measure Theory” (2008), and “Nonlinear Integrals and Their Applications in Data Mining” (2010). He is currently serving as a member of Editorial Board for international journals such as Fuzzy Sets and Systems.
Abstract: In information fusion, regarding the set of considered predictive attributes (in classification, called feature attributes) in a data base as the universal set, nonadditive set functions defined on its power set can effectively describe the interaction among the contribution rates from various predictive attributes towards the fusing target, which can be regarded as a specified objective attribute. Such type of interaction is totally different from the traditional statistical correlationship. Relevantly, the classical linear aggregation tool, weighted sum, which can be expressed as a linear integral defined on the universal set, should be generalized to be some nonlinear integral. The Choquet integral, the upper integral, and the lower integral are the common types of nonlinear integrals. Data mining is just an inverse problem of information fusion. Using nonlinear integrals, some classical models in data mining, such as the multiregression and the classification, can be generalized as well. Once the necessary data set is available, the values of unknown parameters in these nonlinear models can be optimally determined through some soft computing techniques, including genetic algorism and pseudo gradient search, approximately. Since the above-mentioned interaction can be elaborately captured, the introduced new nonlinear models are significant and powerful in practice. They may be widely applied in bioinformatics, medical statistics, economics, forecast, decision making et al. In face of various challenges from big data, these nonlinear models may have relevant generalizations, adjustments, improvements, and deformations.
Prof. Choonkil Park
Hanyang University, Korea
Biography: Prof. Choonkil Park has accomplished his doctoral degree in Mathematics from the University of Maryland and is currently working as a professor at Hanyang University. He is working for several journals such as Journal of Nonlinear Science and Applications and Journal of Computational Analysis and Applications as the associate editors and Journal of Nonlinear Analysis and Applications as the Editor-in-Chief. His main research topics include operator algebras, functional inequalities, functional equations, noncommutative geometry, fixed point theory and fuzzy mappings. He has published a number of academic articles on international journals related to operator algebras, functional inequalities, functional equations, fixed point results related to graph, non-commutative geometry, soft and rough set, fixed point theory and fuzzy mappings. Within the last twenty years, he has successfully published more than 500 articles on SCI-E journals.
Prof. Dong-Won Jung
Jeju National University, Korea
Biography: Prof. Dong-Won Jung has received his D. Phil. degree from Department of Precision Engineering and Mechatronics, February 1995. He was a visiting professor in Department of Mechanical Engineering, Toronto University, Ontario, Canada form 2009-2010. He is also the member of Undergraduate Curriculum Committee from 1997 to present. Now he is currently working as a full professor at School of Mechanical Engineering, Jeju National University, Korea. He is working for several journals such as KSME(Korean Society of Mechanical Engineers) Journal, Ocean Engineering and Technology Journal and Korean Journal of CAE. He received the award including the title of “Excellent Research Award” form Journal of Ocean Engineering and Technology in 2001. He is the Consulting for several institutes, including Sungwoo Hi-Tech. and Hankook Namkyun and Jontronics, Korea. His research interests are Modeling and Computer Simulation. Within the last twenty years, he has successfully published more than 70 articles on academic journals.
Prof. Predrag Stanimirović
University of Niš, Serbia
Speech Title: Gradient Dynamical Systems for Solving Matrix Equations and Computing Generalized Inverses
Biography: Prof. Predrag Stanimirović has accomplished his doctoral degree from Mathematics at University of Niš, Faculty of Mathematics, Niš, Serbia. Now he is working as full Professor at University of Niš, Faculty of Sciences and Mathematics, Departments of Computer Science, Niš, Serbia. Thirty four years of experience in scientific research in diverse fields of mathematics and computer science, which span multiple branches of Numerical linear algebra, recurrent neural networks, linear algebra, symbolic computation, nonlinear optimization and others. His main research topics include Numerical Linear Algebra, Operations Research, Recurrent Neural Networks and Symbolic Computation. Within recent years, he has successfully published 245 publications in scientific journals, including 5 research monographs, 6 text-books, and 75 peer-reviewed research articles published in conference proceedings and book chapters.He is Editor-in-Chief of the scientific journal Facta Universitatis, Series: Mathematics and Informatics and section editor in Filomat and several other journals.
Abstract: The approach based on dynamical system is a powerful tool for solving many kinds of matrix algebra problems because of: possibility of defined evolution to ensure a response within a predefined time-frame in real-time applications, parallel distributed nature of initiated neural networks, convenience of hardware implementation, global convergence without restrictions, dynamical system is applicable to online computation with time-varying matrices.
As a confirmation, various dynamical systems based on the Gradient Neural Network (GNN) for solving matrix equations and computing generalized inverses have been investigated. Also, different types of dynamic state equations corresponding to various kinds of generalized inverses have been proposed and considered. Recurrent Neural Network (RNN) models arising from appropriate simplification of GNN models are also proposed. Convergence properties and exact solutions of considered GNN and RNN models are investigated.