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【題目】：New Models of Data Analysis Based on Nonlinear Integrals

【報告人】：Prof. Zhenyuan Wang , University of Nebraska at Omaha

【時間】：2014年6月27日（周五）上午10：00-11：30

【地點】：bwin必贏唯一官網313教室

【摘要】：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.

【主講人簡介】：王震源教授, 美國內布拉斯加大學(Omaha)數學系終身教授，曾先后在美國賓厄姆頓大學(SUNY) 系統科學系、新墨西哥州立大學數學系、得克薩斯大學(El Paso) 數學系、以及香港中文大學計算機科學和工程學系分別任客座教授/研究員。曾任第七、八、九屆全國政協委員。王震源教授曾獲河北省科技進步一等獎(1985)、國家科委和勞動人事部頒發的國家級具有突出貢獻的中青年科技專家稱號(1986)、ISI (美國科學信息研究院, SCI發布者)的經典引文獎(2000)、美國內布拉斯加大學杰出研究和創造性工作獎(2007)等獎勵和榮譽稱號。已發表科學論文一百五十余篇，并出版三部專著：Fuzzy Measure Theory（Plenum，1992）、Generalized Measure Theory （Springer, 2008）、Nonlinear Integrals and Their Applications in Data Mining （World Scientific，2010）。同時任Fuzzy Sets and Systems等四個國際雜志的編委或副主編。