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

【報(bào)告人】：Prof. Zhenyuan Wang , University of Nebraska at Omaha

【時(shí)間】：2014年6月27日（周五）上午10：00-11：30

【地點(diǎn)】：bwin必贏唯一官網(wǎng)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(jiǎn)介】：王震源教授, 美國(guó)內(nèi)布拉斯加大學(xué)(Omaha)數(shù)學(xué)系終身教授，曾先后在美國(guó)賓厄姆頓大學(xué)(SUNY) 系統(tǒng)科學(xué)系、新墨西哥州立大學(xué)數(shù)學(xué)系、得克薩斯大學(xué)(El Paso) 數(shù)學(xué)系、以及香港中文大學(xué)計(jì)算機(jī)科學(xué)和工程學(xué)系分別任客座教授/研究員。曾任第七、八、九屆全國(guó)政協(xié)委員。王震源教授曾獲河北省科技進(jìn)步一等獎(jiǎng)(1985)、國(guó)家科委和勞動(dòng)人事部頒發(fā)的國(guó)家級(jí)具有突出貢獻(xiàn)的中青年科技專(zhuān)家稱(chēng)號(hào)(1986)、ISI (美國(guó)科學(xué)信息研究院, SCI發(fā)布者)的經(jīng)典引文獎(jiǎng)(2000)、美國(guó)內(nèi)布拉斯加大學(xué)杰出研究和創(chuàng)造性工作獎(jiǎng)(2007)等獎(jiǎng)勵(lì)和榮譽(yù)稱(chēng)號(hào)。已發(fā)表科學(xué)論文一百五十余篇，并出版三部專(zhuān)著：Fuzzy Measure Theory（Plenum，1992）、Generalized Measure Theory （Springer, 2008）、Nonlinear Integrals and Their Applications in Data Mining （World Scientific，2010）。同時(shí)任Fuzzy Sets and Systems等四個(gè)國(guó)際雜志的編委或副主編。