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

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

【时间】：2014年6月27日（周五）上午10：00-11：30

【地点】：tyc234cc 太阳成集团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.

【主讲人简介】：王震源教授, 美国内布拉斯加大学(Omaha)数学系终身教授，曾先后在美国宾厄姆顿大学(SUNY) 系统科学系、新墨西哥州立大学数学系、得克萨斯大学(El Paso) 数学系、以及香港中文大学计算机科学和工程学系分别任客座教授/研究员。曾任第七、八、九届全国政协委员。王震源教授曾获河北省科技进步一等奖(1985)、国家科委和劳动人事部颁发的国家级具有突出贡献的中青年科技专家称号(1986)、ISI (美国科学信息研究院, SCI发布者)的经典引文奖(2000)、美国内布拉斯加大学杰出研究和创造性工作奖(2007)等奖励和荣誉称号。已发表科学论文一百五十余篇，并出版三部专著：Fuzzy Measure Theory（Plenum，1992）、Generalized Measure Theory （Springer, 2008）、Nonlinear Integrals and Their Applications in Data Mining （World Scientific，2010）。同时任Fuzzy Sets and Systems等四个国际杂志的编委或副主编。