讲座题目：Nonlinear Integrals and Their Applications in Data Science
主 讲 人：王振源教授
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 (also called nonlinear measures or fuzzy measures)defined on its power set can effectively describe the interaction among the contribution rates from various predictive attributes towards a given target, which can be regarded asa 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 sometype of nonlinear integrals. The Choquet integral, the upper integral, and the lower integral are common types of nonlinear integrals.In data science, 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 a 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 interactioncan be elaborately captured, theintroduced new nonlinear models are significant and powerful in practice. They may be widely applied in bioinformatics, medical statistics, economics, forecast, decision making et al.Facingvarious challenges from big data, these nonlinear models may have relevant generalizations, adjustments, improvements, and deformations.
王震源，美国内布拉斯加大学(Omaha)数学系终身教授；1986年，国家具有突出贡献的中青年科技专家；2000年，获ISI (美国科学信息研究院)经典引文奖；2007年，获美国内布拉斯加大学杰出研究和创造性工作奖。已发表科学论文160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)。“Fuzzy Sets and Systems” 等四个国际杂志的编委或副主编。