報告時間：2021年4月15日（星期四）16:00
報告地點：北辰校區理學院（西教五）416
報告題目：Outliers Detection Is Not So Hard: Approximation Algorithms for Robust Clustering Problems Using Local Search Techniques
報告嘉賓：徐大川 教授（北京工業大學）
報告摘要：In this talk, we consider two types of robust models of the $k$-median/$k$-means problems: the outlier-version ($k$-MedO/$k$-MeaO) and the penalty-version ($k$-MedP /$k$-MeaP), in which we can mark some points as outliers and discard them. In $k$-MedO /$k$-MeaO, the number of outliers is bounded by a given integer. In $k$-MedO/$k$-MeaO, we do not bound the number of outliers, but each outlier will incur a penalty cost. We develop a new technique to analyze the approximation ratio of local search algorithms for these two problems by introducing an adapted cluster that can capture useful information about outliers in the local and the global optimal solution. For $k$-MeaP, we improve the best known approximation ratio based on local search from $25+\veps$ to $9+\veps$. For $k$-MedP, we obtain the best known approximation ratio. For $k$-MedO/$k$-MeaO, there exists only two bi-criteria approximation algorithms based on local search. One violates the outlier constraint (the constraint on the number of outliers), while the other violates the cardinality constraint (the constraint on the number of clusters). We consider the former algorithm and improve its approximation ratios from $17+\veps$ to $3+\veps$ for $k$-MedO, and from $274+\veps$ to $9+\veps$ for $k$-MeaO. (Joint work with Yishui Wang, Rolf H. Mohring, Chenchen Wu, and Dongmei Zhang)
嘉賓簡介：徐大川，北京工業大學數學學院運籌學與控制論責任教授，數學/統計學博士生導師。北京工業大學區塊鏈研究中心副主任。2002年于中國科學院數學與系統科學研究院獲得博士學位。研究興趣包括：組合優化、近似算法、機器學習等。中國運籌學會數學規劃分會理事長，中國運籌學會常務理事，北京運籌學會副理事長。擔任AMC、APJOR、JORSC、運籌與管理等期刊編委。在科學出版社出版學術專著《設施選址問題的近似算法》，在Mathematical Programming，Operations Research，INFORMS Journal on Computing，Omega，Algorithmica，Journal of Global Optimization，Theoretical Computer Science，Information Process Letters，Journal of Combinatorial Optimization，Operations Research Letters等期刊和AAAI, ICDCS, COCOON等會議發表學術論文100余篇。
