{"type":"ScholarlyArticle","title":"Approximate Algorithms for k-Sparse Wasserstein Barycenter with Outliers","authors":[{"name":"Qingyuan Yang","slug":"qingyuan-yang","given":"Qingyuan","family":"Yang","affiliation":"School of Computer Science and Technolog University of Science and Technology of China"},{"name":"Hu Ding","slug":"hu-ding","given":"Hu","family":"Ding","affiliation":"School of Computer Science and Technolog University of Science and Technology of China"}],"abstract":"Wasserstein Barycenter (WB) is one of the most fundamental optimization problems in  optimal transportation. Given a set of distributions, the goal of WB is to find a new distribution that minimizes the average Wasserstein distance to them. The problem becomes even harder if we restrict the solution to be “k-sparse”. In this paper, we study the k-sparse WB problem in the presence of outliers, which is a more practical setting since real-world data  often contains noise. Existing WB algorithms  cannot be directly extended to handle the case with outliers, and thus it is urgently needed to develop some novel ideas. First, we investigate the relation between k-sparse WB with outliers and the clustering (with outliers) problems. In particular, we propose a clustering based LP method that yields constant approximation factor for the k-sparse WB with outliers  problem. Further, we utilize the coreset technique to achieve the (1+ε)-approximation factor for any ε>0, if the dimensionality is not high. Finally, we conduct the experiments for our proposed algorithms and illustrate their efficiencies in practice.","doi":"10.24963/ijcai.2024/588","url":"https://ijcai.org/proceedings/2024/588","pdf":"https://ijcai.org/proceedings/2024/0588.pdf","markdown":"https://ijcai.org/proceedings/2024/588.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/588","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Machine Learning","track":"Main Track","number":588,"pages":{"first":5316,"last":5325},"keywords":["Machine Learning: ML: Clustering","Machine Learning: ML: Optimization","Data Mining: DM: Anomaly/outlier detection"],"videos":[],"references":[{"position":1,"raw":"[Aggarwal et al., 2009] Ankit Aggarwal, Amit Deshpande, and Ravi Kannan. 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