{"type":"ScholarlyArticle","title":"Multi-Positive and Unlabeled Learning","authors":[{"name":"Yixing Xu","slug":"yixing-xu","given":"Yixing","family":"Xu","affiliation":"† Key Laboratory of Machine Perception (MOE) , Cooperative Medianet Innovation Center ,"},{"name":"Chang Xu","slug":"chang-xu","given":"Chang","family":"Xu","affiliation":"‡ School of Electronics Engineering and Computer Science , PKU , Beijing 100871 , China; UBTech Sydney AI Institute , The School of Information Technologies ,; The University of Sydney , J12 , 1 Cleveland St , Darlington , NSW 2008 , Australia"},{"name":"Chao Xu","slug":"chao-xu","given":"Chao","family":"Xu","affiliation":"† Key Laboratory of Machine Perception (MOE) , Cooperative Medianet Innovation Center ,"},{"name":"Dacheng Tao","slug":"dacheng-tao","given":"Dacheng","family":"Tao","affiliation":"‡ School of Electronics Engineering and Computer Science , PKU , Beijing 100871 , China"}],"abstract":"The positive and unlabeled (PU) learning problem focuses on learning a classifier from positive and unlabeled data. Some methods have been developed to solve the PU learning problem. However, they are often limited in practical applications, since only binary classes are involved and cannot easily be adapted to multi-class data. Here we propose a one-step method that directly enables multi-class model to be trained using the given input multi-class data and that predicts the label based on the model decision. Specifically, we construct different convex loss functions for labeled and unlabeled data to learn a discriminant function F. The theoretical analysis on the generalization error bound shows that it is no worse than k√k times of the fully supervised multi-class classification methods when the size of the data in k classes is of the same order. Finally, our experimental results demonstrate the significance and effectiveness of the proposed algorithm in synthetic and real-world datasets.","doi":"10.24963/ijcai.2017/444","url":"https://ijcai.org/proceedings/2017/444","pdf":"https://ijcai.org/proceedings/2017/0444.pdf","markdown":"https://ijcai.org/proceedings/2017/444.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/444","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning S-Z","track":"Main track","number":444,"pages":{"first":3182,"last":3188},"keywords":["Machine Learning: Machine Learning","Machine Learning: Semi-Supervised Learning","Machine Learning: Classification"],"videos":[],"references":[{"position":1,"raw":"[Blanchard et al., 2010] Gilles Blanchard, Gyemin Lee, and Clayton Scott. 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