{"type":"ScholarlyArticle","title":"Ranking Preserving Nonnegative Matrix Factorization","authors":[{"name":"Jing Wang","slug":"jing-wang","given":"Jing","family":"Wang","affiliation":"Graduate School of Information Science and Technology , The University of Tokyo , Japan; Faculty of Science and Technology , Bournemouth University , UK"},{"name":"Feng Tian","slug":"feng-tian","given":"Feng","family":"Tian","affiliation":"Faculty of Science and Technology , Bournemouth University , UK"},{"name":"Weiwei Liu","slug":"weiwei-liu","given":"Weiwei","family":"Liu","affiliation":"School of Computer Science and Engineering , The University of New South Wales , Australia"},{"name":"Xiao Wang","slug":"xiao-wang","given":"Xiao","family":"Wang","affiliation":"School of Computer Science , Beijing University of Posts and Telecommunications , China"},{"name":"Wenjie Zhang","slug":"wenjie-zhang","given":"Wenjie","family":"Zhang","affiliation":"School of Computer Science and Engineering , The University of New South Wales , Australia"},{"name":"Kenji Yamanishi","slug":"kenji-yamanishi","given":"Kenji","family":"Yamanishi","affiliation":"Graduate School of Information Science and Technology , The University of Tokyo , Japan"}],"abstract":"Nonnegative matrix factorization (NMF),  a well-known technique  to find  parts-based representations of nonnegative data, has been widely studied. In reality,  ordinal relations often exist among data,  such as data i is more related to j than to q.  Such relative order is naturally available, and more importantly, it truly reflects the latent data structure.  Preserving the ordinal relations enables us to find structured representations of data that are faithful to the relative order, so that the learned representations become  more discriminative. However, current NMFs pay no attention to this. In this paper, we make the first attempt towards incorporating the ordinal relations and  propose a novel ranking preserving nonnegative matrix factorization (RPNMF) approach, which enforces the learned representations to be ranked according to the relations. We derive  iterative updating rules to solve RPNMF's objective function with  convergence guaranteed.  Experimental results with several datasets for clustering and classification have demonstrated that RPNMF achieves greater performance against the state-of-the-arts,  not only  in terms of  accuracy, but also interpretation of orderly data structure.","doi":"10.24963/ijcai.2018/385","url":"https://ijcai.org/proceedings/2018/385","pdf":"https://ijcai.org/proceedings/2018/0385.pdf","markdown":"https://ijcai.org/proceedings/2018/385.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/385","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Machine Learning","track":"Main track","number":385,"pages":{"first":2776,"last":2782},"keywords":["Machine Learning: Clustering","Machine Learning: Semi-Supervised Learning"],"videos":[],"references":[{"position":1,"raw":"[Amid and Ukkonen, 2015] Ehsan Amid and Antti Ukkonen. 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