{"type":"ScholarlyArticle","title":"Quantum Divide-and-Conquer Anchoring for Separable Non-negative Matrix Factorization","authors":[{"name":"Yuxuan Du","slug":"yuxuan-du","given":"Yuxuan","family":"Du","affiliation":"UBTECH Sydney AI Centre , SIT , FEIT , University of Sydney , Australia"},{"name":"Tongliang Liu","slug":"tongliang-liu","given":"Tongliang","family":"Liu","affiliation":"UBTECH Sydney AI Centre , SIT , FEIT , University of Sydney , Australia"},{"name":"Yinan Li","slug":"yinan-li","given":"Yinan","family":"Li","affiliation":"Centre for Quantum Software and Information , University of Technology Sydney"},{"name":"Runyao Duan","slug":"runyao-duan","given":"Runyao","family":"Duan","affiliation":"Centre for Quantum Software and Information , University of Technology Sydney; Institute for Quantum Computing , Baidu Inc. , Beijing 100193 , China"},{"name":"Dacheng Tao","slug":"dacheng-tao","given":"Dacheng","family":"Tao","affiliation":"UBTECH Sydney AI Centre , SIT , FEIT , University of Sydney , Australia"}],"abstract":"It is NP-complete to find non-negative factors W and H with fixed rank r from a non-negative matrix X by minimizing ||X-WH^Τ ||^2. Although the separability assumption (all data points are in the conical hull of the extreme rows) enables polynomial-time algorithms, the computational cost is not affordable for big data. This paper investigates how the power of quantum computation can be capitalized to solve the non-negative matrix factorization with the separability assumption (SNMF) by devising a quantum algorithm based on the divide-and-conquer anchoring (DCA) scheme [Zhou et al., 2013]. The design of quantum DCA (QDCA) is challenging. In the divide step,  the random projections in  DCA is completed by a quantum algorithm for linear operations, which achieves the exponential speedup. We then  devise a heuristic post-selection procedure which extracts the information of anchors stored in the quantum states efficiently. Under a plausible assumption, QDCA performs efficiently, achieves the quantum speedup, and is beneficial for high dimensional problems.","doi":"10.24963/ijcai.2018/289","url":"https://ijcai.org/proceedings/2018/289","pdf":"https://ijcai.org/proceedings/2018/0289.pdf","markdown":"https://ijcai.org/proceedings/2018/289.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/289","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":289,"pages":{"first":2093,"last":2099},"keywords":["Machine Learning: New Problems","Machine Learning: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Aaronson, 2015] Scott Aaronson. 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