{"type":"ScholarlyArticle","title":"A Quantum-inspired Classical Algorithm for Separable Non-negative Matrix Factorization","authors":[{"name":"Zhihuai Chen","slug":"zhihuai-chen","given":"Zhihuai","family":"Chen","affiliation":"CAS Key Lab of Network Data Science and Technology , Institute of Computing Technology , Chinese Academy of Sciences , 100190 , Beijing , China; University of Chinese Academy of Sciences , 100049 , Beijing , China"},{"name":"Yinan Li","slug":"yinan-li","given":"Yinan","family":"Li","affiliation":"Centrum Wiskunde & Informatica and QuSoft , Science Park 123 , 1098XG Amsterdam , Netherlands"},{"name":"Xiaoming Sun","slug":"xiaoming-sun","given":"Xiaoming","family":"Sun","affiliation":"CAS Key Lab of Network Data Science and Technology , Institute of Computing Technology , Chinese Academy of Sciences , 100190 , Beijing , China; University of Chinese Academy of Sciences , 100049 , Beijing , China"},{"name":"Pei Yuan","slug":"pei-yuan","given":"Pei","family":"Yuan","affiliation":"CAS Key Lab of Network Data Science and Technology , Institute of Computing Technology , Chinese Academy of Sciences , 100190 , Beijing , China; University of Chinese Academy of Sciences , 100049 , Beijing , China"},{"name":"Jialin Zhang","slug":"jialin-zhang","given":"Jialin","family":"Zhang","affiliation":"CAS Key Lab of Network Data Science and Technology , Institute of Computing Technology , Chinese Academy of Sciences , 100190 , Beijing , China; University of Chinese Academy of Sciences , 100049 , Beijing , China"}],"abstract":"Non-negative Matrix Factorization (NMF) asks to decompose a (entry-wise) non-negative matrix into the product of two smaller-sized nonnegative matrices, which has been shown intractable in general. In order to overcome this issue, separability assumption is introduced which assumes all data points are in a conical hull. This assumption makes NMF tractable and widely used in text analysis and image processing, but still impractical for huge-scale datasets. In this paper, inspired by recent development on dequantizing techniques, we propose a new classical algorithm for separable NMF problem. Our new algorithm runs in polynomial time in the rank and logarithmic in the size of input matrices, which achieves an exponential speedup in the low-rank setting.","doi":"10.24963/ijcai.2019/627","url":"https://ijcai.org/proceedings/2019/627","pdf":"https://ijcai.org/proceedings/2019/0627.pdf","markdown":"https://ijcai.org/proceedings/2019/627.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/627","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Machine Learning Applications","track":"Main track","number":627,"pages":{"first":4511,"last":4517},"keywords":["Machine Learning Applications: Big data ; Scalability","Machine Learning Applications: Applications of Unsupervised Learning"],"videos":[],"references":[{"position":1,"raw":"[Arora et al., 2012a] Sanjeev Arora, Rong Ge, Ravindran Kannan, and Ankur Moitra. 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