{"type":"ScholarlyArticle","title":"Exact Recovery of Sparse-Used Dictionaries","authors":[{"name":"Huan Wang","slug":"huan-wang-2","given":"Huan","family":"Wang","affiliation":""},{"name":"Daniel A. Spielman","slug":"daniel-a-spielman","given":"Daniel A.","family":"Spielman","affiliation":""},{"name":"John Wright","slug":"john-wright","given":"John","family":"Wright","affiliation":""}],"abstract":"We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that O (n log n) samples are sufficient to uniquely determine the coefficient matrix. Based on this proof, we design a polynomial-time algorithm, called Exact Recovery of Sparsely-Used Dictionaries (ER-SpUD), and prove that it probably recovers the dictionary and coefficient matrix when the coefficient matrix is sufficiently sparse. Simulation results show that ER-SpUD reveals the true dictionary as well as the coefficients with probability higher than many state-of-the-art algorithms.","doi":null,"url":"https://ijcai.org/proceedings/2013/462","pdf":"https://ijcai.org/proceedings/2013/0462.pdf","markdown":"https://ijcai.org/proceedings/2013/462.md","bibtex":"https://ijcai.org/proceedings/2013/bibtex/462","volume":{"slug":"2013","title":"Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2013","url":"https://ijcai.org/proceedings/2013/","year":2013,"location":"Beijing, China","dates":"3–9 August 2013","editors":"Francesca Rossi","isbn":"978-1-57735-633-2","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":462,"pages":{"first":3087,"last":3089},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}