{"type":"ScholarlyArticle","title":"Heuristic Search for Approximating One Matrix in Terms of Another Matrix","authors":[{"name":"Guihong Wan","slug":"guihong-wan","given":"Guihong","family":"Wan","affiliation":""},{"name":"Haim Schweitzer","slug":"haim-schweitzer","given":"Haim","family":"Schweitzer","affiliation":""}],"abstract":"We study the approximation of a target matrix in terms of several selected columns of another matrix, sometimes called \"a dictionary\".\r\nThis approximation problem arises in various domains, such as signal processing, computer vision, and machine learning. \r\nAn optimal column selection algorithm for the special case where the target matrix has only one column is known since the 1970's,\r\nbut most previously proposed column selection algorithms for the general case are greedy.\r\nWe propose the first nontrivial optimal algorithm for the general case, using a heuristic search setting similar to the classical A* algorithm.\r\nWe also propose practical sub-optimal algorithms in a setting similar to the classical Weighted A* algorithm.\r\nExperimental results show that our sub-optimal algorithms compare favorably with the current state-of-the-art greedy algorithms.\r\nThey also provide bounds on how close their solutions are to the optimal solution.","doi":"10.24963/ijcai.2021/221","url":"https://ijcai.org/proceedings/2021/221","pdf":"https://ijcai.org/proceedings/2021/0221.pdf","markdown":"https://ijcai.org/proceedings/2021/221.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/221","volume":{"slug":"2021","title":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2021","url":"https://ijcai.org/proceedings/2021/","year":2021,"location":"Montreal","dates":"19-27 August 2021","editors":"Prof. Zhi-Hua Zhou","isbn":"978-0-9992411-9-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2021"},"section":"Data Mining","track":"Main Track","number":221,"pages":{"first":1600,"last":1606},"keywords":["Machine Learning: Dimensionality Reduction","Heuristic Search and Game Playing: Heuristic Search","Data Mining: Feature Extraction, Selection and Dimensionality Reduction","Machine Learning: Learning Sparse Models"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}