{"type":"ScholarlyArticle","title":"On Trivial Solution and Scale Transfer Problems in Graph Regularized NMF","authors":[{"name":"Quanquan Gu","slug":"quanquan-gu","given":"Quanquan","family":"Gu","affiliation":""},{"name":"Chris H. Q. Ding","slug":"chris-h-q-ding","given":"Chris H. Q.","family":"Ding","affiliation":""},{"name":"Jiawei Han","slug":"jiawei-han","given":"Jiawei","family":"Han","affiliation":""}],"abstract":"Combining graph regularization with nonnegative matrix (tri-)factorization (NMF) has shown great performance improvement compared with traditional nonnegative matrix (tri-)factorization models due to its ability to utilize the geometric structure of the documents and words. In this paper, we show that these models are not well-defined and suffering from trivial solution and scale transfer problems. In order to solve these common problems, we propose two models for graph regularized nonnegative matrix (tri-)factorization, which can be applied for document clustering and co-clustering respectively. In the proposed models, a Normalized Cut-like constraint is imposed on the cluster assignment matrix to make the optimization problem well-defined. We derive a multiplicative updating algorithm for the proposed models, and prove its convergence. Experiments of clustering and co-clustering on benchmark text data sets demonstratethat the proposed models outperform the originalmodels as well as many other state-of-the-art clustering methods.","doi":"10.5591/978-1-57735-516-8/IJCAI11-218","url":"https://ijcai.org/proceedings/2011/218","pdf":"https://ijcai.org/proceedings/2011/0218.pdf","markdown":"https://ijcai.org/proceedings/2011/218.md","bibtex":"https://ijcai.org/proceedings/2011/bibtex/218","volume":{"slug":"2011","title":"Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2011","url":"https://ijcai.org/proceedings/2011/","year":2011,"location":"Barcelona, Catalonia, Spain","dates":"16–22 July 2011","editors":"Toby Walsh","isbn":"978-1-57735-512-0; 978-1-57735-513-7; 978-1-57735-514-4; 978-1-57735-515-1; 978-1-57735-516-8","publisher":"AAAI Press/International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":218,"pages":{"first":1288,"last":1292},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}