{"type":"ScholarlyArticle","title":"Locality Preserving Nonnegative Matrix Factorization","authors":[{"name":"Deng Cai","slug":"deng-cai","given":"Deng","family":"Cai","affiliation":""},{"name":"Xiaofei He","slug":"xiaofei-he","given":"Xiaofei","family":"He","affiliation":""},{"name":"Xuanhui Wang","slug":"xuanhui-wang","given":"Xuanhui","family":"Wang","affiliation":""},{"name":"Hujun Bao","slug":"hujun-bao","given":"Hujun","family":"Bao","affiliation":""},{"name":"Jiawei Han","slug":"jiawei-han","given":"Jiawei","family":"Han","affiliation":""}],"abstract":"Matrix factorization techniques have been frequently applied in information processing tasks. Among them, Non-negative Matrix Factorization (NMF) have received considerable attentions due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts-based in human brain. On the other hand, from geometric perspective the data is usually sampled from a low dimensional manifold embedded in high dimensional ambient space. One hopes then to find a compact representation which uncovers the hidden topics and simultaneously respects the intrinsic geometric structure. In this paper, we propose a novel algorithm, called {em Locality Preserving Non-negative Matrix Factorization} (LPNMF), for this purpose. For two data points, we use KL-divergence to evaluate their similarity on the hidden topics. The optimal maps are obtained such that the feature values on hidden topics are restricted to be non-negative and vary smoothly along the geodesics of the data manifold. Our empirical study shows the encouraging results of the proposed algorithm in comparisons to the state-of-the-art algorithms on two large high-dimensional databases.Deng Cai, Xiaofei He, Xuanhui Wang, Hujun Bao, Jiawei Han","doi":null,"url":"https://ijcai.org/proceedings/2009/171","pdf":"https://ijcai.org/proceedings/2009/0171.pdf","markdown":"https://ijcai.org/proceedings/2009/171.md","bibtex":"https://ijcai.org/proceedings/2009/bibtex/171","volume":{"slug":"2009","title":"Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2009","url":"https://ijcai.org/proceedings/2009/","year":2009,"location":"Pasadena, California, USA","dates":"","editors":"Hiroaki Kitano","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":171,"pages":{"first":1010,"last":1014},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}