{"type":"ScholarlyArticle","title":"Linear Manifold Regularization with Adaptive Graph for Semi-supervised Dimensionality Reduction","authors":[{"name":"Kai Xiong","slug":"kai-xiong","given":"Kai","family":"Xiong","affiliation":"Northwestern Ploytechnical University , Xi'an , 710072 , P. R. China"},{"name":"Feiping Nie","slug":"feiping-nie","given":"Feiping","family":"Nie","affiliation":"Northwestern Ploytechnical University , Xi'an , 710072 , P. R. China; University of Texas at Arlington , USA"},{"name":"Junwei Han","slug":"junwei-han","given":"Junwei","family":"Han","affiliation":"Northwestern Ploytechnical University , Xi'an , 710072 , P. R. China"}],"abstract":"Many previous graph-based methods perform dimensionality reduction on a pre-defined graph. However, due to the noise and redundant information in the original data, the pre-defined graph has no clear structure and may not be appropriate for the subsequent task. To overcome the drawbacks, in this paper, we propose a novel approach called linear manifold regularization with adaptive graph (LMRAG) for semi-supervised dimensionality reduction. LMRAG directly incorporates the graph construction into the objective function, thus the projection matrix and the optimal graph can be simultaneously optimized. Due to the structure constraint, the learned graph is sparse and has clear structure. Extensive experiments on several benchmark datasets demonstrate the effectiveness of the proposed method.","doi":"10.24963/ijcai.2017/439","url":"https://ijcai.org/proceedings/2017/439","pdf":"https://ijcai.org/proceedings/2017/0439.pdf","markdown":"https://ijcai.org/proceedings/2017/439.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/439","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning S-Z","track":"Main track","number":439,"pages":{"first":3147,"last":3153},"keywords":["Machine Learning: Semi-Supervised Learning","Machine Learning: Data Mining","Machine Learning: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Belhumeur et al., 1997] Peter N. 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