{"type":"ScholarlyArticle","title":"Tensor Completion with Side Information: A Riemannian Manifold Approach","authors":[{"name":"Tengfei Zhou","slug":"tengfei-zhou","given":"Tengfei","family":"Zhou","affiliation":"College of Computer Science and Technology , Zhejiang University , China"},{"name":"Hui Qian","slug":"hui-qian","given":"Hui","family":"Qian","affiliation":"College of Computer Science and Technology , Zhejiang University , China"},{"name":"Zebang Shen","slug":"zebang-shen","given":"Zebang","family":"Shen","affiliation":"College of Computer Science and Technology , Zhejiang University , China"},{"name":"Chao Zhang","slug":"chao-zhang","given":"Chao","family":"Zhang","affiliation":"College of Computer Science and Technology , Zhejiang University , China"},{"name":"Congfu Xu","slug":"congfu-xu","given":"Congfu","family":"Xu","affiliation":"College of Computer Science and Technology , Zhejiang University , China"}],"abstract":"By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily accessible side information, due to their format mismatch. Consequently, there is still room for improvement. To fill the gap, in this paper, a novel Riemannian model is proposed to tightly integrate the original model and the side information by overcoming their inconsistency. For this model, an efficient Riemannian conjugate gradient descent solver is devised based on a new metric that captures the curvature of the objective. Numerical experiments suggest that our method is more accurate than the state-of-the-art without compromising the efficiency.","doi":"10.24963/ijcai.2017/495","url":"https://ijcai.org/proceedings/2017/495","pdf":"https://ijcai.org/proceedings/2017/0495.pdf","markdown":"https://ijcai.org/proceedings/2017/495.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/495","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":495,"pages":{"first":3539,"last":3545},"keywords":["Machine Learning: Learning Preferences or Rankings","Machine Learning: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Absil et al., 2009] P-A Absil, Robert Mahony, and Rodolphe Sepulchre. 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