{"type":"ScholarlyArticle","title":"Towards Generalized and Efficient Metric Learning on Riemannian Manifold","authors":[{"name":"Pengfei Zhu","slug":"pengfei-zhu","given":"Pengfei","family":"Zhu","affiliation":"School of Computer Science and Technology , Tianjin University , Tianjin 300350 , China"},{"name":"Hao Cheng","slug":"hao-cheng","given":"Hao","family":"Cheng","affiliation":"School of Computer Science and Technology , Tianjin University , Tianjin 300350 , China"},{"name":"Qinghua Hu","slug":"qinghua-hu","given":"Qinghua","family":"Hu","affiliation":"School of Computer Science and Technology , Tianjin University , Tianjin 300350 , China"},{"name":"Qilong Wang","slug":"qilong-wang","given":"Qilong","family":"Wang","affiliation":"School of Computer Science and Technology , Tianjin University , Tianjin 300350 , China"},{"name":"Changqing Zhang","slug":"changqing-zhang","given":"Changqing","family":"Zhang","affiliation":"School of Computer Science and Technology , Tianjin University , Tianjin 300350 , China"}],"abstract":"Modeling data as points on non-linear Riemannian manifold has attracted increasing attentions in many computer vision tasks, especially visual recognition. Learning an appropriate metric on Riemannian manifold plays a key role in achieving promising performance. For widely used symmetric positive definite (SPD) manifold and Grassmann manifold, most of existing metric learning methods are designed for one manifold, and are not straightforward for the other one. Furthermore, optimizations in previous methods usually rely on computationally expensive iterations. To address above limitations, this paper makes an attempt to propose a generalized and efficient Riemannian manifold metric learning (RMML) method, which can be flexibly adopted to both SPD and Grassmann manifolds. By minimizing the geodesic distance of similar pairs and the interpoint geodesic distance of dissimilar ones on nonlinear manifolds, the proposed RMML is optimized by computing the geodesic mean between inverse of similarity matrix and dissimilarity matrix, benefiting a global closed-form solution and high efficiency. The experiments are conducted on various visual recognition tasks, and the results demonstrate our RMML performs favorably against its counterparts in terms of both accuracy and efficiency.","doi":"10.24963/ijcai.2018/449","url":"https://ijcai.org/proceedings/2018/449","pdf":"https://ijcai.org/proceedings/2018/0449.pdf","markdown":"https://ijcai.org/proceedings/2018/449.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/449","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Machine Learning","track":"Main track","number":449,"pages":{"first":3235,"last":3241},"keywords":["Machine Learning: Classification","Machine Learning: Dimensionality Reduction and Manifold Learning"],"videos":[],"references":[{"position":1,"raw":"[Arsigny et al., 2007] Vincent Arsigny, Pierre Fillard, X- avier Pennec, and Nicholas Ayache. 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