Dictionary Learning and Sparse Coding on Grassmann Manifolds: An Extrinsic Solution
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Sanderson, Conrad
Shen, Chunhua
Lovell, Brian
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Sydney, Australia
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Abstract
Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping, which enables us to devise a closed-form solution for updating a Grassmann dictionary, atom by atom. Furthermore, to handle non-linearity in data, we propose a kernelised version of the dictionary learning algorithm. Experiments on several classification tasks (face recognition, action recognition, dynamic texture classification) show that the proposed approach achieves considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelised Affine Hull Method and graph-embedding Grassmann discriminant analysis.
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2013 IEEE International Conference on Computer Vision
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© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
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Harandi, M; Sanderson, C; Shen, C; Lovell, B, Dictionary Learning and Sparse Coding on Grassmann Manifolds: An Extrinsic Solution, 2013 IEEE International Conference on Computer Vision, 2013