Dictionary Learning and Sparse Coding on Grassmann Manifolds: An Extrinsic Solution

• Published in: 2013 IEEE International Conference on Computer Vision pp. 3120 - 3127
• Main Authors: Harandi, Mehrtash, Sanderson, Conrad, Chunhua Shen, Lovell, Brian
• Format: Conference Proceeding Journal Article
• Language: English
• Published: IEEE 01.12.2013
• Subjects: action recognition; Classification; Computer vision; Dictionaries; dictionary learning; dynamic texture classification; Encoding; Face recognition; Grassmann manifolds; image-set; Kernel; Learning; Manifolds; Mathematical models; sparse coding; Sparse matrices; Surface layer; Symmetric matrices; Texture; Vectors
• ISSN: 1550-5499
• DOI: 10.1109/ICCV.2013.387

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.