Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Mehrtash Harandi*, Richard Hartley, Chunhua Shen, Brian Lovell, Conrad Sanderson

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    78 Citations (Scopus)

    Abstract

    Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning in Grassmann manifolds, i.e., the space of linear subspaces. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose an algorithm for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into higher dimensional Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.

    Original languageEnglish
    Pages (from-to)113-136
    Number of pages24
    JournalInternational Journal of Computer Vision
    Volume114
    Issue number2-3
    DOIs
    Publication statusPublished - 22 Sept 2015

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