8,656 research outputs found
Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds
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 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. This in turn enables
us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we
propose closed-form solutions 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 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.Comment: Appearing in International Journal of Computer Visio
The Intrinsic Dimensionality of Attractiveness: A Study in Face Profiles
The study of human attractiveness with pattern analysis techniques is an emerging research field. One still largely unresolved problem is which are the facial features relevant to attractiveness, how they combine together, and the number of independent parameters required for describing and identifying harmonious faces. In this paper, we present a first study about this problem, applied to face profiles. First, according to several empirical results, we hypothesize the existence of two well separated manifolds of attractive and unattractive face profiles. Then, we analyze with manifold learning techniques their intrinsic dimensionality. Finally, we show that the profile data can be reduced, with various techniques, to the intrinsic dimensions, largely without loosing their ability to discriminate between attractive and unattractive face
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