Riemannian Sparse Coding for Positive Definite Matrices

Anoop Cherian 1 Suvrit Sra 2
1 LEAR - Learning and recognition in vision
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 Max Planck Insitute for Intelligent Systems
MPI - Max Planck Institute for Biological Cybernetics
Abstract : Inspired by the great success of sparse coding for vector valued data, our goal is to represent symmetric positive definite (SPD) data matrices as sparse linear combinations of atoms from a dictionary, where each atom itself is an SPD matrix. Since SPD matrices follow a non-Euclidean (in fact a Riemannian) geometry, existing sparse coding techniques for Euclidean data cannot be directly extended. Prior works have approached this problem by defining a sparse coding loss function using either extrinsic similarity measures (such as the log-Euclidean distance) or kernelized variants of statistical measures (such as the Stein divergence, Jeffrey's divergence, etc.). In contrast, we propose to use the intrinsic Riemannian distance on the manifold of SPD matrices. Our main contribution is a novel mathematical model for sparse coding of SPD matrices; we also present a computationally simple algorithm for optimizing our model. Experiments on several computer vision datasets showcase superior classification and retrieval performance compared with state-of-the-art approaches.
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Communication dans un congrès
David Fleet; Tomas Pajdla; Bernt Schiele; Tinne Tuytelaars. ECCV 2014 - European Conference on Computer Vision, Sep 2014, Zurich, Switzerland. Springer, Lecture Notes in Computer Science, 8691, pp.299-314, 2014, <10.1007/978-3-319-10578-9_20>
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Dernière modification le : mardi 13 décembre 2016 - 15:41:05
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Anoop Cherian, Suvrit Sra. Riemannian Sparse Coding for Positive Definite Matrices. David Fleet; Tomas Pajdla; Bernt Schiele; Tinne Tuytelaars. ECCV 2014 - European Conference on Computer Vision, Sep 2014, Zurich, Switzerland. Springer, Lecture Notes in Computer Science, 8691, pp.299-314, 2014, <10.1007/978-3-319-10578-9_20>. <hal-01057703>

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