With the rapid increase of online videos, recognition and search in videos becomes a new trend in multimedia computing. Action recognition in videos thus draws intensive research concerns recently. Second, sparse representation has become state-of-the-art solution in computer vision because it has several advantages for data representation including easy interpretation, quick indexing and considerable connection with biological vision. One prominent sparse representation algorithm is Laplacian regularized sparse coding (LaplacianSC). However, LaplacianSC biases the results toward a constant and thus results in poor generalization. In this paper, we propose Hessian regularized sparse coding (HessianSC) for action recognition. In contrast to LaplacianSC, HessianSC can well preserve the local geometry and steer the sparse coding varying linearly along the manifold of data distribution. We also present a fast iterative shrinkage-thresholding algorithm (FISTA) for HessianSC. Extensive experiments on human motion database (HMDB51) demonstrate that HessianSC significantly outperforms LaplacianSC and the traditional sparse coding algorithm for action recognition.
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