Toward sparse coding on cosine distance

Sparse coding is a regularized least squares solution using the L1 or L0 constraint, based on the Euclidean distance between original and reconstructed signals with respect to a predefined dictionary. The Euclidean distance, however, is not a good metric for many feature descriptors, especially histogram features, e.g. many visual features including SIFT, HOG, LBP and Bag-of-visual-words. In contrast, cosine distance is a more appropriate metric for such features. To leverage the benefit of the cosine distance in sparse coding, we formulate a new sparse coding objective function based on approximate cosine distance by constraining a norm of the reconstructed signal to be close to the norm of the original signal. We evaluate our new formulation on three computer vision datasets (UCF101 Action dataset, AR dataset and Extended YaleB dataset) and show improvements over the Euclidean distance based objective.