Connecting the Dots: Image Classification via Sparse Representation from a Constrained Subspace Perspective

We consider the problem of classifier design via sparse representation based on a constrained subspace model. We argue that the data points in the linear span of the training samples should be constrained in order to yield a more accurate approximation to the corresponding data manifold. For this purpose, the constrained set of data points is formulated as a union of affine subspaces in the form of affine hulls spanned by training samples. We argue that the intrinsic dimension of the affine subspaces should be equal to that of data manifold. Thus, a classifier based on this model has a high classification accuracy similar to that of the conceptual NM (Nearest Manifold) classifier. Based on this model, we connect the dots of some classical classifiers including NN (Nearest Neighbor), NFL (Nearest Feature Line), NS (Nearest subspace) and the recently emerged state-of-the-art SRC (Sparse Representation Classifiers) and interpret the mechanism of SRC and Yang's variant of the SRC using the constrained subspace perspective. Experiments on the Extended Yale B database for image classification corroborate our claims and demonstrate the possibility of a proposed classifier called NCSC-CSR which has higher classification accuracy and robustness. Keywords—sparse representation; constrained subspace; manifold approximation