  Motivated by the remarkable successes of Graph-based Transduction (GT) and
Sparse Representation (SR), we present a novel Classifier named Sparse
Graph-based Classifier (SGC) for image classification. In SGC, SR is leveraged
to measure the correlation (similarity) of each two samples and a graph is
constructed for encoding these correlations. Then the Laplacian eigenmapping is
adopted for deriving the graph Laplacian of the graph. Finally, SGC can be
obtained by plugging the graph Laplacian into the conventional GT framework. In
the image classification procedure, SGC utilizes the correlations, which are
encoded in the learned graph Laplacian, to infer the labels of unlabeled
images. SGC inherits the merits of both GT and SR. Compared to SR, SGC improves
the robustness and the discriminating power of GT. Compared to GT, SGC
sufficiently exploits the whole data. Therefore it alleviates the undercomplete
dictionary issue suffered by SR. Four popular image databases are employed for
evaluation. The results demonstrate that SGC can achieve a promising
performance in comparison with the state-of-the-art classifiers, particularly
in the small training sample size case and the noisy sample case.
