The label estimation technique provides a new way to design semi-supervised learning algorithms. If the labels of the unlabeled data can be estimated correctly, the semi-supervised methods can be replaced by the corresponding supervised versions. In this paper, we propose a novel semi-supervised learning algorithm, called Geodesic Weighted Sparse Representation (GWSR), to estimate the labels of the unlabeled data. First, the geodesic distance and geodesic weight are calculated. The geodesic weight is utilized to reconstruct the labeled samples. The Euclidean distance between the reconstructed labeled sample and the unlabeled sample equals the geodesic distance between the original labeled sample and the unlabeled sample. Then, the unlabeled samples are sparsely reconstructed and the sparse reconstruction weight is obtained by minimizing the L1-norm. Finally, the sparse reconstruction weight is utilized to estimate the labels of the unlabeled samples. Experiments on synthetic data and USPS hand-written digit database demonstrate the effectiveness of our method.
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