This paper proposes a computationally efficient offline semi-supervised algorithm that yields a more accurate prediction than the label propagation algorithm, which is commonly used in online graph-based semi-supervised learning (SSL). Our proposed method is an offline method that is intended to assist online graph-based SSL algorithms. The efficacy of the tool in creating new learning algorithms of this type is demonstrated in numerical experiments.

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.

For the 3D face recognition numerous methods have been proposed, but little attention has been given to the local-based representation for the texture map of the 3D models. In this paper, we propose a novel 3D face recognition approach based on locally extracted Geodesic Pseudo Zernike Moment Array (GPZMA) of the texture map when only one exemplar per person is available. In the proposed method, the function of the PZM is controlled by the geodesic deformations to tackle the problem of face recognition under the expression and pose variations. The feasibility and effectiveness investigation for the proposed method is conducted through a wide range of experiments using publicly available BU-3DFE and Bosphorus databases including samples with different expression and pose variations. The performance of the proposed method is compared with the performance of three state-of-the-art benchmark approaches. The encouraging experimental results demonstrate that the proposed method achieves much higher accuracy than the benchmarks in single-model databases.