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The orthogonal subspace projection (OSP) algorithm is substantially a kind of matched filter that requires the evaluation of a prototype for each class to be detected. The kernel OSP (KOSP) has recently demonstrated improved results for target detection in hyperspectral images. The use of kernel methods (KMs) makes the method nonlinear, helps to combat the high-dimensionality problem, and improves robustness to noise. This paper presents a semisupervised graph-based approach to improve KOSP. The proposed algorithm deforms the kernel by approximating the marginal distribution using the unlabeled samples. Two further improvements are presented. First, a contextual selection of unlabeled samples is proposed. This strategy helps in better modeling the data manifold, and thus, improved sensitivity-specificity rates are obtained. Second, given the high computational burden involved, we present two alternative formulations based on the Nystroumlm method and the incomplete Cholesky factorization to achieve operational processing times. The good performance of the proposed method is illustrated in a toy data set and two relevant hyperspectral image target-detection applications: crop identification and thermal hot-spot detection. A clear improvement is observed with respect to the linear and the nonlinear kernel-based OSP, demonstrating good generalization capabilities when a low number of labeled samples are available, which is usually the case in target-detection problems. The relevance of unlabeled samples and the computational cost are also analyzed in detail.