SSKOSP [Semi-supervised Kernel Orthogonal Subspace Projection]
Authors	Luca Capobianco, Andrea Garzelli and Gustavo Camps-Valls
Download	Full Matlab Package
Code for the paper (please cite this paper!)	"Target Detection with Semisupervised Kernel Orthogonal Subspace Projection" Luca Capobianco, Andrea Garzelli and Gustavo Camps-Valls IEEE Transactions on Geoscience and Remote Sensing, 47(11), 3822-3834, Nov. 2009
Abstract	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 the kernel method makes the method non-linear, helps to combat the high dimensionality problem and improves robustness to noise. This paper presents a semi-supervised 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 Nyström method and the Incomplete Cholesky Factorization to achieve operational processing times. The good performance of the proposed method is illustrated in a toy dataset,  and two relevant hyperspectral image target detection applications: crop identification and thermal hot spot detection. A clear improvement is observed with respect the linear and the non-linear kernel-based OSP, demonstrating good generalization capabilities when 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.
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