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In this paper, we present a kernel realization of a matched subspace detector (MSD) that is based on a subspace mixture model defined in a high-dimensional feature space associated with a kernel function. The linear subspace mixture model for the MSD is first reformulated in a high-dimensional feature space and then the corresponding expression for the generalized likelihood ratio test (GLRT) is obtained for this model. The subspace mixture model in the feature space and its corresponding GLRT expression are equivalent to a nonlinear subspace mixture model with a corresponding nonlinear GLRT expression in the original input space. In order to address the intractability of the GLRT in the feature space, we kernelize the GLRT expression using the kernel eigenvector representations as well as the kernel trick where dot products in the feature space are implicitly computed by kernels. The proposed kernel-based nonlinear detector, so-called kernel matched subspace detector (KMSD), is applied to several hyperspectral images to detect targets of interest. KMSD showed superior detection performance over the conventional MSD when tested on several synthetic data and real hyperspectral imagery.
Index Terms- Target detection, subspace detectors, matched signal detectors, kernel-based learning, hyperspectral data, spectral mixture models, nonlinear detection.

H. Kwon and N. M. Nasrabadi, "Kernel Matched Subspace Detectors for Hyperspectral Target Detection," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 28, no. , pp. 178-194, 2006.
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