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This paper introduces a new Support Vector Machine (SVM) formulation for the direction of arrival (DOA) estimation problem. We establish a theoretical relationship between the Minimum Variance Distortionless Response (MVDR) and the MUltiple SIgnal Characterization (MUSIC) methods. This leads naturally to the derivation of an SVM-MUSIC algorithm, which combines the benefits of subspace methods with those of SVM. Spatially smoothed versions and a recursive form of the algorithms exhibit good performance against coherent signals. We test the method's performance in scenarios with noncoherent and coherent signals, and in small-sample size-situations obtaining an improved performance in comparison with existing standard approaches.