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In this letter, a novel ensemble-learning approach for anomaly detection is presented. The proposed technique aims to optimize an ensemble of kernel-based one-class classifiers, such as support vector data description (SVDD) classifiers, by estimating optimal sparse weights of the subclassifiers. In this method, the features of a given multivariate data set representing normalcy are first randomly subsampled into a large number of feature subspaces. An enclosing hypersphere that defines the support of the normalcy data in the reproducing kernel Hilbert space (RKHS) of each respective feature subspace is estimated using standard SVDD. The joint hypersphere in the RKHS of the combined kernel is learned by optimally combining the weighted individual kernels while imposing the l1 constraint on the combining weights. The joint hypersphere representing the optimal compact support of the multivariate data in the joint RKHS is then used to test a new data point to determine if it belongs to the normalcy data or not. A performance comparison between the proposed algorithm and regular SVDD is reported using hyperspectral image data as well as general multivariate data.