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We introduce a new model to deal with imbalanced data sets for novelty detection problems where the normal class of training data set can be majority or minority class. The key idea is to construct an optimal hypersphere such that the inside margin between the surface of this sphere and the normal data and the outside margin between that surface and the abnormal data are as large as possible. Depending on a specific real application of novelty detection, the two margins can be adjusted to achieve the best true positive and false positive rates. Experimental results on a number of data sets showed that the proposed model can provide better performance comparing with current models for novelty detection.