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In this paper, we systematize a family of constrained quadratic classifiers that belong to the class of one-class classifiers. One-class classifiers such as the single-class support vector machine or the subspace methods are widely used for pattern classification and detection problems because they have many advantages over binary classifiers. We interpret subspace methods as rank-constrained quadratic classifiers in the framework. We also introduce two constraints and a method of suppressing the effect of competing classes to make them more accurate and retain their advantages over binary classifiers. Experimental results demonstrate the advantages of our methods over conventional classifiers.