Graph-embedded subspace support vector data description

•A novel subspace learning framework for one-class classification is proposed.•The framework presents the problem in the form of graph embedding and includes the previously proposed subspace one-class techniques as its special cases.•The proposed framework reveals spectral and spectral regression-based solutions as alternatives to the previously used gradient-based technique.•Similarities to the traditional subspace learning techniques and other novel insights revealed by the framework are discussed.