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Representation learning is a fundamental challenge for feature selection and plays an important role in applications such as dimension reduction, data mining and object recognition. Traditional linear representation methods, such as principal component analysis (PCA), independent component analysis (ICA) and linear discriminate analysis (LDA), have good performance on certain applications based on corresponding criteria. However, these linear representation methods are not optimal in general. Sphere factor analysis (SFA) is a recently proposed method which provides a general framework for optimization problems. In term of object recognition, SFA seeks to optimize the discriminant ability of the nearest neighbor classifier for data classification and labeling. Based on the geometry structure of the search space, a gradient search algorithms have been applied to obtain an optimal basis. A detail presentation of these algorithm is given in this paper. Furthermore, to speed up the search procedure of SFA, a two-stage strategy is proposed, which we called two-stage SFA. We illustrate the effectiveness of the original SFA and two-stage SFA methods on UCI data sets and two face data sets.