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Past decades, numerous spectral analysis based algorithms have been proposed for dimensionality reduction, which plays an important role in machine learning and artificial intelligence. However, most of these existing algorithms are developed intuitively and pragmatically, i.e., on the base of the experience and knowledge of experts for their own purposes. Therefore, it will be more informative to provide some a systematic framework for understanding the common properties and intrinsic differences in the algorithms. In this paper, we propose such a framework, i.e., ldquopatch alignmentrdquo, which consists of two stages: part optimization and whole alignment. With the proposed framework, various algorithms including the conventional linear algorithms and the manifold learning algorithms are reformulated into a unified form, which gives us some new understandings on these algorithms.