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Learning Low Dimensional Patterns with Multi-Scale Local Representation

Manifold learning has been extensively applied to the field of data dimensionality reduction and pattern recognition in recent years since the related algorithms can efficiently retrieve the intrinsic geometric features of image data in computational intelligence. In this paper, we propose a new manifold learning model based on the nonnegative matrix factorization. In this model, α-divergence with locally linear representation is adopted as the objective function for nonnegative matrix decomposition for both basis and low dimensional representation or encoding vectors to capture features in high dimensional space. With a variable neighborhood size in the learning, the proposed model can learn the linear features and at the same time learn the local similarity of images in a neighborhood. Test results on JAFFE and ORL image datasets show that the proposed algorithms can obtain the state of art performance on the tasks of image clustering.