With the increasing availability of high dimensional data and demand in sophisticated data analysis algorithms, manifold learning becomes a critical technique to perform dimensionality reduction, unraveling the intrinsic data structure. The real-world data however often come with noises and outliers; seldom, all the data live in a single linear subspace. Inspired by the recent advances in sparse subspace learning and diffusion-based approaches, we propose a new manifold denoising algorithm in which data neighborhoods are adaptively inferred via sparse subspace reconstruction; we then derive a new formulation to perform denoising to the original data. Experiments carried out on both toy and real applications demonstrate the effectiveness of our method; it is insensitive to parameter tuning and we show significant improvement over the competing algorithms.
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