Density based graph denoising for manifold learning

Abstract : Processing high dimension data often makes use of a dimension reduction step. Indeed, high dimension data generally rely on a low dimension underlying structure. When the data are noisy, dimension reduction may fail because of shortcuts appearing on the graph catching the underlying structure. Our paper presents a method to suppress shortcuts in the underlying structure graph. The method is based on a skeleton graph that approximates the data and that is built using a data probability density estimation. This approximating graph is then used to select the edges of the underlying structure graph used in the dimension reduction. The proposed algorithm is tested on the capacity to suppress shortcuts and to conserve the underlying structure geodesic distance. Our method outperforms the state-of-the-art methods in the experiments on six 3D synthetic dataset and one tomographic dataset with different noise levels.
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Yves Michels, Etienne Baudrier, Loïc Mazo, Mohamed Tajine. Density based graph denoising for manifold learning. 2019. ⟨hal-02012395⟩

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