Local high-order regularization on data manifolds

Kim, Kwang In and Tompkin, James and Pfister, Hanspeter and Theobalt, Christian (2015) Local high-order regularization on data manifolds. In: Computer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference on :. IEEE, pp. 5473-5481.

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The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The iterated graph Laplacian enables high-order regularization, but it has a high computational complexity and so cannot be applied to large problems. We introduce a new regularizer which is globally high order and so does not suffer from the degeneracy of the graph Laplacian regularizer, but is also sparse for efficient computation in semi-supervised learning applications. We reduce computational complexity by building a local first-order approximation of the manifold as a surrogate geometry, and construct our high-order regularizer based on local derivative evaluations therein. Experiments on human body shape and pose analysis demonstrate the effectiveness and efficiency of our method.

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18 Jun 2015 06:10
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04 May 2024 23:22