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Local High-order Regularization on Data Manifolds

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45610

Theobalt,  Christian
Computer Graphics, MPI for Informatics, Max Planck Society;

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arXiv:1602.03805.pdf
(Preprint), 4MB

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Citation

Kim, K. I., Tompkin, J., Pfister, H., & Theobalt, C. (2016). Local High-order Regularization on Data Manifolds. Retrieved from http://arxiv.org/abs/1602.03805.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002C-2428-A
Abstract
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.