Local High-Order Regularization on Data Manifolds

Kwang In Kim, James Tompkin, Hanspeter Pfister, Christian Theobalt; The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015, pp. 5473-5481

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.

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[bibtex]
@InProceedings{Kim_2015_CVPR,
author = {In Kim, Kwang and Tompkin, James and Pfister, Hanspeter and Theobalt, Christian},
title = {Local High-Order Regularization on Data Manifolds},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2015}
}