Local High-order Regularization on Data Manifolds

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.

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Kwang In Kim, James Tompkin, Hanspeter Pfister, Christian Theobalt
• Keywords: CORR 2016, Education