CVPR 2015
Local High-order Regularization on Data Manifolds

Kwang In Kim James Tompkin Hanspeter Pfister Christian Theobalt
Lancaster University MPI für Informatik Harvard University SEAS

The graph Laplacian regularizer (Lap) fails to regularize this toy example, leading to spiky functions. Our local Gaussian (LG) regularizer leads to smooth functions.

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.

author = {Kwang In Kim and James Tompkin and Hanspeter Pfister and Christian Theobalt},
title = {Local High-order Regularization on Data Manifolds},
booktitle = {Proc. IEEE CVPR},
pages = {5473--5481},
year = {2015},
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Kwang In Kim thanks EPSRC EP/M00533X/1 and EP/M006255/1, James Tompkin and Hanspeter Pfister thank NSF CGV-1110955, and James Tompkin and Christian Theobalt thank the Intel Visual Computing Institute.