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Free keywords:
Computer Science, Computer Vision and Pattern Recognition, cs.CV
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.
