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.

介绍了一种新型的正则化方法，它是全局高阶的，不会出现图拉普拉斯正则化中的退化问题。通过构建一个局部一阶替代几何形式，有助于减少计算复杂度，并基于局部导数评估构造高阶正则化方法，该方法在人体形状和姿势分析中的实验表明了其有效性和效率。