Local High-order Regularization on Data Manifolds
This addresses a computational bottleneck in semi-supervised learning for applications like human body analysis, but it is incremental as it builds on existing high-order regularization methods.
The paper tackled the degeneracy of graph Laplacian regularizers in high-dimensional manifolds by introducing a globally high-order regularizer that is sparse for efficient computation, achieving effectiveness and efficiency in experiments on human body shape and pose analysis.
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.