Local high-order regularization on data manifolds
Local high-order regularization on data manifolds
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DOI：
10.1109/cvpr.2015.7299186
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
K. Kim;J. Tompkin;H. Pfister;C. Theobalt
中科院分区：
文献类型：
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作者：
K. Kim;J. Tompkin;H. Pfister;C. Theobalt
常见的图拉普拉斯正则化器在半监督学习和谱降维方面已经很成熟。然而，作为一阶正则化器，它可能导致高维流形中的简并函数。迭代图拉普拉斯可以实现高阶正则化，但计算复杂度较高，无法应用于大型问题。我们引入了一种新的正则化器，它是全局高阶的，因此不会受到图拉普拉斯正则化器的简并性的影响，但对于半监督学习应用中的高效计算来说也是稀疏的。我们通过构建流形的局部一阶近似作为代理几何来降低计算复杂性，并基于其中的局部导数评估构建我们的高阶正则化器。人体形状和姿势分析的实验证明了我们方法的有效性和效率。
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.