Manifold Regularization : A Geometric Framework for Learning from Examples
Manifold Regularization : A Geometric Framework for Learning from Examples
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发表时间：
2004
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通讯作者：
M. Belkin;P. Niyogi;Vikas Sindhwani
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作者：
M. Belkin;P. Niyogi;Vikas Sindhwani
我们提出了一系列基于新形式的正则化的学习算法，使我们能够利用边缘分布的几何形状。我们专注于一个半监督框架，它将标记和未标记数据合并到通用学习器中。一些转导图学习算法和标准方法（包括支持向量机和正则化最小二乘法）可以作为特例获得。我们利用再生核希尔伯特空间的性质来证明新的表示定理，为算法提供理论基础。结果（与纯粹基于图形的方法相比），我们获得了对新颖示例的自然样本外扩展，因此能够处理转导式和真正的半监督设置。我们提供的实验证据表明我们的半监督算法能够有效地使用未标记的数据。最后，我们在总体框架内简要讨论无监督学习和完全监督学习。
We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning algorithms and standard methods including Support Vector Machines and Regularized Least Squares can be obtained as special cases. We utilize properties of Reproducing Kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely graph based approaches) we obtain a natural out-of-sample extension to novel examples and so are able to handle both transductive and truly semi-supervised settings. We present experimental evidence suggesting that our semi-supervised algorithms are able to use unlabeled data effectively. Finally we have a brief discussion of unsupervised and fully supervised learning within our general framework.