On Manifold Regularization
On Manifold Regularization
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2005
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我们提出了一类基于一种新的正则化形式的学习算法，它允许我们利用边缘分布的几何。我们专注于一个半监督框架，它在通用学习者中合并了已标记和未标记的数据。作为特例，可以得到支持向量机和正则化最小二乘等一些直导图学习算法和标准方法。我们利用再生核Hilbert空间的性质证明了新的表示定理，为算法提供了理论基础。结果(与纯粹基于图形的方法相反)，我们获得了对新示例的自然超出样本的扩展，从而能够处理传导性和真正的半监督设置。我们给出的实验证据表明，我们的半监督算法能够有效地利用未标记数据。在没有带标签的例子的情况下，我们的框架产生了带有样本外扩展的正则化形式的谱聚类。
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 semisupervised framework that incorporates labeled and unlabeled data in a generalpurpose 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 are thus able to handle both transductive and truly semi-supervised settings. We present experimental evidence suggesting that our semisupervised algorithms are able to use unlabeled data effectively. In the absence of labeled examples, our framework gives rise to a regularized form of spectral clustering with an out-of-sample extension.