Properly-Weighted Graph Laplacian for Semi-supervised Learning
Properly-Weighted Graph Laplacian for Semi-supervised Learning
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DOI：
10.1007/s00245-019-09637-3
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发表时间：
2018-10
影响因子：
1.8
通讯作者：
J. Calder;D. Slepčev
中科院分区：
文献类型：
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作者：
J. Calder;D. Slepčev
由于图拉普拉斯的简并性，用于半监督学习的传统图拉普拉斯方法的性能随着标记数据与未标记数据的比率的下降而大幅下降。最近提出了几种方法来解决这个问题，但是我们表明其中一些方法在大数据限制下仍然不适定。在本文中，我们展示了一种正确设置拉普拉斯正则化中的权重的方法，以便估计器在大样本限制下保持良好的姿势和稳定。我们证明，我们的半监督学习算法在无限样本量限制下收敛于连续变分问题的平滑解，连续获得标记值。我们的方法快速且易于实施。
The performance of traditional graph Laplacian methods for semi-supervised learning degrades substantially as the ratio of labeled to unlabeled data decreases, due to a degeneracy in the graph Laplacian. Several approaches have been proposed recently to address this, however we show that some of them remain ill-posed in the large-data limit. In this paper, we show a way to correctly set the weights in Laplacian regularization so that the estimator remains well posed and stable in the large-sample limit. We prove that our semi-supervised learning algorithm converges, in the infinite sample size limit, to the smooth solution of a continuum variational problem that attains the labeled values continuously. Our method is fast and easy to implement.