图 书 馆
图拉普拉斯算法的收敛性及其在维数估计和图像分割中的应用Convergence of the graph Laplacian application to dimensionality estimation and image segmentation |
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| 课程网址: | http://videolectures.net/sicgt07_audibert_cotg/ |
| 主讲教师: | Jean Yves Audibert |
| 开课单位: | 巴黎大学 |
| 开课时间: | 2007-09-07 |
| 课程语种: | 英语 |
| 中文简介: |  给定一个支持欧几里德空间子流形的概率测度样本，我们可以构建一个邻域图，该图可以看作是子流形的近似。这种图的拉普拉斯算子用于多种机器学习方法，如半监督学习、降维和聚类。随着样本大小的增加和邻域大小接近于零，我们将展示文献中使用的三种不同图拉普拉斯算子的逐点限制。我们表明，对于子流形上的统一度量，所有图拉普拉斯算子在常数之前都有相同的限制。然而，在子流形上的非均匀度量的情况下，只有所谓的随机游走图拉普拉斯算子收敛到加权拉普拉斯贝尔特拉米算子。我们将给出这些理论结果的两个应用。 |
| 课程简介: | Given a sample from a probability measure with support on a submanifold in Euclidean space one can construct a neighborhood graph which can be seen as an approximation of the submanifold. The graph Laplacian of such a graph is used in several machine learning methods like semi-supervised learning, dimensionality reduction and clustering. We will present the pointwise limit of three different graph Laplacians used in the literature as the sample size increases and the neighborhood size approaches zero. We show that for a uniform measure on the submanifold all graph Laplacians have the same limit up to constants. However in the case of a nonuniform measure on the submanifold only the so called random walk graph Laplacian converges to the weighted Laplace-Beltrami operator. We will give two applications of these theoretical results. |
| 关 键 词: | 邻域图; 拉普拉斯算子; 逐点限制 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2021-07-17：nkq |
| 最后编审: | 2021-07-17：nkq |
| 阅读次数: | 74 |