图 书 馆
图的多尺度分析Multiscale analysis on graphs |
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| 课程网址: | http://videolectures.net/mlss05us_gioni_mag/ |
| 主讲教师: | Mauro Maggioni |
| 开课单位: | 杜克大学 |
| 开课时间: | 2007-02-25 |
| 课程语种: | 英语 |
| 中文简介: |  最近已经证明对图的分析可以产生强大的学习算法，特别是在回归、分类和聚类方面。拉普拉斯算子在图上的特征函数是分析图上函数的自然基础，正如我们在本次会议的参与者最近工作的介绍中看到的那样。在本次演讲中，我们介绍了一组新的灵活基函数，称为扩散小波，它允许对图上的函数进行多尺度分析，与经典小波在欧几里德空间中执行多尺度分析的方式非常相似。它们允许对图上的函数进行高效的表示、压缩、去噪，并且非常适合学习以及无监督算法。它们还与图的多尺度分解相关联，图本身具有应用程序。我们将通过几个例子讨论这个结构，从流形和图上的信号处理，到最近的一些初步应用到聚类和学习。 |
| 课程简介: | Analysis on graphs has recently been shown to lead to powerful algorithms in learning, in particular for regression, classification andclustering. Eigenfunctions of the Laplacian on a graph are a natural basis for analyzing functions on a graph, as we have seen in presentations of recent work by partecipants to this conference. In this talk we introduce a new flexible set of basis functions, called Diffusion Wavelets, that allow for a multiscale analysis of functions on a graph, very much in the same way classical wavelets perform a multiscale analysis in Euclidean spaces. They allow efficient, representation, compression, denoising of functions on the graph, and are very well-suited for learning, as well as unsupervised algorithms. They are also associated with a multiscale decomposition of the graph, which has applications by itself. We will discuss this construction with several examples, going from signal processing on manifolds and graphs, to some recent preliminary applications to clustering and learning. |
| 关 键 词: | 拉普拉斯算子; 多尺度分析; 信号处理 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2021-07-15：nkq |
| 最后编审: | 2021-07-15：nkq |
| 阅读次数: | 53 |