图 书 馆
流形自适应维数估计Manifold-adaptive dimension estimation |
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| 课程网址: | http://videolectures.net/icml07_farahmand_made/ |
| 主讲教师: | Amir-massoud Farahmand |
| 开课单位: | 阿尔伯塔大学 |
| 开课时间: | 2007-06-24 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Intuitively, learning should be easier when the data points lie on a low-dimensional submanifold of the input space. Recently there has been a growing interest in algorithms that aim to exploit such geometrical properties of the data. Oftentimes these algorithms require estimating the dimension of the manifold first. In this paper we propose an algorithm for dimension estimation and study its finite-sample behaviour. The algorithm estimates the dimension locally around the data points using nearest neighbor techniques and then combines these local estimates. We show that the rate of convergence of the resulting estimate is independent of the dimension of the input space and hence the algorithm is "manifold-adaptive". Thus, when the manifold supporting the data is low dimensional, the algorithm can be exponentially more efficient than its counterparts that are not exploiting this property. Our computer experiments confirm the obtained theoretical results. |
| 关 键 词: | 低维子流形; 维数估计算法; 有限样本 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-04-17：lxf |
| 阅读次数: | 71 |