图 书 馆
从流形到流形：SPD矩阵的几何感知降维From Manifold to Manifold: Geometry-Aware Dimensionality Reduction for SPD Matrices |
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| 课程网址: | http://videolectures.net/eccv2014_salzmann_dimensionality_reducti... |
| 主讲教师: | Mathieu Salzmann |
| 开课单位: | 澳大利亚ICT卓越研究中心 |
| 开课时间: | 2014-10-29 |
| 课程语种: | 英语 |
| 中文简介: |  使用对称正定（SPD）矩阵表示图像和视频并考虑结果空间的黎曼几何已证明对许多识别任务有益。不幸的是，基于SPD矩阵的黎曼流形（尤其是高维矩阵）的计算成本很高，从而限制了现有技术的适用性。在本文中，我们介绍了一种方法，该方法可通过构造一个低维，更具区分性的SPD流形来处理高维SPD矩阵。为此，我们使用正交投影对高维SPD流形到低维SPD流形的映射进行建模。特别是，我们搜索一个投影，该投影产生一个低维流形，该流形具有基于流形上的度量的亲和加权相似度度量编码的最大判别能力。然后，可以将学习表示为格拉斯曼流形上的优化问题。我们对几个分类任务的评估表明，与现有方法相比，我们的方法可显着提高准确性。 |
| 课程简介: | Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian manifold of SPD matrices –especially of high-dimensional ones– comes at a high cost that limits the applicability of existing techniques. In this paper we introduce an approach that lets us handle high-dimensional SPD matrices by constructing a lower-dimensional, more discriminative SPD manifold. To this end, we model the mapping from the high-dimensional SPD manifold to the low-dimensional one with an orthonormal projection. In particular, we search for a projection that yields a low-dimensional manifold with maximum discriminative power encoded via an affinity-weighted similarity measure based on metrics on the manifold. Learning can then be expressed as an optimization problem on a Grassmann manifold. Our evaluation on several classification tasks shows that our approach leads to a significant accuracy gain over state-of-the-art methods. |
| 关 键 词: | 黎曼流形; 几何感知; SPD矩阵 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-12-16：zyk |
| 最后编审: | 2020-12-16：zyk |
| 阅读次数: | 210 |