Where are linear feature extraction methods applicable?
Where are linear feature extraction methods applicable?
复制标题
DOI：
10.1109/tpami.2005.250
复制
发表时间：
2005-12-01
影响因子：
23.6
通讯作者：
Zhu, ML
中科院分区：
文献类型：
--
作者：
Martínez, AM;Zhu, ML
计算机视觉和模式识别中的一个基本问题是确定在哪里，以及最重要的是，为什么一个给定的技术是适用的。这不仅是必要的，因为它帮助我们决定在每个给定的时间应用哪些技术。知道为什么当前的算法不能被应用，有利于设计新的算法鲁棒性，这样的问题。在本文中，我们报告了一项理论研究，该研究证明了基于广义本征的线性方程在哪里以及为什么不起作用。特别是，我们表明，当第i个特征向量的度量最大化和第一个i个特征向量的度量最小化之间的最小角度接近于零时，我们的结果不能保证是正确的。这种模型的几个属性也被提出。为了说明，我们集中在分类和特征提取的经典应用。我们还展示了如何使用我们的研究结果来设计更强大的算法。最后，我们讨论了我们的结果的更广泛的影响。
A fundamental problem in computer vision and pattern recognition is to determine where and, most importantly, why a given technique is applicable. This is not only necessary because it helps us decide which techniques to apply at each given time. Knowing why current algorithms cannot be applied facilitates the design of new algorithms robust to such problems. In this paper, we report on a theoretical study that demonstrates where and why generalized eigen-based linear equations do not work. In particular, we show that when the smallest angle between the ith eigenvector given by the metric to be maximized and the first i eigenvectors given by the metric to be minimized is close to zero, our results are not guaranteed to be correct. Several properties of such models are also presented. For illustration, we concentrate on the classical applications of classification and feature extraction. We also show how we can use our findings to design more robust algorithms. We conclude with a discussion on the broader impacts of our results.