Mahalanobis Distance on Extended Grassmann Manifolds for Variational Pattern Analysis
Mahalanobis Distance on Extended Grassmann Manifolds for Variational Pattern Analysis
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DOI：
10.1109/tnnls.2014.2301178
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发表时间：
2014-01
影响因子：
10.4
通讯作者：
Y. Washizawa;S. Hotta
中科院分区：
文献类型：
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作者：
Y. Washizawa;S. Hotta
在模式分类问题中，模式变化通常被建模为线性流形或低维子空间。传统方法使用这样的模型并定义相似性或不相似性的度量。然而，这些相似性度量是确定性的，并且不考虑线性流形或低维子空间的分布。因此，如果分布不是同位素的，距离测量是不可靠的，以及在欧几里得空间中基于向量的距离测量。我们以前系统化的表示变分模式使用格拉斯曼流形和引入马氏距离格拉斯曼流形作为一个自然的扩展欧几里德的情况。本文给出了两种在广义Grassmann流形上灵活推广马氏距离的方法。这些方法可以用来衡量模式（不）相似性的基础上的模式结构。对所提出方法的性能进行的实验评估表明，它们具有较低的错误分类率。
In pattern classification problems, pattern variations are often modeled as a linear manifold or a low-dimensional subspace. Conventional methods use such models and define a measure of similarity or dissimilarity. However, these similarity measures are deterministic and do not take into account the distribution of linear manifolds or low-dimensional subspaces. Therefore, if the distribution is not isotopic, the distance measurements are not reliable, as well as vector-based distance measurement in the Euclidean space. We previously systematized the representations of variational patterns using the Grassmann manifold and introduce the Mahalanobis distance to the Grassmann manifold as a natural extension of Euclidean case. In this paper, we present two methods that flexibly extend the Mahalanobis distance on the extended Grassmann manifolds. These methods can be used to measure pattern (dis)similarity on the basis of the pattern structure. Experimental evaluation of the performance of the proposed methods demonstrated that they exhibit a lower error classification rate.