IEEE Trans Neural Netw Learn Syst. 2014 Nov;25(11):1980-90. doi: 10.1109/TNNLS.2014.2301178.
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.
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。传统方法使用这些模型并定义相似性或相异性的度量。然而，这些相似性度量是确定性的，并且没有考虑到线性流形或低维子空间的分布。因此，如果分布不是等变的，那么距离测量就不可靠，就像欧几里得空间中的基于向量的距离测量一样。我们之前使用 Grassmann 流形系统地表示变分模式，并将 Mahalanobis 距离引入 Grassmann 流形，作为欧几里得情况的自然延伸。在本文中，我们提出了两种灵活扩展扩展 Grassmann 流形上的 Mahalanobis 距离的方法。这些方法可用于根据模式结构来测量模式（不）相似性。对所提出方法性能的实验评估表明，它们表现出较低的错误分类率。
