论文标题
双重不变的两样本测试中的谎言组进行形状分析
Bi-invariant Two-Sample Tests in Lie Groups for Shape Analysis
论文作者
论文摘要
我们建议对Hotelling的$ t^2 $统计数据和Bhattacharayya距离进行概括，以获取数据以谎言组的值。衍生度量的一个关键特征是，即使对于不接受任何双重视度度量的流形的歧管，它们也与组结构兼容。该属性，例如，确保不取决于参考形状的分析，因此可以防止其任意选择引起的偏见。此外，概括与保证一致性的平坦矢量空间特殊情况的共同定义一致。我们采用置换测试设置，进一步获得了非参数的两样本测试程序，本身是双重不变且一致的。我们在小组测试中验证了我们的方法，揭示了轻度认知障碍和正常对照的个体之间海马形状的显着差异。
We propose generalizations of the Hotelling's $T^2$ statistic and the Bhattacharayya distance for data taking values in Lie groups. A key feature of the derived measures is that they are compatible with the group structure even for manifolds that do not admit any bi-invariant metric. This property, e.g., assures analysis that does not depend on the reference shape, thus, preventing bias due to arbitrary choices thereof. Furthermore, the generalizations agree with the common definitions for the special case of flat vector spaces guaranteeing consistency. Employing a permutation test setup, we further obtain nonparametric, two-sample testing procedures that themselves are bi-invariant and consistent. We validate our method in group tests revealing significant differences in hippocampal shape between individuals with mild cognitive impairment and normal controls.
