论文标题
procrustes分析高维数据
Procrustes analysis for high-dimensional data
论文作者
论文摘要
基于Procrustes的扰动模型（Goodall，1991）允许通过相似性转换矩阵之间的Frobenius距离最小化。但是，它遭受了不可识别性，对转化矩阵的关键解释以及在高维数据中的不适用性。我们提供了扰动模型的扩展，该模型集中在高维数据框架上，称为Promises（Procrustes Von Mises-Fisher）模型。通过对正交矩阵参数（即von mises-fisher分布）施加适当的先验分布来解决不适合和解释性问题，该分布是共轭的，从而导致快速估计过程。此外，我们为高维框架提供了有效的承诺模型，该模型在神经影像学上有用，在该神经影像学上，该问题的具有三个以上的维度。我们发现功能磁共振成像（fMRI）连接分析有了很大的改善，因为承诺模型允许将拓扑脑信息纳入对齐过程中。
The Procrustes-based perturbation model (Goodall, 1991) allows minimization of the Frobenius distance between matrices by similarity transformation. However, it suffers from non-identifiability, critical interpretation of the transformed matrices, and inapplicability in high-dimensional data. We provide an extension of the perturbation model focused on the high-dimensional data framework, called the ProMises (Procrustes von Mises-Fisher) model. The ill-posed and interpretability problems are solved by imposing a proper prior distribution for the orthogonal matrix parameter (i.e., the von Mises-Fisher distribution) which is a conjugate prior, resulting in a fast estimation process. Furthermore, we present the Efficient ProMises model for the high-dimensional framework, useful in neuroimaging, where the problem has much more than three dimensions. We found a great improvement in functional magnetic resonance imaging (fMRI) connectivity analysis because the ProMises model permits incorporation of topological brain information in the alignment's estimation process.
