Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these correlations. Traditional work has focused on determining only the model order, i.e., the dimension of the correlated subspace, a number that depends on how the model-order problem is defined. Moreover, identifying the model order is often not enough to understand the relationship among the components in different data sets. We aim at solving the complete modelselection problem, i.e., determining which components are correlated across which data sets. We prove that the eigenvalues and eigenvectors of the normalized covariance matrix of the composite data vector, under certain conditions, completely characterize the underlying correlation structure. We use these results to solve the model-selection problem by employing bootstrap-based hypothesis testing.

中文翻译：

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确定跨多个数据集相关的子空间的维度和结构

由于组件之间存在大量可能的相关结构，因此检测跨多个数据集的共同或相关组件具有挑战性。更具挑战性的是确定这些相关性的精确结构。传统工作只关注确定模型阶数，即相关子空间的维数，这个数字取决于模型阶数问题的定义方式。此外，识别模型顺序通常不足以理解不同数据集中组件之间的关系。我们的目标是解决完整的模型选择问题，即确定哪些组件在哪些数据集上相关。我们证明复合数据向量归一化协方差矩阵的特征值和特征向量，在一定条件下，完全表征潜在的相关结构。我们使用这些结果通过采用基于引导的假设检验来解决模型选择问题。