确定多个数据集相关子空间的维数和结构
Determining the Dimension and Structure of the Subspace Correlated Across Multiple Data Sets
摘要：
检测跨多个数据集的共同或相关的分量是具有挑战性的，因为分量之间存在大量可能的相关结构。更大的挑战是确定这些相关性的精确结构。传统的工作集中在仅确定模型阶数，即，相关子空间的维度，这个数字取决于模型阶次问题的定义方式。而且，识别模型阶数往往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。我们证明了复合数据向量的归一化协方差矩阵的特征值和特征向量，在一定条件下，完全刻画了潜在的相关结构。我们使用这些结果来解决模型选择问题，采用基于引导的假设检验。
英文摘要：
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.
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