论文标题
相关矩阵的新参数化
A New Parametrization of Correlation Matrices
论文作者
论文摘要
我们引入了相关矩阵的新型参数化。重新训练促进了通过不受限制的向量对相关和协方差矩阵的建模，在这种情况下，积极的确定性是天生的特性。该参数化可以看作是Fisther对更高维度的Z-转化的概括，并且具有广泛的潜在应用。提供了用于重建来自任何D维矢量的唯一N X N相关矩阵（带有D = N（N-1）/2）的算法，我们得出了其数值复杂性。
We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisther's Z-transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n x n correlation matrix from any d-dimensional vector (with d = n(n-1)/2) is provided, and we derive its numerical complexity.
