论文标题
条件号的有效数值方法约束协方差矩阵近似
An efficient numerical method for condition number constrained covariance matrix approximation
论文作者
论文摘要
在高维数据设置中，样品协方差矩阵是单数的。为了在高维数据设置中对样品协方差矩阵进行数值稳定且积极的确定修改，在本文中，我们考虑条件数限制了协方差矩阵近似问题，并提出了相对于Frobenius Norm的明确解决方案。条件数的约束保证了同时近似形式的数值稳定性和正定性。通过在高维数据设置中利用数据矩阵的特殊结构，我们还基于有效的矩阵分解技术提出了一些新算法。还进行了数值实验以显示所提出算法的计算效率。
In the high-dimensional data setting, the sample covariance matrix is singular. In order to get a numerically stable and positive definite modification of the sample covariance matrix in the high-dimensional data setting, in this paper we consider the condition number constrained covariance matrix approximation problem and present its explicit solution with respect to the Frobenius norm. The condition number constraint guarantees the numerical stability and positive definiteness of the approximation form simultaneously. By exploiting the special structure of the data matrix in the high-dimensional data setting, we also propose some new algorithms based on efficient matrix decomposition techniques. Numerical experiments are also given to show the computational efficiency of the proposed algorithms.
