An efficient numerical method for condition number constrained covariance matrix approximation
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In high-dimensional data setting, the sample covariance matrix is singular. In order to get a numerical stable and positive definite modification of the sample covariance matrix in the high-dimensional data setting, we in this paper consider the condition number constrained covariance matrix approximation problem and present its explicit solution with respect to 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 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.
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