Assessing loan eligibility through correlation matrix approximation for credit estimation

The correlation problem is a central focus in statistical analysis and data science, as it aims to quantify the relationships between variables. This paper explores efficient methods for approximating correlation matrices to assess loan eligibility for bank customers. We propose a novel algorithm that utilizes advanced optimization techniques to minimize the difference between actual noisy matrices and approximated correlation matrices. The algorithm is designed for large-scale correlation matrices, such as those with thousands of variables, and employs the interior point primal-dual path-following method. We provide a comprehensive comparative analysis of our methods and the commonly used modified alternating projection method, evaluating their efficacy and computational efficiency based on numerical results.