In this work, we propose an efficient two-step algorithm to solve the joint problem of correlation detection and permutation recovery between two Gaussian databases. Correlation detection is a hypothesis testing problem. Under the null hypothesis, the databases are independent, and under the alternative hypothesis, they are correlated under unknown row permutations. Creating relatively tight bounds on the type I and type II error probabilities, the detectors analyzed outperform the recently proposed detectors for at least some specific parameter choices. indicates Since the proposed detector relies on the statistic being the sum of the dependent index random variables, we develop a new graph-theoretical method to bound the k-th order moments in order to bound the Type I probability of error. To do. of such statistics. If the database is found to be correlated, the algorithm also outputs an estimate of the underlying row permutation. By comparing with the known inverse result of this problem, we prove that the alignment error probability converges to zero under the lowest possible correlation coefficient asymptotically.
