Portfolio optimization relies on an accurate covariance matrix estimation; however, empirical matrices are often noisy and can lead to suboptimal asset allocations. Traditional cleaning methods are based on Random Matrix Theory (RMT) and rely on the assumption of rotational invariance. While mathematically convenient, they completely neglects the underlying structure of financial markets: they focuses on cleaning the eigenvalues of the covariance matrix but ignores the eigenvectors. However, euristic methods have shown that hierarchical structures exist in financial markets, and that they can be used to clean covariance matrices. This thesis explores the possibility of moving beyond the rotational invariance assumption. We proposes to use a custom Graph Neural Network (GNN) to learn the underlying hierarchy of financial markets from noisy data and use it to procure a cleaner covariance matrix.