In this report we address a subtle but important limitation found in the literature for Estimation of Distribution Algorithms (EDAs): symmetric initializations of the EDAs around the optimal solution. We focus our study on the performance of certain EDAs (EMNA-global and PBIL-C) that are asymmetrically initialized far from the optimum. We show and explain the failure of these EDAs under these conditions. These observations lead us to develop a new EDA based on an eigenspace analysis, which we denote by EEDA (Eigenspace EDA). We conclude by analyzing this new EDA and by showing its strengths when compared with EMNA-global and PBIL-C when the optimal solution is unknown.