Most existing feature selection methods focus on ranking features based on an information criterion to select the best K features. However, several authors have found that the optimal feature combinations do not give the best classification performance [8],[7]. The reason for this is that although an individual feature may have limited relevance to a particular class, when taken in combination with other features it can be strongly relevant to the class. To overcome this problem, we draw on recent work on the graph embedding formulation of subspace learning where the projection matrix is constrained to be selection matrix [14] designed to select the optimal feature subset. In this paper, we derive a trace ratio (TR) criterion which selects features using a subset-level score rather than a feature-level score to perform feature selection. We apply the method to the challenging problem of gender determination using features delivered by principal geodesic analysis (PGA). A variational EM (VBEM) algorithm is used to learn a Gaussian mixture model on the selected feature subset and this is used to design a classifier for gender determination. We obtain a classification accuracy as high as 95% on 2.5D facial needle-maps, demonstrating the effectiveness of our feature selection method.