Abstract: A very important aspect in manifold learning is represented by automatic estimation of the intrinsic dimensionality. Unfortunately, this problem has received few attention in the literature of manifold learning. In this paper, we argue that feature selection paradigm can be used to the problem of automatic dimensionality estimation. Besides this, it also leads to improved recognition rates. Our approach for optimal feature selection is based on a Genetic Algorithm. As a case study for manifold learning, we have considered Laplacian Eigenmaps (LE) and Locally Linear Embedding (LLE). The effectiveness of the proposed framework was tested on the face recognition problem. Extensive experiments carried out on ORL, UMIST, Yale, and Extended Yale face data sets confirmed our hypothesis.