This paper presents a method named "orthogonal projection reduction by affinity", or OPRA-faces, for face recognition. As its name indicates, the method consists of an (explicit) orthogonal mapping from the data space to the reduced space. In addition, the method attempts to preserve the local geometry, i.e., the affinity of the points in a geometric representation of the data. The method starts by computing an affinity mapping W, of the data, which optimally expresses each point as a convex combination of a few nearest neighbors. This mapping can be viewed as an optimal representation of the intrinsic neighborhood geometries and is computed in a manner that is identical with the method of locally linear embedding (LLE). Next, and in contrast with LLE, the proposed scheme computes an explicit linear mapping between the high dimensional samples and their corresponding images in the reduced space, which is designed to preserve this affinity representation W. OPRA-faces shares some properties with Laplacianfaces, a recently proposed technique for face recognition, which computes the linear approximation of the Laplace-Beltrami operator on the image manifold. Laplacianfaces aims at preserving locality but does not explicitly consider the intrinsic geometries of the neighborhoods as does OPRA. As a result of the preservation of the affinity mapping W, OPRA will tend to produce a linear subspace which captures the essential geometric characteristics of the dataset. This feature, which appears to be crucial in representing images, makes the method very effective as a tool for face recognition. OPRA is tested on standard face databases and its effectiveness is compared with that of Laplacianfaces, eigenfaces and Fisherfaces. The experimental results indicate that the proposed technique produces results that are sharply superior to the other methods, at a comparable or lower cost.