The article is devoted to experimental research of the face recognition method based on an elastic graph matching. The face images are transforming to the face image graphs that contain both a geometric and local image features. As a local image features in the graph nodes is used a convolutions of face image with a family of complex Gabor kernels that have different scales and orientations. We assume that such face feature space has some smaller dimension subspace in which total recognition error decreases. To obtain basis looked for we research methods based on the Fisher's linear discriminant. The obtained results show that total recognition error can be decreases significantly when the dimension of space reduces more then 2 times.