In a large-scale automatic fingerprint identification system (AFIS), fingerprint classification is an essential indexing step to reduce the search time in a large database for accurate matching. Fingerprint classification is still a challenging machine learning problem due to large intra-class and small inter-class variability. Nonlinear elastic deformation is one of the main sources of intra-class variability, which occurs due to the non-uniform pressure applied during fingerprint acquisition and the elastic nature of the fingerprint itself. This paper proposes a novel approach to fingerprint classification based on a scattering wavelet network to extract translation and small deformation invariant local features. The resulting sparse invariant feature vectors are used as input to a simple generative PCA affine classifier for the classification. The experiments evaluated with two different protocols on a benchmark NIST SD-4 database show the effectiveness and robustness of the proposed fingerprint classification algorithm in terms of classification accuracy.