Target classification is a crucial component in automatic target recognition systems, yet one of the most difficult to develop due to the high level of variability in target signatures. Classification in low-dimensional manifold space is a promising approach since the manifold learning algorithm embeds the target chips into a low-dimensional space using key class features, and therefore is effective in the presence of noise and when the training and testing data exhibit variations due to differences in target range, aspect angles or other factors. This work develops an approach using support vector machine (SVM) classification in a nonlinear manifold space learned from real target imagery, outperforming classification in the image space. The proposed approach is very robust with respect to the dimensionality of the embedding as well as to the parameter settings, demonstrating the practicality of this approach for automatic target recognition applications.