We study the convergence and the rate of convergence of a particular manifold-based learning algorithm: local tangent space alignment (LTSA) . The main technical tool is the perturbation analysis on the linear invariant subspace that corresponds to the solution of LTSA. We derive the upper bound for errors under the worst case for LTSA; it naturally leads to a convergence result. We then derive the rate of convergence for LTSA in a special case.