Matrix perturbation analysis of local tangent space alignment

We consider the performance of Local Tangent Space Alignment (Zhang & Zha [1]), one of several manifold learning algorithms, which have been proposed as a dimension reduction method. Matrix perturbation theory is applied to obtain a worst-case upper bound on the angle between the computed linear invariant subspace and the linear invariant subspace that is associated with the embedded intrinsic parametrization. Our result is the first performance bound that has been derived.