Error analysis for transduction on manifold learning

Given samples of a finite-dimensional differentiable manifolds, but not know any of the manifold´s geometry or topology. Although there are various algorithms to implement manifold learning task, the crucial issue of dependence of generalization error on the number examples is still very poorly understood. In this paper, we consider a transduction manifold learning algorithm and give some error analysis for it. The convergence rates of the regularization algorithm, related to structural invariants of the manifold, are established.