Fig. 3

Plot showing consistency of the predicted responses based on raw-stress embeddings on unknown manifold. The arclength parameterized manifold is taken to be \(\psi ([0,1])\) where \(\psi (t)=(t/2,t/2,t/2,t/2)\). The sample mean of the squared difference between the predicted response \({\hat{y}}_{sub}\) based on raw-stress embeddings and predicted response \({\hat{y}}_{true}\) based on the true regressors is plotted against the total number of nodes in the graph. The substitute predicted response \({\hat{y}}_{sub}\) performs significantly worse than \({\hat{y}}_{true}\) for moderate number of auxiliary nodes (\(n \le 1000\)). However, as the number of auxiliary nodes increases further, the mean squared difference between \({\hat{y}}_{true}\) and \({\hat{y}}_{sub}\) goes to zero