Fig. 10

Boxplot showing comparison of performances of predicted responses based on one-dimensional, two-dimensional and three-dimensional raw-stress embeddings. The manifold is \({\mathcal {M}}=\psi ([0,1])\) where \(\psi (t)=\frac{1}{\sqrt{2}}(cos(t),sin(t),cos(t),sin(t))\), the size of the graph is \(n=750\), and the regression model is \(y_i=\alpha +\beta t_i +\epsilon _i\) with \(\epsilon _i \sim ^{iid} N(0,10^{-4})\), \(i \in [s]\), \(s=5\), \(\alpha =2.0\) and \(\beta =5.0\). The red box corresponds to the predicted response obtained from the true regressors. The orange box corresponds to the predicted response obtained from one-dimesnional embeddings. The green box corresponds to the predicted response obtained from the two-dimensional embeddings. The blue box corresponds to the predicted response obtained from the three-dimensional embeddings