Fig. 1

Impact of changes in the data distribution on streaming NLDR. In the top panel, the true data lies on a 2D manifold (top-left) and the observed data is in \({\mathbb {R}}^3\) obtained by using the swiss-roll transformation of the 2D data (top-middle). The streaming algorithm (S-Isomap [5]) uses a batch of samples from a 2D Gaussian (black), and maps streaming points sampled from a uniform distribution (gray). The streaming algorithm performs well on mapping the batch points to \({\mathbb {R}}^2\) but fails on the streaming points that “drift” away from the batch (top-right). In the bottom panel, the streaming algorithm (S-Isomap++ [6]) uses a batch of samples from three 2D Gaussians (black). The stream points are sampled from the three Gaussians and a new Gaussian (gray). The streaming algorithm performs well on mapping the batch points to \({\mathbb {R}}^2\) but fails on the streaming points that are “shifted” from the batch (bottom-right). Both streaming algorithms are discussed in Sect. “Problem statement and preliminaries”