  Spectral dimensionality reduction is frequently used to identify
low-dimensional structure in high-dimensional data. However, learning
manifolds, especially from the streaming data, is computationally and memory
expensive. In this paper, we argue that a stable manifold can be learned using
only a fraction of the stream, and the remaining stream can be mapped to the
manifold in a significantly less costly manner. Identifying the transition
point at which the manifold is stable is the key step. We present error metrics
that allow us to identify the transition point for a given stream by
quantitatively assessing the quality of a manifold learned using Isomap. We
further propose an efficient mapping algorithm, called S-Isomap, that can be
used to map new samples onto the stable manifold. We describe experiments on a
variety of data sets that show that the proposed approach is computationally
efficient without sacrificing accuracy.
