Error Metrics for Learning Reliable Manifolds from Streaming Data [chapter]

Frank Schoeneman, Suchismit Mahapatra, Varun Chandola, Nils Napp, Jaroslaw Zola
2017 Proceedings of the 2017 SIAM International Conference on Data Mining  
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.
more » ... 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.
doi:10.1137/1.9781611974973.84 dblp:conf/sdm/SchoenemanMCNZ17 fatcat:3yiuyy7yyfdane3htuocje2q5e