2016/11/30 by Frank Schoeneman, Suchismit Mahapatra, Varun Chandola +3
Computer Science · Mathematics · #Algorithm #Artificial intelligence #Combinatorics #Computer science #Curse of dimensionality #Data Stream Mining Techniques #Dimensionality reduction #Face and Expression Recognition #Geometry #Isomap #Key (lock) #Manifold (fluid mechanics) #Manifold alignment #Mathematics #Neural Networks and Applications #Nonlinear dimensionality reduction #Pattern recognition (psychology) #Point (geometry) #Topology (electrical circuits) #stat.ML
paper · pdf · doi:10.1137/1.9781611974973.84
arxiv created 2017/01/11 · openalex publication_date 2017/06/09 · arxiv updated 2017/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.