MOSES: A Streaming Algorithm for Linear Dimensionality Reduction

TL;DR

MOSES is a streaming algorithm that efficiently estimates principal components and reduces data dimensionality in real-time, with theoretical guarantees and superior empirical performance over existing methods.

Contribution

It generalizes incremental SVD to handle data blocks, providing the first theoretically sound variant with comprehensive analysis and practical effectiveness.

Findings

MOSES outperforms existing methods in numerical experiments.

It provides a theoretically justified approach to streaming PCA.

MOSES is computationally inexpensive and scalable.

Abstract

This paper introduces Memory-limited Online Subspace Estimation Scheme (MOSES) for both estimating the principal components of streaming data and reducing its dimension. More specifically, in various applications such as sensor networks, the data vectors are presented sequentially to a user who has limited storage and processing time available. Applied to such problems, MOSES can provide a running estimate of leading principal components of the data that has arrived so far and also reduce its dimension. MOSES generalises the popular incremental Singular Vale Decomposition (iSVD) to handle thin blocks of data, rather than just vectors. This minor generalisation in part allows us to complement MOSES with a comprehensive statistical analysis, thus providing the first theoretically-sound variant of iSVD, which has been lacking despite the empirical success of this method. This generalisation also enables us to concretely interpret MOSES as an approximate solver for the underlying non-convex optimisation program. We find that MOSES consistently surpasses the state of the art in our numerical experiments with both synthetic and real-world datasets, while being computationally inexpensive.