Streaming PCA and Subspace Tracking: The Missing Data Case

Laura Balzano

doi:10.1109/JPROC.2018.2847041

Streaming PCA and Subspace Tracking: The Missing Data Case

2018-08-01

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DOI：10.1109/JPROC.2018.2847041

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For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a timely manner for decision making. This often is coupled with the missing data problem, such that only a small fraction of data attributes are observed. These complications impose significant, and unconventional, constraints on the problem of streaming principal component analysis (PCA) and subspace tracking, which is an essential building block for many inference tasks in signal processing and machine learning. This survey article reviews a variety of classical and recent algorithms for solving this problem with low computational and memory complexities, particularly those applicable in the big data regime with missing data. We illustrate that streaming PCA and subspace tracking algorithms can be understood through algebraic and geometric perspectives, and they need to be adjusted carefully to handle missing data. Both asymptotic and nonasymptotic convergence guarantees are reviewed. Finally, we benchmark the performance of several competitive algorithms in the presence ofmissing data for both well-conditioned and ill-conditioned systems.

Keywords:

Missing data

ordinary differential equation (ODE) analysis

subspace tracking

streaming principal component analysis (PCA)

subspace and low-rank models

Streaming PCA and Subspace Tracking: The Missing Data Case

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