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Streaming PCA and Subspace Tracking: The Missing Data Case.

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Summary
This summary is machine-generated.

This survey reviews streaming Principal Component Analysis (PCA) and subspace tracking algorithms for time-varying data with missing information. It highlights methods for efficient processing under memory and computational constraints, crucial for big data applications.

Keywords:
ODE analysismissing datastreaming PCAsubspace and low-rank modelssubspace tracking

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Area of Science:

  • Signal Processing and Machine Learning
  • Data Science and Big Data Analytics

Background:

  • Modern applications require processing streaming, time-varying data with limited resources.
  • Missing data is a common challenge, where only a fraction of attributes are observed.
  • These constraints complicate traditional streaming Principal Component Analysis (PCA) and subspace tracking.

Purpose of the Study:

  • To survey classical and recent algorithms for streaming PCA and subspace tracking under memory and computational constraints.
  • To address the specific challenges posed by missing data in these streaming scenarios.
  • To provide a comprehensive overview for practitioners in big data regimes.

Main Methods:

  • Review of various classical and recent algorithms for streaming PCA and subspace tracking.
  • Analysis of algebraic and geometric perspectives for understanding these algorithms.
  • Examination of necessary adjustments for handling missing data.
  • Review of asymptotic and non-asymptotic convergence guarantees.

Main Results:

  • Identification of algorithms with low computational and memory complexities suitable for big data.
  • Demonstration of how streaming PCA and subspace tracking need careful adaptation for missing data.
  • Benchmarking of competitive algorithms' performance with missing data in various system conditions.

Conclusions:

  • Streaming PCA and subspace tracking are essential but require specialized algorithms for missing data.
  • The reviewed methods offer efficient solutions for real-time processing of incomplete streaming data.
  • Understanding algorithmic adjustments and convergence is key for reliable inference in signal processing and machine learning.