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Armin Eftekhari, Raphael A Hauser, Andreas Grammenos

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    Memory-limited Online Subspace Estimation Scheme (MOSES) estimates principal components and reduces dimension for streaming data. This computationally inexpensive method offers a theoretically-sound variant of incremental SVD, outperforming existing techniques.

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    Area of Science:

    • Machine Learning
    • Data Science
    • Signal Processing

    Background:

    • Streaming data analysis presents challenges due to limited storage and processing time.
    • Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) are crucial for dimension reduction and feature extraction.
    • Existing incremental SVD (iSVD) methods lack comprehensive theoretical grounding.

    Purpose of the Study:

    • Introduce the Memory-limited Online Subspace Estimation Scheme (MOSES) for online principal component estimation and dimension reduction.
    • Provide a theoretically-sound variant of iSVD.
    • Interpret MOSES as an approximate solver for non-convex optimization problems.

    Main Methods:

    • MOSES generalizes incremental SVD to handle thin blocks of data.
    • The method provides a running estimate of leading principal components.
    • MOSES is interpreted as an approximate solver for non-convex optimization.

    Main Results:

    • MOSES consistently surpasses the state-of-the-art in numerical experiments.
    • The scheme is effective on both synthetic and real-world datasets.
    • MOSES demonstrates computational efficiency.

    Conclusions:

    • MOSES offers a computationally inexpensive and theoretically sound approach for streaming data analysis.
    • The method effectively performs online subspace estimation and dimension reduction.
    • MOSES represents a significant advancement over existing iSVD variants.