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Algebraic Clustering of Affine Subspaces.

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Low-Rank Matrix Completion Theory via Plücker Coordinates.

Manolis C Tsakiris

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |April 7, 2023
    PubMed
    Summary

    This study introduces novel patterns for low-rank matrix completion, addressing non-random data structures. It uses Plücker coordinates to enable unique matrix completions for various sizes and ranks.

    Area of Science:

    • Mathematics
    • Computer Science
    • Data Science

    Background:

    • Low-rank matrix completion theory often assumes random data sampling.
    • Understanding non-random patterns is crucial for practical applications.

    Purpose of the Study:

    • To identify specific data patterns enabling unique or finite low-rank matrix completions.
    • To extend matrix completion theory to non-random observation scenarios.

    Main Methods:

    • Novel formulation of low-rank matrix completion using Plücker coordinates.
    • Analysis of specific pattern families for guaranteed completion properties.

    Main Results:

    • Three families of patterns are identified that ensure unique or finite completions.

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  • The approach is valid for any matrix rank and size.

    • Conclusions:

    • Plücker coordinates offer a powerful framework for analyzing low-rank matrix completion with non-random patterns.
    • This work has implications for matrix and subspace learning with incomplete data.