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    This study introduces two novel unsupervised feature selection methods, FOG-R and FOG-C, which construct flexible optimal graphs for adaptive similarity matrices. These methods outperform existing algorithms in comparative experiments.

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    Area of Science:

    • Machine Learning
    • Data Mining
    • Computer Science

    Background:

    • Constructing reliable similarity matrices is crucial for unsupervised feature selection based on spectral analysis.
    • Existing methods struggle with linear low-dimensional projections, hindering similarity matrix reliability.

    Purpose of the Study:

    • To propose novel unsupervised feature selection methods that overcome limitations in similarity matrix construction.
    • To introduce flexible optimal graph learning integrated with feature selection for adaptive similarity matrices.

    Main Methods:

    • Developed unsupervised feature selection with flexible optimal graph and l2,1-norm regularization (FOG-R).
    • Proposed unsupervised feature selection with flexible optimal graph and l2,0-norm constraint (FOG-C) to avoid parameter tuning.
    • Designed iterative algorithms with convergence proofs for both FOG-R and FOG-C.

    Main Results:

    • FOG-R learns a flexible optimal graph, unifying graph learning and feature selection for adaptive similarity.
    • FOG-C avoids additional parameter tuning and achieves a sparser projection matrix.
    • Both FOG-R and FOG-C demonstrated superior performance against nine state-of-the-art methods on 12 public datasets.

    Conclusions:

    • FOG-R and FOG-C offer effective solutions for unsupervised feature selection by improving similarity matrix construction.
    • The proposed methods provide robust and efficient alternatives to existing techniques.
    • Flexible optimal graph learning is a promising direction for enhancing unsupervised feature selection.