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Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size LEfSe in Microbiome Data
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Efficient Linear Discriminant Analysis Based on Randomized Low-Rank Approaches.

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    This study introduces efficient methods for linear discriminant analysis (LDA) to overcome small sample size (SSS) issues and reduce computational load. New algorithms for trace ratio LDA and ratio trace LDA significantly speed up calculations while maintaining classification accuracy.

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    Area of Science:

    • Machine Learning
    • Pattern Recognition
    • Data Science

    Background:

    • Linear Discriminant Analysis (LDA) is crucial for classification but struggles with small sample size (SSS) and high computational costs.
    • Existing solutions for SSS in ratio trace LDA and trace ratio LDA (TRLDA) often involve computationally intensive matrix operations.
    • Iterative processing of large matrices in TRLDA leads to cumbersome computations.

    Purpose of the Study:

    • To develop computationally efficient methods for LDA that address the SSS problem.
    • To reduce the computational complexity of TRLDA and ratio trace LDA.
    • To maintain or improve classification accuracy while significantly decreasing computation time.

    Main Methods:

    • Proposed a novel random method for TRLDA to extract orthogonal bases, enabling computations on smaller matrices.
    • Introduced a fast generalized singular value decomposition (GSVD) algorithm for ratio trace LDA.
    • Integrated the fast GSVD algorithm into ratio trace LDA, creating the FGSVD-LDA method.

    Main Results:

    • The novel random method for TRLDA significantly reduces computational time without sacrificing accuracy.
    • The fast GSVD algorithm for ratio trace LDA outperforms MATLAB's built-in GSVD in speed.
    • FGSVD-LDA demonstrates low computational complexity and effective classification performance.
    • Both proposed methods achieve successful dimensionality reduction and satisfactory classification accuracy.

    Conclusions:

    • The developed random method and fast GSVD algorithm offer efficient solutions for LDA under SSS conditions.
    • These advancements make LDA more practical for applications with limited data and computational resources.
    • The proposed techniques effectively balance computational efficiency with classification performance.