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O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression
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Robust Supervised and Semisupervised Least Squares Regression Using ℓ2,p-Norm Minimization.

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    Robust Least Squares Regression (RSLSR) enhances statistical analysis by mitigating noise and outliers in corrupted datasets. This method improves discriminative ability for supervised and semisupervised learning tasks.

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    Area of Science:

    • Statistics
    • Machine Learning
    • Data Science

    Background:

    • Least Squares Regression (LSR) is a foundational statistical method.
    • LSR's performance degrades significantly with noisy or corrupted data.
    • Unavoidable noise impacts error construction in standard LSR.

    Purpose of the Study:

    • To develop a robust supervised LSR (RSLSR) method.
    • To eliminate the effects of noise and outliers in regression analysis.
    • To extend the robust approach to semisupervised learning (RSSLSR).

    Main Methods:

    • Proposed RSLSR utilizes an l2,p-norm loss function instead of square loss.
    • Introduced probability weights to identify and downweight outliers.
    • Developed an iterative algorithm to solve the concave optimization problem.
    • Extended RSLSR to a robust semisupervised LSR (RSSLSR) framework.

    Main Results:

    • RSLSR effectively eliminates the influence of noise and outliers.
    • The probability weighting scheme clearly distinguishes normal samples from outliers.
    • The iterative algorithm efficiently solves the proposed robust regression problem.
    • RSSLSR demonstrated effectiveness in utilizing limited labeled data.

    Conclusions:

    • The proposed RSLSR and RSSLSR methods exhibit significant robustness against data corruption.
    • These novel approaches maintain strong discriminative ability even with noisy datasets.
    • The methods offer improved performance in supervised and semisupervised learning scenarios with corrupted data.