Laplacian Welsch Regularization for Robust Semisupervised Learning.

Area of Science:

• Machine Learning
• Artificial Intelligence
• Data Science

Background:

• Semisupervised learning (SSL) is crucial when labeled data is scarce but unlabeled data is abundant.
• Existing SSL methods are vulnerable to outliers in limited labeled data, compromising classifier performance.
• Robustness to outliers is a key challenge in practical SSL applications.

Purpose of the Study:

• To propose a novel SSL algorithm, Laplacian Welsch regularization (LapWR), to improve robustness against outliers.
• To introduce a bounded, smooth, and nonconvex Welsch loss function to mitigate outlier effects.
• To provide theoretical guarantees and demonstrate empirical superiority of the proposed method.

Main Methods:

• Laplacian Welsch regularization (LapWR) incorporating a Welsch loss function.
• Iterative half-quadratic (HQ) optimization to handle model nonconvexity.
• Nyström method for computational efficiency on large datasets.
• Rademacher complexity analysis for theoretical generalization bounds.

Main Results:

• LapWR demonstrates significant robustness to outliers in labeled data.
• The proposed algorithm consistently achieves top-level performance across benchmark and real-world datasets.
• The Welsch loss effectively suppresses the adverse impact of outliers.
• The accelerated model maintains performance while reducing computational complexity.

Conclusions:

• Laplacian Welsch regularization (LapWR) offers a robust and effective solution for semisupervised learning with outlier-corrupted labeled data.
• The method provides theoretical guarantees and strong empirical evidence of its effectiveness.
• LapWR represents a significant advancement in developing reliable SSL algorithms for practical applications.