A rotation based regularization method for semi-supervised learning.

Area of Science:

• Computational geometry
• Machine learning
• Data science

Background:

• Manifold learning aims to preserve intrinsic data geometry by identifying optimal local neighborhoods.
• Nonlinear manifold properties pose challenges in accurately defining these neighborhoods, potentially leading to errors.
• Sub-optimal neighborhood selection can result in incorrect data representations and inferences.

Purpose of the Study:

• To propose a rotation-based affinity metric for accurate graph Laplacian approximation in manifold learning.
• To address the challenge of finding optimal local neighborhoods on nonlinear manifolds.
• To improve the accuracy of nonlinear dimensionality reduction and subsequent data analysis.

Main Methods:

• Developed a rotation-based affinity metric leveraging aligned tangent spaces of observations.
• Approximated the correct affinity between data points within an optimal neighborhood.
• Applied the method to both synthetic and real-world datasets for evaluation.

Main Results:

• The proposed method demonstrated superior performance over existing nonlinear dimensionality reduction techniques on synthetic datasets.
• Experiments on real-world datasets, including COVID-19 data, showed increased classification accuracy.
• The approach effectively enhances Laplacian regularization for improved data representation.

Conclusions:

• The rotation-based affinity metric offers a robust solution for accurate graph Laplacian approximation in manifold learning.
• This method improves the fidelity of low-dimensional representations and enhances classification performance.
• The technique shows significant potential for applications in various scientific and medical data analyses.