Local Regression and Global Information-Embedded Dimension Reduction.

Area of Science:

• Machine Learning
• Data Science
• Computational Statistics

Background:

• Unsupervised dimension reduction methods rely on local and global data structures.
• Existing techniques often fail to accurately model local geometry due to high dimensionality and noise.
• Inaccurate local structure modeling degrades overall performance.

Purpose of the Study:

• To propose a novel unsupervised dimension reduction method.
• To effectively address issues of high dimensionality and noise in local data modeling.
• To preserve both local and global data information for enhanced performance.

Main Methods:

• Local data denoising by preserving principal components.
• Regularization of the local modeling function to handle ill-posed problems.
• Linear regression for robust local geometrical structure capture.
• Dual criteria for simultaneous local and global information modeling.

Main Results:

• The proposed method effectively denoises local data while preserving principal components.
• Regularization successfully addresses the ill-posed nature of high-dimensional local modeling.
• Linear regression proves to be a parameter-insensitive approach for local structure.
• Simultaneous modeling of local and global information enhances dimension reduction effectiveness.
• Theoretical analysis confirms relationships with classical methods.
• Experimental validation on diverse datasets demonstrates superior performance.

Conclusions:

• The novel method offers a robust solution for unsupervised dimension reduction.
• It effectively handles noisy and high-dimensional data by improving local structure learning.
• Preservation of both local and global data properties leads to superior results in dimension reduction tasks.