A General Matrix Function Dimensionality Reduction Framework and Extension for Manifold Learning.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Dimensionality reduction techniques in manifold learning often suffer from the small-sample-size (SSS) problem.
• Existing methods for SSS have limitations in performance and applicability.

Purpose of the Study:

• To develop a unified framework for dimensionality reduction that addresses the SSS problem.
• To propose novel dimensionality reduction methods with improved pattern classification ability and reduced computational complexity.

Main Methods:

• A unified criterion function was constructed by summarizing existing dimensionality reduction methods.
• A general matrix function dimensionality reduction framework was proposed by combining the unified criterion with matrix functions.
• Specific functions (inverse hyperbolic tangent and linear) were used to derive new methods.

Main Results:

• The proposed matrix function framework is configurable, allowing for the derivation of new dimensionality reduction methods.
• New methods derived from the framework demonstrate superior pattern classification ability compared to existing SSS solutions.
• The novel methods exhibit reduced computational complexity.

Conclusions:

• The proposed general matrix function dimensionality reduction framework effectively addresses the SSS problem.
• The derived methods offer a promising solution for enhancing pattern classification in high-dimensional data with limited samples.
• Experimental validation on diverse datasets confirms the superiority of the new approaches.