Dual-Graph Global and Local Concept Factorization for Data Clustering.

Area of Science:

• Machine Learning
• Data Mining
• Dimensionality Reduction

Background:

• Nonnegative Matrix Factorization (NMF) is widely applied but struggles with complex data structures.
• Existing NMF variants fail to fully capture intricate global and local manifold properties of data.
• Extracting complex structural information from high-dimensional data remains a challenge.

Purpose of the Study:

• To propose a novel NMF method, Dual-Graph Global and Local Concept Factorization (DGLCF).
• To address limitations in describing complex inner global and local manifold structures.
• To enhance the extraction of complex structural information from data.

Main Methods:

• DGLCF integrates global and local data manifold structures.
• It incorporates the geometric structure of the feature manifold into concept factorization.
• Two local regularization terms preserve the inherent geometry of both data and features.

Main Results:

• The global manifold structure enhances model discriminative power.
• Local regularization terms preserve data and feature geometry.
• Convergence and iterative update rules for DGLCF are analyzed.

Conclusions:

• DGLCF offers a more comprehensive approach to NMF by considering manifold structures.
• The method demonstrates improved clustering performance compared to state-of-the-art algorithms.
• DGLCF effectively extracts complex structural information for enhanced data analysis.