Semi-Supervised Graph Regularized Deep NMF With Bi-Orthogonal Constraints for Data Representation.

Area of Science:

• Machine Learning
• Data Mining
• Dimensionality Reduction

Background:

• Non-negative matrix factorization (NMF) excels at learning local data information.
• Semi-supervised NMF effectively utilizes limited labeled data for learning.
• Single-layer clustering struggles with complex hierarchical information in NMF's low-dimensional representations.

Purpose of the Study:

• To propose a novel deep learning method, semi-supervised graph regularized deep NMF with bi-orthogonal constraints (SGDNMF).
• To address the limitations of single-layer clustering in extracting complex information from NMF representations.
• To improve dimensionality reduction and clustering performance using limited labeled data.

Main Methods:

• Developed SGDNMF, a deep learning architecture incorporating graph regularization and bi-orthogonal constraints.
• Introduced bi-orthogonal constraints on factor matrices for solution uniqueness and performance enhancement.
• Incorporated dual-hypergraph Laplacian regularization to preserve data's intrinsic geometric structure and high-order relationships.

Main Results:

• SGDNMF learns representations from hidden layers suitable for clustering, capturing varied attributes.
• Bi-orthogonal constraints enhance clustering performance and ensure a unique solution.
• Dual-hypergraph regularization effectively retains the original data's geometric structure.
• Empirical experiments demonstrated state-of-the-art performance against six other algorithms on four datasets.

Conclusions:

• SGDNMF offers a powerful approach for dimensionality reduction and clustering, especially with limited labeled data.
• The proposed deep learning framework effectively extracts complex hierarchical and structural information.
• SGDNMF significantly outperforms existing methods in various data analysis tasks.