Robust (semi) nonnegative graph embedding.

Area of Science:

• Machine Learning
• Computer Vision
• Pattern Recognition

Background:

• Nonnegative matrix factorization (NMF) is widely used but sensitive to noisy data.
• Nonnegative graph embedding (NGE) extends NMF but faces challenges with unreliable graphs and labels.
• Real-world data often contains noise, impacting the performance of existing NGE algorithms.

Purpose of the Study:

• To develop robust frameworks for nonnegative graph embedding that can handle noisy data.
• To extend NGE to handle data that is not strictly nonnegative.
• To provide a general formulation for robust graph embedding methods.

Main Methods:

• Proposed Robust Nonnegative Graph Embedding (RNGE) framework utilizing joint sparsity for noise resilience.
• Developed Robust Semininonnegative Graph Embedding (RsNGE) framework, relaxing nonnegativity constraints on the base matrix.
• Implemented efficient multiplicative updating solutions for RNGE and RsNGE with convergence analysis.

Main Results:

• RNGE and RsNGE demonstrated robustness against noise in data, graphs, and labels.
• RsNGE showed broader applicability to non-nonnegative data and enhanced discriminative power.
• Experimental results on four real-world datasets confirmed the effectiveness of the proposed methods.

Conclusions:

• RNGE and RsNGE offer general and effective solutions for robust graph embedding.
• The proposed frameworks significantly improve upon existing NMF and NGE variants in noisy conditions.
• These methods provide a valuable extension for various unsupervised and supervised learning tasks.