Robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization.

Area of Science:

• Machine Learning
• Data Mining
• Matrix Factorization

Background:

• Non-negative matrix factorization (NMF) is a common technique.
• Non-negative matrix tri-factorization (NMTF) offers more flexibility but is sensitive to noise and outliers.
• Existing methods often neglect geometric information within data manifolds.

Purpose of the Study:

• To introduce a novel robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization (RCHNMTF) algorithm.
• To address the limitations of standard NMTF, particularly its sensitivity to outliers and failure to capture geometric structures.
• To enhance data representation and clustering performance.

Main Methods:

• Utilizing a robust capped norm to mitigate the impact of extreme outliers.
• Incorporating dual hyper-graph regularization to leverage intrinsic geometric information from feature and sample manifolds.
• Applying orthogonality constraints for unique data representation and improved clustering.

Main Results:

• The proposed RCHNMTF method demonstrates significant robustness against outliers.
• The algorithm effectively captures geometric information from both feature and sample manifolds.
• Experimental results on seven datasets confirm the superiority of RCHNMTF over existing methods.

Conclusions:

• RCHNMTF offers a robust and effective approach for non-negative matrix tri-factorization.
• The method enhances data analysis by handling outliers and exploiting geometric structures.
• RCHNMTF shows superior performance in clustering and data representation tasks.