Robust Matrix Factorization With Spectral Embedding.

Area of Science:

• Machine Learning
• Data Mining
• Computer Science

Background:

• Nonnegative matrix factorization (NMF) and spectral clustering are popular but have limitations.
• NMF struggles with nonlinear data, while spectral clustering requires postprocessing.
• Existing methods are sensitive to outliers and often require parameter tuning.

Purpose of the Study:

• To develop a robust data clustering approach that overcomes NMF and spectral clustering limitations.
• To introduce a parameter-free method for enhanced clustering performance.
• To extend the approach for multiview data with self-tuned view weights.

Main Methods:

• Proposed Robust Matrix factorization with Spectral embedding (RMS) by integrating NMF and spectral clustering.
• Utilized the l2,1-norm instead of the squared Frobenius-norm to mitigate outlier effects.
• Developed a multiview version (M-RMS) with self-tuning weights for different data views.

Main Results:

• The proposed RMS and M-RMS methods successfully capture nonlinear data structures.
• The l2,1-norm objective function enhances robustness against outliers.
• Experiments show superior clustering performance compared to state-of-the-art methods on various datasets.

Conclusions:

• RMS and M-RMS offer a robust, parameter-free solution for single-view and multiview data clustering.
• The integration of spectral clustering and matrix factorization effectively addresses data nonlinearity.
• The methods demonstrate significant improvements in clustering accuracy and outlier handling.