Support Matrix Machine via Joint ℓ_2,1 and Nuclear Norm Minimization Under Matrix Completion Framework for...

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Traditional Support Vector Machines (SVMs) are susceptible to outliers, degrading performance in high-dimensional datasets with corrupted columns.
• Classification accuracy diminishes significantly when even a small fraction of data features are corrupted.

Purpose of the Study:

• To propose an efficient Support Matrix Machine (SSMRe) for high-dimensional data classification in the presence of arbitrarily corrupted columns.
• To develop a method that simultaneously performs matrix recovery (feature selection) and classification.

Main Methods:

• Introduced Support Matrix Machine that simultaneously performs matrix Recovery (SSMRe).
• Employed joint minimization of l2,1 norm (nuclear norm of L) for feature selection and classification.
• Assumed data comprises a low-rank clean matrix plus a sparse noisy matrix, leveraging spectral extension of the elastic net.

Main Results:

• SSMRe demonstrates effective matrix recovery and classification under incoherence and ambiguity conditions.
• The method successfully recovers an intrinsic matrix of higher rank even with densely corrupted data.
• Significant performance gains observed on BCI, face recognition, and person identification datasets, particularly with outlier presence.

Conclusions:

• SSMRe provides a robust solution for high-dimensional classification with corrupted data and outliers.
• The proposed method combines matrix recovery, low-rank properties, and joint sparsity for complex noisy data.
• SSMRe achieves significant improvements in real-world applications while maintaining a reasonable number of support vectors.