L1-Norm Distance Minimization-Based Fast Robust Twin Support Vector $k$ -Plane Clustering.

Area of Science:

• Machine Learning
• Data Mining
• Pattern Recognition

Background:

• Twin Support Vector Clustering (TWSVC) is a k-plane clustering method.
• TWSVC is sensitive to outliers due to L2-norm distance and computationally expensive due to solving multiple quadratic programming problems.

Purpose of the Study:

• To develop a robust and efficient k-plane clustering method.
• To address the limitations of TWSVC, specifically its susceptibility to outliers and high computational cost.

Main Methods:

• Introduced L1-norm distance minimization-based robust TWSVC (RTWSVC) using a novel iterative algorithm.
• Developed Fast RTWSVC with an iterative algorithm requiring only linear equation computations for improved speed and robustness.

Main Results:

• The proposed RTWSVC and Fast RTWSVC methods demonstrate enhanced robustness against outliers compared to TWSVC.
• Fast RTWSVC significantly reduces computational complexity, making it more efficient for large datasets.
• Experimental results validate the theoretical insights on convergence and local minima, showing superior performance.

Conclusions:

• The novel RTWSVC and Fast RTWSVC methods offer powerful and efficient alternatives to TWSVC for k-plane clustering.
• These methods effectively mitigate outlier influence and improve computational performance.
• The study provides theoretical guarantees and empirical evidence for the proposed algorithms' effectiveness.