Twin minimax probability machine for pattern classification

Area of Science:

• Machine Learning
• Pattern Recognition
• Statistical Classification

Background:

• Traditional classifiers like Support Vector Machines (SVMs) often require careful parameter tuning and can be computationally intensive.
• Minimax Probability Machine (MPM) and Twin Support Vector Machine (TWSVM) offer alternative approaches to classification with distinct advantages.
• There is a need for robust, distribution-free classifiers that balance accuracy with computational efficiency.

Purpose of the Study:

• To propose a novel distribution-free Bayes optimal classifier, the twin minimax probability machine (TWMPM).
• To combine the strengths of MPM and TWSVM for improved classification performance.
• To develop efficient algorithms for solving the TWMPM optimization problem.

Main Methods:

• The TWMPM constructs two nonparallel hyperplanes to maximize class separation probability while maintaining distance.
• It controls worst-case misclassification error by minimizing the upper bound on misclassification probability.
• The method is transformed into concave fractional programming using the multivariate Chebyshev inequality, then reformulated as convex quadratic programming (QP) for global optimality.

Main Results:

• A convex QP algorithm is developed, offering lower computational burden compared to an iterative alternative.
• Both linear and nonlinear (kernel-based) versions of TWMPM are presented.
• Experimental results on diverse datasets demonstrate the feasibility and effectiveness of TWMPM and its QP algorithm, showing low complexity and fewer parameters.

Conclusions:

• The proposed TWMPM is a feasible and effective distribution-free classifier.
• The convex QP algorithm provides an efficient solution with computational complexity comparable to TWSVM.
• TWMPM offers a promising approach for classification tasks requiring robust performance and computational efficiency.