Novel multiclass classifiers based on the minimization of the within-class variance

Area of Science:

• Machine Learning
• Computer Vision
• Pattern Recognition

Background:

• Traditional multiclass classification methods often struggle with high-dimensional data and complex decision boundaries.
• Support Vector Machines (SVMs) are effective but typically designed for binary classification.
• Optimizing Fisher's discriminant ratio is a common approach for dimensionality reduction and feature extraction.

Purpose of the Study:

• To introduce a novel class of multiclass classifiers, Minimum Within-Class Variance Multiclass Classifiers (MWCVMC).
• To formulate and solve the MWCVMC optimization problem in arbitrary Hilbert spaces using Mercer's kernels.
• To extend MWCVMC to handle dissimilarity measures and indefinite kernels via pseudo-Euclidean embedding.

Main Methods:

• Formulation and solution of the MWCVMC optimization problem in Hilbert spaces.
• Application of indefinite kernels and pseudo-Euclidean embedding for solving MWCVMCs.
• Utilizing pseudo-Euclidean embedding of Hausdorff distances for facial expression recognition with partial occlusion.

Main Results:

• Demonstrated the effectiveness of MWCVMC in facial expression recognition, achieving up to 99% accuracy.
• Successfully handled partial facial occlusion in experiments.
• Validated the applicability of MWCVMC to face recognition and other classification tasks using Mercer's kernels.

Conclusions:

• MWCVMC offers a powerful and flexible framework for multiclass classification problems.
• The proposed method shows significant promise for real-world applications, particularly in computer vision tasks like facial expression and face recognition.
• The integration with kernel methods and pseudo-Euclidean embedding enhances its capability to handle complex data and dissimilarity measures.