KPCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and recognition.

Area of Science:

• Machine Learning
• Pattern Recognition
• Computer Vision

Background:

• Kernel Fisher Discriminant Analysis (KFD) is a powerful technique for dimensionality reduction and classification.
• Existing KFD methods may not fully exploit all available discriminant information.
• Understanding the theoretical underpinnings of KFD in Hilbert spaces is crucial for developing advanced algorithms.

Purpose of the Study:

• To theoretically examine Kernel Fisher Discriminant Analysis (KFD) in Hilbert space.
• To propose a novel two-phase KFD framework: Kernel Principal Component Analysis (KPCA) plus Linear Discriminant Analysis (LDA).
• To introduce a Complete Kernel Fisher Discriminant Analysis (CKFD) algorithm that utilizes both regular and irregular discriminant information.

Main Methods:

• Developed a two-phase KFD framework combining KPCA and LDA.
• Proposed the Complete Kernel Fisher Discriminant Analysis (CKFD) algorithm.
• Evaluated CKFD on the FERET face database and CENPARMI handwritten numeral database.

Main Results:

• The proposed CKFD framework offers novel insights into KFD theory.
• CKFD enables discriminant analysis in "double discriminant subspaces."
• Experimental results demonstrate CKFD's superior performance compared to other KFD algorithms.

Conclusions:

• CKFD is a more powerful discriminator due to its ability to utilize both regular and irregular discriminant information.
• The proposed CKFD algorithm shows significant improvements in classification tasks.
• The theoretical framework provides a foundation for future advancements in kernel-based discriminant analysis.