Nonlinear Kernel Fisher Discriminant Analysis Based on Local Fisher Criterion

This paper presents a method for nonlinear kernel Fisher discriminant analysis based on the local Fisher criterion. This approach can be applied to supervised feature extraction and achieves effective dimensionality reduction for high-dimensional data. Specifically, the method enhances feature extraction capability by incorporating nonlinear kernel functions. To ensure robustness and locality in feature extraction, we employ the local Fisher criterion for optimization. The key advantage of this method lies in its ability to not only improve feature extraction accuracy but also handle high-dimensional data with high efficiency when processing large-scale datasets. Implementation typically involves kernel matrix computation using functions like RBF or polynomial kernels, followed by local scatter matrix optimization through neighborhood preservation algorithms. Therefore, this method shows broad application prospects in fields such as computer vision, signal processing, and pattern recognition.