Kernel Discriminant Analysis via Singular Value Decomposition

In this paper, we present a novel methodology based on Singular Value Decomposition, termed "Kernel Linear Discriminant Analysis via SVD." This approach integrates two classical techniques to enhance both accuracy and computational efficiency in data classification tasks. The implementation typically involves: first mapping input data to a high-dimensional feature space using kernel functions (e.g., RBF or polynomial kernels), then applying SVD to decompose the kernel matrix for stable dimensionality reduction. Through this method, we can effectively transform high-dimensional data into lower-dimensional subspaces, significantly improving computational tractability while preserving discriminatory information. Key implementation steps include computing the kernel matrix K using a chosen kernel function, performing SVD on the centered kernel matrix to obtain orthogonal bases, and solving the discriminant optimization problem in the reduced subspace. Notable advantages of this approach include its capability to handle nonlinear classification problems through kernel trick implementation, demonstrated robustness against multicollinearity issues via SVD-based regularization, and scalability to large datasets through efficient matrix decomposition techniques. Consequently, we anticipate this methodology will play an increasingly vital role in future research and practical applications involving complex pattern recognition tasks.