Kernel Space

Kernel methods are powerful machine learning tools that operate in high-dimensional spaces (kernel spaces) defined by kernel functions, mapping data into reproducing kernel Hilbert spaces (RKHS) or the more general reproducing kernel Krein spaces (RKKS). Current research focuses on developing efficient algorithms for kernel selection and combination, including online learning schemes and Bayesian optimization techniques, as well as exploring the theoretical properties of kernel spaces, such as the size of epsilon-covers and the relationship between kernels and feature subspaces. These advancements improve the efficiency and accuracy of kernel-based methods across various applications, including neural network training, clustering, and regression, by addressing challenges like kernel selection bias and computational complexity.