Positive Definite Kernel

Positive definite kernels are fundamental mathematical objects used to define similarity measures between data points, enabling powerful machine learning methods like kernel ridge regression and support vector machines. Current research focuses on improving kernel approximation techniques, such as random Fourier features and Nyström methods, to handle high-dimensional data and developing kernels for non-Euclidean spaces and complex data structures (e.g., sequential data, probability measures). This work is significant because efficient and effective kernels are crucial for scaling kernel methods to large datasets and extending their applicability to diverse domains, impacting fields ranging from reinforcement learning to topological data analysis.