Kernels and Spectrum Perturbations
摘要
Kernel Methods are part of a category of algorithms used for pattern analysis. The most well-known member within this class is the Support Vector Machine (SVM)SVM. Kernels operate by transforming the data into a high-dimensional feature space, where each axis corresponds to a specific feature of the data points. Kernel method can effectively convert the gathered data into a collection of points within the Euclidean space. Kernels facilitate operations within the feature space by simply calculating the inner products between all pairs of data points instead of directly computing the coordinates of the data within that space. Very often, this approach is proved to be more computationally efficient than explicitly computing the coordinates. The Positive Semi-Definite (PSD) property of a kernel matrix is necessary to ensure the existence of a Reproducing Kernel Hilbert Space (RKHS),Reproducing kernel hilbert space as noted in [15], where a convex optimization formulation can be derived to obtain an optimal solution.