Omar De La Cruz CabreraMAHDI ALI ABDULLAH ALMAHDAWI2022-06-042022-03-292022-06-04110629https://drepo.sdl.edu.sa/handle/20.500.14154/64205Over the last decades, learning methods using kernels have become very popular. A main reason is that real data analysis often requires nonlinear methods to detect the dependencies that allow successful predictions of properties of interest. Gaussian kernels have been used in many studies implementing learning algorithms and data analysis. Most of these studies have shown that the bandwidth parameter chosen for a Gaussian kernel can have a huge impact on the results. Therefore, it is essential to understand this impact at a theoretical level. Our contribution consists of two parts. First, we study the effect of the Gaussian kernel bandwidth parameter on how well an empirical operator defined from data approximates its continuous counterpart. Second, we study the convergence of what we call kernel-smoothed graph Laplacians. Some results in spectral approximations are provided as well as some examples.83enThesis