Concentration of kernel matrices with application to kernel spectral clustering

We study the concentration of random kernel matrices around their mean. derive nonasymptotic exponential inequalities for Lipschitz kernels assuming that data points are independent draws from a class multivariate distributions on $\mathbb{R}^{d}$, including strongly log-concave under affine transformations. A feature our result is need not have identical or zero mean, which key in certain applications such as clustering. Our bound dimension-free and sharp up to constants. For comparison, we also companion Euclidean (inner product) sub-Gaussian distributions. notable difference between two cases that, contrast kernel, case, inequality does depend mean underlying vectors. As an application these inequalities, misclassification rate spectral clustering (KSC) algorithm, perturbed nonparametric mixture model. show example where this establishes high-dimensional consistency (as $d\to \infty $) KSC, when applied with Gaussian noisy model nested nonlinear manifolds.