Kernel-based adaptive filters are sequential learning algorithms, operating on reproducing kernel Hilbert spaces. Their learning performance is susceptible to the selection of appropriate values for kernel bandwidth and learning-rate parameters. Additionally, as these algorithms train the model using a sequence of input vectors, their computation scales with the number of samples. We propose a framework that addresses the previous open challenges of kernel-based adaptive filters. In contrast to similar methods, our proposal sequentially optimizes the bandwidth and learning-rate parameters using stochastic gradient algorithms that maximize the correntropy function. To remove redundant samples, a sparsification approach based on dimensionality reduction is introduced. The framework is validated on both synthetic and real-world data sets. Results show that our proposal converges to relatively low values of mean-square-error while provides stable solutions in real-world applications.