Support vector machines (SVMs) are a widely-used machine learning technique, but they suffer from a significant drawback of high time and memory training complexity, which should be endured especially in big data problems. SVMs incorporate kernel functions - it involves selecting the kernel and induces an additional computational effort. In this paper, we address these issues and propose an SVM framework that automatically determines the kernel and selects data to train SVMs. It embodies the neuro-fuzzy system for creating the kernel along with the memetic algorithm to select training samples. Extensive experiments indicate that our approach enables obtaining high classification scores.