This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding, and seamlessly integrates multiple kernels to enhance the learning process. Our theoretical analysis offers a population-level characterization of this approach using random variables. Empirically, our method demonstrates superior running time compared to standard approaches such as support vector machines and two-layer neural network, while achieving comparable classification accuracy across various simulated and real datasets.