This paper studies online kernel learning (OKL) for graph classification problem, since the large approximation space provided by reproducing kernel Hilbert spaces often contains an accurate function. Nonetheless, optimizing over this space is computationally expensive. To address this issue, approximate OKL is introduced to reduce the complexity either by limiting the support vector (SV) used by the predictor, or by avoiding the kernelization process altogether using embedding. Nonetheless, as long as the size of the approximation space or the number of SV does not grow over time, an adversarial environment can always exploit the approximation process. In this paper, we introduce an online kernel sampling (OKS) technique, a new second-order OKL method that slightly improve the bound from $O(d log(T))$ down to $O(r log(T))$ where $r$ is the rank of the learned data and is usually much smaller than d. To reduce the computational complexity of second-order methods, we introduce a randomized sampling algorithm for sketching kernel matrix $K_t$ and show that our method is effective to reduce the time and space complexity significantly while maintaining comparable performance. Empirical experimental results demonstrate that the proposed model is highly effective on real-world graph datasets.
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