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Recent publications and developments based on SVM have shown that using multiple kernels instead of a single one can enhance interpretability of the decision function and improve classifier performance, which motivates researchers to explore the use of homogeneous model obtained as linear combinations of kernels. However, the use of multiple kernels faces the challenge of choosing the kernel weights, and an increased number of parameters that may lead to overfitting. In this paper we show that MKL problem with a enhanced spatial pyramid match kernel can be solved efficiently using projected gradient method. Weights on each kernel matrix (level) are included in the standard SVM empirical risk minimization problem with a L2 constraint to encourage sparsity. We demonstrate our algorithm on classification tasks, which is based on a linear combination of the proposed kernels computed at multiple pyramid levels of image encoding, and we show that the proposed method is accurate and significantly more efficient than current approaches.