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This paper presents Support Vector Machine (SVM) with weighted summation kernel obtained by Adaboost. In recent years, SVM with local summation kernel is proposed to use local features in SVM effectively. However, the computational cost of original method is high because all local kernels are used. In general, the effective position and size are different for recognition task. However, original method applied local kernel with same size to all scalar features and all local kernels are integrated with equal weight. To improve the performance and reduce the computational cost, local kernels with various size are prepared at all positions of a recognition target and effective local kernels are selected by Adaboost. Since 1-Nearest Neighbor (1-NN) of the output of local Gaussian kernel at certain size and position is used as weak learner, a strong classifier obtained by Adaboost becomes a new weighted summation kernel specialized for given recognition task. The proposed method is applied to face detection task. We confirmed that the proposed weighted summation kernel gives better performance than original local summation kernel though the proposed method uses the smaller number of local kernels than local summation kernel.