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A support vector machine (SVM), which employs a kernel corresponding to feature extraction of local higher order moment spectra (LHOMS) of an image, is introduced. In order to overcome the curse of dimensionality when utilizing LHOMS image features in conventional multi channel filtering, an inner product kernel of LHOMS is derived. In the experiments, the SVM with LHOMS kernel is applied to image texture classification. It is shown that it can efficiently utilize the higher order features, and that the classification ratio is improved due to the introduction of the Gaussian window function for a stable local feature extraction. Further, it is discussed that the kernels for higher-order moment spectra and higher-order moments in the same orders becomes identical, indicating the equivalence of the two types of features in the kernel-function level.