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This paper presents a fast and efficient computational approach to higher order spectral graph matching. Exploiting the redundancy in a tensor representing the affinity between feature points, we approximate the affinity tensor with the linear combination of Kronecker products between bases and index tensors. The bases and index tensors are highly compressed representations of the approximated affinity tensor, requiring much smaller memory than in previous methods, which store the full affinity tensor. We compute the principal eigenvector of the approximated affinity tensor using the small bases and index tensors without explicitly storing the approximated tensor. To compensate for the loss of matching accuracy by the approximation, we also adopt and incorporate a marginalization scheme that maps a higher order tensor to matrix as well as a one-to-one mapping constraint into the eigenvector computation process. The experimental results show that the proposed method is faster and requires smaller memory than the existing methods with little or no loss of accuracy.