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In edge computing, for dimensionality reduction and core data extraction, both edge computing node (ECN) and cloud server may implement a high-order singular value decomposition (HOSVD) algorithm before data are passed to local computing models. However, at present, many edge computing systems regard the two HOSVD procedures as two independent parts, which leads to repeated calculations in the cloud. In this paper, we propose an aggregative HOSVD method by reusing intermediate results of subtensor HOSVD in ECNs to reduce the HOSVD computing cost of the merged tensor in the cloud server. First, two equivalence lemmas of singular value decomposition (SVD) are proven. Second, the SVD left mergence algorithm (SVDLM), hierarchical-SVDLM (H-SVDLM) algorithm and aggregative HOSVD (AHOSVD) algorithm are proposed to obtain the HOSVD result of the merged tensor by efficiently merging the unfolded matrix SVD results of the subtensors. Finally, the efficiency and accuracy between the HOSVD and the AHOSVD are compared, and the experimental results validate that the proposed AHOSVD algorithm improves efficiency compared with the HOSVD algorithm in circumstances with comparable accuracy results with the HOSVD algorithm.