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We propose a novel rank-adaptive higher-order orthogonal iteration (HOOI)algorithm to compute the truncated Tucker decomposition of higher-order tensorswith a given error tolerance, and prove that the method is locally optimal andmonotonically convergent. A series of numerical experiments related to bothsynthetic and real-world tensors are carried out to show that the proposedrank-adaptive HOOI algorithm is advantageous in terms of both accuracy andefficiency. Some further analysis on the HOOI algorithm and the classicalalternating least squares method are presented to further understand why rankadaptivity can be introduced into the HOOI algorithm and how it works.

A rank-adaptive higher-order orthogonal iteration algorithm for truncated Tucker decomposition