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

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