Tensor Deflation for CANDECOMP/PARAFAC. Part 3: Rank Splitting

CANDECOMP/PARAFAC (CPD) approximates multiway data by sum of rank-1 tensors. Our recent study has presented a method to rank-1 tensor deflation, i.e. sequential extraction of the rank-1 components. In this paper, we extend the method to block deflation problem. When at least two factor matrices have full column rank, one can extract two rank-1 tensors simultaneously, and rank of the data tensor is reduced by 2. For decomposition of order-3 tensors of size R× R× R and rank-R, the block deflation has a complexity ofO(R 3 ) per iteration which is lower than the costO(R 4 ) of the ALS algorithm for the overall CPD.

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