CANDECOMP/PARAFAC (CP) approximates multiway data by a sum of rank-1 tensors. Our recent study has presented a method to rank-1 tensor deflation, i.e. sequential extraction of rank-1 tensor 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 of O(R3) per iteration which is lower than the cost O(R4) of the ALS algorithm for the overall CP decomposition.
CITATION STYLE
Phan, A. H., Tichavský, P., & Cichocki, A. (2015). Rank splitting for CANDECOMP/PARAFAC. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9237, pp. 31–40). Springer Verlag. https://doi.org/10.1007/978-3-319-22482-4_4
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