Abstract
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 \(R \times R \times R\) and rank-R, the block deflation has a complexity of \({\mathcal {O}}(R^3)\) per iteration which is lower than the cost \({\mathcal {O}}(R^4)\) of the ALS algorithm for the overall CP decomposition.
P. Tichavský—The work of P. Tichavský was supported by The Czech Science Foundation through Project No. 14-13713S.
A. Cichocki—Also affiliated with the EE Dept., Warsaw University of Technology and with Systems Research Institute, Polish Academy of Science, Poland.
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Phan, AH., Tichavský, P., Cichocki, A. (2015). Rank Splitting for CANDECOMP/PARAFAC. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_4
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