2015/06/16 by Anh Huy Phan, Phan, Anh-Huy, Petr Tichavský +3
Chemistry · Mathematics · Medicine · #Advanced NMR Techniques and Applications #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1506.04971
openalex publication_date 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 x R x 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 CPD.