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Tensor Deflation for CANDECOMP/PARAFAC— Part I: Alternating Subspace Update Algorithm.
- Source :
- IEEE Transactions on Signal Processing; Nov2015, Vol. 63 Issue 22, p5924-5938, 15p
- Publication Year :
- 2015
-
Abstract
- CANDECOMP/PARAFAC (CP) approximates multiway data by sum of rank-1 tensors. Unlike matrix decomposition, the procedure which estimates the best rank-R tensor approximation through R sequential best rank-1 approximations does not work for tensors, because the deflation does not always reduce the tensor rank. In this paper, we propose a novel deflation method for the problem. When one factor matrix of a rank-R CP decomposition is of full column rank, the decomposition can be performed through (R-1) rank-1 reductions. At each deflation stage, the residue tensor is constrained to have a reduced multilinear rank. For decomposition of order-3 tensors of size R\times R\times R and rank-R, estimation of one rank-1 tensor has a computational cost of \cal O(R^3) per iteration which is lower than the cost \cal O(R^4) of the ALS algorithm for the overall CP decomposition. The method can be extended to tracking one or a few rank-one tensors of slow changes, or inspect variations of common patterns in individual datasets. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 1053587X
- Volume :
- 63
- Issue :
- 22
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Signal Processing
- Publication Type :
- Academic Journal
- Accession number :
- 110255813
- Full Text :
- https://doi.org/10.1109/TSP.2015.2458785