Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Tensor-based techniques for the blind separation of DS-CDMA signals
Signal Processing
SIAM Journal on Matrix Analysis and Applications
Decompositions of a Higher-Order Tensor in Block Terms—Part I: Lemmas for Partitioned Matrices
SIAM Journal on Matrix Analysis and Applications
Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness
SIAM Journal on Matrix Analysis and Applications
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
A comparison of algorithms for fitting the PARAFAC model
Computational Statistics & Data Analysis
SIAM Journal on Matrix Analysis and Applications
Blind PARAFAC receivers for DS-CDMA systems
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Parallel factor analysis in sensor array processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
A Constrained Factor Decomposition With Application to MIMO Antenna Systems
IEEE Transactions on Signal Processing
Constrained Tensor Modeling Approach to Blind Multiple-Antenna CDMA Schemes
IEEE Transactions on Signal Processing
Blind Deconvolution of DS-CDMA Signals by Means of Decomposition in Rank- Terms
IEEE Transactions on Signal Processing
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In this paper, we derive uniqueness conditions for a constrained version of the parallel factor (Parafac) decomposition, also known as canonical decomposition (Candecomp). Candecomp/Parafac (CP) decomposes a three-way array into a prespecified number of outer product arrays. The constraint is that some vectors forming the outer product arrays are linearly dependent according to a prespecified pattern. This is known as the PARALIND family of models. An important subclass is where some vectors forming the outer product arrays are repeated according to a prespecified pattern. These are known as CONFAC decompositions. We discuss the relation between PARALIND, CONFAC, and the three-way decompositions CP, Tucker3, and the decomposition in block terms. We provide both essential uniqueness conditions and partial uniqueness conditions for PARALIND and CONFAC and discuss the relation with uniqueness of constrained Tucker3 models and the block decomposition in rank-$(L,L,1)$ terms. Our results are demonstrated by means of examples.