TY - JOUR
T1 - Robust Iterative Fitting of Multilinear Models
AU - Vorobyov, Sergiy A.
AU - Rong, Yue
AU - Sidiropoulos, Nicholas D.
AU - Gershman, Alex B.
PY - 2005/8
Y1 - 2005/8
N2 - Parallel factor (PARAFAC) analysis is an extension of low-rank matrix decomposition to higher way arrays, also referred to as tensors. It decomposes a given array in a sum of multi-linear terms, analogous to the familiar bilinear vector outer products that appear in matrix decomposition. PARAFAC analysis generalizes and unifies common array processing models, like joint diagonalization and ESPRIT; it has found numerous applications from blind multiuser detection and multidimensional harmonic retrieval, to clustering and nuclear magnetic resonance. The prevailing fitting algorithm in all these applications is based on (alter-nating) least squares, which is optimal for Gaussian noise. In many cases, however, measurement errors are far from being Gaussian. In this paper, we develop two iterative algorithms for the least absolute error fitting of general multilinear models. The first is based on efficient interior point methods for linear programming, employed in an alternating fashion. The second is based on a weighted median filtering iteration, which is particularly appealing from a simplicity viewpoint. Both are guaranteed to converge in terms of absolute error. Performance is illustrated by means of simulations, and compared to the pertinent Cramér-Rao bounds (CRBs).
AB - Parallel factor (PARAFAC) analysis is an extension of low-rank matrix decomposition to higher way arrays, also referred to as tensors. It decomposes a given array in a sum of multi-linear terms, analogous to the familiar bilinear vector outer products that appear in matrix decomposition. PARAFAC analysis generalizes and unifies common array processing models, like joint diagonalization and ESPRIT; it has found numerous applications from blind multiuser detection and multidimensional harmonic retrieval, to clustering and nuclear magnetic resonance. The prevailing fitting algorithm in all these applications is based on (alter-nating) least squares, which is optimal for Gaussian noise. In many cases, however, measurement errors are far from being Gaussian. In this paper, we develop two iterative algorithms for the least absolute error fitting of general multilinear models. The first is based on efficient interior point methods for linear programming, employed in an alternating fashion. The second is based on a weighted median filtering iteration, which is particularly appealing from a simplicity viewpoint. Both are guaranteed to converge in terms of absolute error. Performance is illustrated by means of simulations, and compared to the pertinent Cramér-Rao bounds (CRBs).
KW - Array signal processing
KW - non-Gaussian noise
KW - parallel factor analysis
KW - robust model fitting
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U2 - 10.1109/TSP.2005.850343
DO - 10.1109/TSP.2005.850343
M3 - Article
AN - SCOPUS:85008006603
SN - 1053-587X
VL - 53
SP - 2678
EP - 2689
JO - IRE Transactions on Audio
JF - IRE Transactions on Audio
IS - 8
ER -