From time series to linear system—Part III. Approximate modelling
Automatica (Journal of IFAC)
The SVD and reduced rank signal processing
Signal Processing - Theme issue on singular value decomposition
Algorithms for global total least squares modelling of finite multivariable time series
Automatica (Journal of IFAC)
Displacement structure: theory and applications
SIAM Review
Total Least Norm Formulation and Solution for Structured Problems
SIAM Journal on Matrix Analysis and Applications
Introduction to mathematical systems theory: a behavioral approach
Introduction to mathematical systems theory: a behavioral approach
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
On approximate GCDs of univariate polynomials
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem
SIAM Journal on Matrix Analysis and Applications
Common factor estimation and two applications in signal processing
Signal Processing - Special issue on independent components analysis and beyond
Numerical Polynomial Algebra
Block-Toeplitz/Hankel Structured Total Least Squares
SIAM Journal on Matrix Analysis and Applications
Global optimization of rational functions: a semidefinite programming approach
Mathematical Programming: Series A and B
Exact and Approximate Modeling of Linear Systems: A Behavioral Approach (Mathematical Modeling and Computation) (Mathematical Modeling and Computation)
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Survey paper: Errors-in-variables methods in system identification
Automatica (Journal of IFAC)
Overview of total least-squares methods
Signal Processing
Survey paper: Structured low-rank approximation and its applications
Automatica (Journal of IFAC)
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
SIAM Journal on Matrix Analysis and Applications
Singular value decompositions and low rank approximations of tensors
IEEE Transactions on Signal Processing
Estimation of a signal waveform from noisy data using low-rankapproximation to a data matrix
IEEE Transactions on Signal Processing
The constrained total least squares technique and its applicationsto harmonic superresolution
IEEE Transactions on Signal Processing
The geometry of weighted low-rank approximations
IEEE Transactions on Signal Processing
Technical Communique: Linear dynamic filtering with noisy input and output
Automatica (Journal of IFAC)
Bounded Matrix Low Rank Approximation
ICDM '12 Proceedings of the 2012 IEEE 12th International Conference on Data Mining
Software for weighted structured low-rank approximation
Journal of Computational and Applied Mathematics
Hi-index | 0.08 |
Rank deficiency of a data matrix is equivalent to the existence of an exact linear model for the data. For the purpose of linear static modeling, the matrix is unstructured and the corresponding modeling problem is an approximation of the matrix by another matrix of a lower rank. In the context of linear time-invariant dynamic models, the appropriate data matrix is Hankel and the corresponding modeling problems becomes structured low-rank approximation. Low-rank approximation has applications in: system identification; signal processing, machine learning, and computer algebra, where different types of structure and constraints occur. This paper gives an overview of recent progress in efficient local optimization algorithms for solving weighted mosaic-Hankel structured low-rank approximation problems. In addition, the data matrix may have missing elements and elements may be specified as exact. The described algorithms are implemented in a publicly available software package. Their application to system identification, approximate common divisor, and data-driven simulation problems is described in this paper and is illustrated by reproducible simulation examples. As a data modeling paradigm the low-rank approximation setting is closely related to the behavioral approach in systems and control, total least squares, errors-in-variables modeling, principal component analysis, and rank minimization.