Orthogonal least squares methods and their application to non-linear system identification
TLDR
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram- Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed.Abstract:
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram-Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed. The classical Gram-Schmidt, modified Gram-Schmidt, and Householder transformation algorithms are then extended to combine structure determination, or which terms to include in the model, and parameter estimation in a very simple and efficient manner for a class of multivariate discrete-time non-linear stochastic systems which are linear in the parameters.read more
Citations
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Identification of Coupled Map Lattice Models of Stochastic Spatio-Temporal Dynamics Using Wavelets
TL;DR: In this paper, a new approach for the local reconstruction of coupled map lattice (CML) models of stochastic spatio-temporal dynamics from measured data is introduced.
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A Model Selection Method for Nonlinear System Identification Based fMRI Effective Connectivity Analysis
TL;DR: The results show that LARS can be used for model selection in an fMRI effective connectivity study with phase-encoded, standard block, and random block designs, and it is shown that the LOO cross-validation method for nonlinear model selection has less residual sum squares than the AICc algorithm for the study.
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Retinal image assessment using bi-level adaptive morphological component analysis.
TL;DR: A novel framework based on morphological component analysis (MCA) is presented which benefits from the adaptive representations obtained via dictionary learning and the reported experimental results demonstrate that the obtained components can be used to achieve competitive results with regard to the state-of-the-art vessel and exudate segmentation methods.
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Substructural Time-Varying Parameter Identification Using Wavelet Multiresolution Approximation
Yuanfeng Shi,Chih-Chen Chang +1 more
TL;DR: In this article, an offline substructure method based on wavelet multiresolution approximation (WMRA) is proposed for the identification of arbitrary time-varying parameters in a shear-beam building.
DissertationDOI
Channel Coding Inspired Contributions to Compressed Sensing
TL;DR: An equivalence relation is introduced by the concept of antipodal spherical codes, which ensures that vector pairs of minimal coherence correspond to those of largest minimum distance for these antipodAL codes as it is proven within this thesis.
References
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Book
Applied Regression Analysis
Norman R. Draper,Harry Smith +1 more
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
Journal ArticleDOI
Singular value decomposition and least squares solutions
Gene H. Golub,C. Reinsch +1 more
TL;DR: The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.
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Linear regression analysis
TL;DR: In this paper, the authors take into serious consideration the further development of regression computer programs that are efficient, accurate, and considered an important part of statistical research, and provide up-to-date accounts of computational methods and algorithms currently in use without getting entrenched in minor computing details.
Journal ArticleDOI
Input-output parametric models for non-linear systems Part II: stochastic non-linear systems
TL;DR: Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined.