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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Proceedings ArticleDOI
Fast sparse representation with prototypes
Jia-Bin Huang,Ming-Hsuan Yang +1 more
TL;DR: This work proposes an algorithm that exploits the fact that signals in most problems can be modeled by a small set of prototypes and shows that the l\-norm minimization problem can be reduced to a much smaller problem, thereby gaining significant speed-ups with much less memory requirements.
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A sparsity detection framework for on-off random access channels
TL;DR: In this article, a simple on-off random multiple access channel (MAC) was considered, where n users communicate simultaneously to a single receiver and each user is assigned a single codeword which it transmits with some probability λ over m degrees of freedom.
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Speaker identification using multilayer perceptrons and radial basis function networks
TL;DR: The results showed that the Multilayer Perceptrons networks were superior in memory usage and classification time, however, they suffered from long training time and the error rate was slightly higher than that of Radial Basis Function networks.
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A bootstrap method for structure detection of NARMAX models
TL;DR: A bootstrap structure detection (BSD) algorithm is developed as a means of determining the structure of highly over-parameterized models and provides accurate estimates of parameter statistics without relying on assumptions made by traditional procedures and yields a parsimonious description of the system.
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Time-varying model identification for time-frequency feature extraction from EEG data
TL;DR: Simulation studies and applications to real EEG data show that the proposed algorithm can provide important transient information on the inherent dynamics of nonstationary processes.
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.