Structured low rank approximation
نویسندگان
چکیده
منابع مشابه
Structured Low Rank Approximation
Abstract. This paper concerns the construction of a structured low rank matrix that is nearest to a given matrix. The notion of structured low rank approximation arises in various applications, ranging from signal enhancement to protein folding to computer algebra, where the empirical data collected in a matrix do not maintain either the specified structure or the desirable rank as is expected ...
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Polynomially structured low-rank approximation problems occur in • algebraic curve fitting, e.g., conic section fitting, • subspace clustering (generalized principal component analysis), and • nonlinear and parameter-varying system identification. The maximum likelihood estimation principle applied to these nonlinear models leads to nonconvex optimization problems and yields inconsistent estima...
متن کاملRegularized structured low-rank approximation with applications
We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among others. We impose the low-rank by modeling the approximation as a product of two factors with reduced dimension. The structure of the low-rank model is enforc...
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A software package is presented that computes locally optimal solutions to low-rank approximation problems with the following features: • mosaic Hankel structure constraint on the approximating matrix, • weighted 2-norm approximation criterion, • fixed elements in the approximating matrix, • missing elements in the data matrix, and • linear constraints on an approximating matrix’s left kernel b...
متن کاملRecent process on structured low-rank approximation
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 ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00505-0