Structured low-rank approximation as a rational function minimization
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...
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In this paper, we consider the so-called structured low rank approximation (SLRA) problem as a problem of optimization on the set of either matrices or vectors. Briefly, SLRA is defined as follows. Given an initial matrix with a certain structure (for example, Hankel), the aim is to find a matrix of specified lower rank that approximates this initial matrix, whilst maintaining the initial struc...
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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...
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ژورنال
عنوان ژورنال: IFAC Proceedings Volumes
سال: 2012
ISSN: 1474-6670
DOI: 10.3182/20120711-3-be-2027.00143