Low-rank approximation

rdf:langString Low-rank approximation

rdf:langString In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling and data compression. The rank constraint is related to a constraint on the complexity of a model that fits the data. In applications, often there are other constraints on the approximating matrix apart from the rank constraint, e.g., non-negativity and Hankel structure. Low-rank approximation is closely related to: * principal component analysis, * factor analysis, * total least squares, * latent semantic analysis * orthogonal regression, and * dynamic mode decomposition.