Low-rank Approximation

In mathematics, low-rank approximation is a minimization problem in which a cost function measures the goodness of fit between a given matrix (the data) and an approximation matrix (the optimization variables), but the rank of the approximation matrix must be reduced. This problem is used in mathematical modeling and data compression. The rank constraint is related to the complexity constraints of the model that fits the data. In applications, the approximation matrix often has other constraints in addition to the rank constraint, such as non-negativity and Hankel structure.

Low-rank approximation is closely related to many other techniques, including principal component analysis, factor analysis, total least squares, latent semantic analysis, orthogonal regression, and dynamic pattern decomposition.

References

【1】Wikipedia