Non-Negative Least Squares (NNLS) Task

A Non-Negative Least Squares (NNLS) Task is a least-squares optimization task that ...

• Context:
  • It can be solved by a Non-Negative Least Squares (NNLS) System (that can implement a non-negative least squares (NNLS) algorithm).
• Example(s):
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• See: Non-Negative Matrix Factorization, Mathematical Optimization, Constrained Optimization, Linear Least Squares (Mathematics), Response Variable, Euclidean Norm, Matrix Decomposition, CP Decomposition, Neural Computation.

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Non-negative_least_squares Retrieved:2017-9-11.
  • In mathematical optimization, the problem of non-negative least squares (NNLS) is a constrained version of the least squares problem where the coefficients are not allowed to become negative. That is, given a matrix A and a (column) vector of response variables y, the goal is to find : [math]\displaystyle{ \operatorname{arg\,min}\limits_\mathbf{x} \|\mathbf{Ax} - \mathbf{y}\|_2 }[/math] subject to x ≥ 0.

    Here x ≥ 0 means that each component of the vector x should be non-negative, and ‖·‖₂ denotes the Euclidean norm.

    Non-negative least squares problems turn up as subproblems in matrix decomposition, e.g. in algorithms for PARAFAC and non-negative matrix/tensor factorization. The latter can be considered a generalization of NNLS. Another generalization of NNLS is bounded-variable least squares (BVLS), with simultaneous upper and lower bounds αᵢ ≤ xᵢ ≤ βᵢ.

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