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Make norms explicit
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dkoslicki authored Jan 12, 2024
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Expand Up @@ -73,12 +73,12 @@ In practice, we've observed that the matrix `A` is rank deficient, yet over-dete
Thus there is no unique solution to `Ax=y` where `y` is the vector of pairwise distances between all KOs. We can,
however, find a unique "shortest length" solution by adding a regularization term to the objective function:
```
min ||Ax - y||^2 + lambda * ||x||^2
min ||Ax - y||_2^2 + lambda * ||x||_2^2
s.t. x>=0
```
where `lambda` is a regularization parameter. This can be cast as a NNLS problem via:
```
min ||A'x - y'||^2
min ||A'x - y'||_2^2
s.t. x>=0
where
A' = [A; sqrt(lambda)*ones(1, n)]
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