From 067afcb3bcb8dcd7ab495ee259fa75a7071a2237 Mon Sep 17 00:00:00 2001 From: David Koslicki Date: Fri, 12 Jan 2024 12:35:50 -0500 Subject: [PATCH 1/2] Make norms explicit --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 8a42c8c..7dbd3be 100644 --- a/README.md +++ b/README.md @@ -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)] From 4367eec8d6707abcd1f0090da30a03e3116dbd78 Mon Sep 17 00:00:00 2001 From: David Koslicki Date: Fri, 12 Jan 2024 12:46:33 -0500 Subject: [PATCH 2/2] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 7dbd3be..68f4857 100644 --- a/README.md +++ b/README.md @@ -73,7 +73,7 @@ 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||_2^2 + lambda * ||x||_2^2 +min ||Ax - y||_2^2 + lambda * ||x||_1^2 s.t. x>=0 ``` where `lambda` is a regularization parameter. This can be cast as a NNLS problem via: