# Tag Info

### Why Do Most of The Papers Use the Frobenius Norm for Denoising?

The Frobenius Norm has multiple equivalent definitions – the useful for error measure is probably this one: $$\left\|M\right\|_\mathrm F = \sqrt{\sum_{p\in M}\left\lvert p\right\rvert^2}$$ That's a ...

### How to Formulate a Constraint Which Ensures All Variables Have the Same Sign

The solution from the blog you linked goes as following (Coordinating Variable Signs by Paul Rubin, Web Archive): Someone asked me today (or yesterday, depending on whose time zone you go by) how to ...
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### Difference Between Iteratively Reweighted Least Squares (IRLS) and Sequential Quadratic Programming?

SQP is a method for solving smooth (objective and constraint functions are at least twice differentiable) constrained nonlinear optimization problems. It solves a series of quadratic programming ...
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### To find the unitary matrix which is the null of the results of multiplication with another matrix

Here is an attempt, tell me what I misunderstood. You say that $F\times F^{H}$ (which is of dimension $m\times m$ ) is unitary, which implies it is invertible. Therefore it means that $F$ is of full ...
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### Solving LASSO (${L}_{1}$ Regularized Least Squares) with Gradient Descent

Due to the non-smoothness of the $l_1$ norm, the algorithm is called subgradient descent. Because the you are looking for a solution that has a lot of zeros in it, you are still going to have to ...
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### Why Do Most of The Papers Use the Frobenius Norm for Denoising?

There are many types of matrix norms. Three are quite standard: element-wise norms: unfolding the matrix into a long vector, and compute a norm for that vector. Schatten norms: (power) vector noms ...
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### Least Angle Regression (LARS) without Matrix Inversion

If you want to solve for single value of $\lambda$ in the model: $$\arg \min_{x} \frac{1}{2} {\left\| A x - b \right\|}_{2}^{2} + \lambda {\left\| x \right\|}_{1}$$ Then you can use Coordinate ...
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### Ideas on Matrix Factorization / Transformations for ${L}_{1}$ Minimization

Since $\epsilon$ is a parameter you need to set, why not trade it with another parameter you need to set to create an easily solvable problem (Relaxation of the Problem)? You can transform the ...
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