Can Matlab do L1 minimization?

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Rex 2012-4-30

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评论： SAMVIT MAHARAJ 2015-3-18

Hi, I'm trying to implement face recognition algorithm based on sparse representation. It has to do L1 minimization for optimization.

I am using linprog function for L1 minimization, but i'm not sure if matlab actually can solve this or it just gives an approximate solution.

I'm trying to find solution after L1 minimization of x using the constraint Aeq * x = y. lb is the lower bound (set to be zeros)

x1 = linprog(f,[],[],Aeq,y,lb,[],[],[]);

This is actually giving me good results. But I just want to confirm if this is the actual L1 minimization solution or just an approximate solution.

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Answer 1

Richard Brown 2012-4-30

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Assming f is all ones, and you're wanting to minimise the 1-norm of x, then your code will be doing what you wish

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Rex 2012-4-30

One more question, in sparse representation paper it says that if we expect errors, we can model our optimization as

y = Aeq * x + e

instead of

y = Aeq * x

The vector e will have the errors after x has converged to its best state. Can I use matlab for this implementation?

Richard Brown 2012-4-30

Yes, but you need to set up the problem a bit differently. Here you want to minimise ||A*x - y|| + lambda ||x||, where the second term is called a "regularization" term, with a parameter lambda that you might need to experiment with

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Answer 2

Geoff 2012-4-30

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在 MATLAB Online 中打开

It will do its best to minimise the residual errors. If a real solution exists, it will converge on that. Yes, it's 'approximate' in the sense that there is a termination tolerance value to control how many decimal places you care about. If you want it more exact, set the TolFun option using optimset, and pass your options into linprog.

opts = optimset('linprog');
set( opts, 'TolFun', 1e-12 );
x1 = linprog( f, [], [], Aeq, y, lb, [], [], opts );

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Rex 2012-4-30

Thanks for letting me know that we can set the tolerance.

SAMVIT MAHARAJ 2015-3-18

Hello, I am also working on the same program. Can you tell me how can I find the recognition rate?

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