Plot of the L0 norm penalty function in matlab

Question

I am interested to plot the L0-norm penalty function in matlab.

In fact, I know that the L0-norm of a vector x, ||x||_0, returns a value which designates the total number of nonzero elements in x. In other terms, ||x||_0 = #(i | xi !=0).

For example, for the L1-norm of x, it returns the sum of the absolute values of the elements in x. The matlab code to plot the L_1 norm penalty function is:

clear all;
clc;

x = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5];
penal = zeros (length(x),1);
lambda = 2; % the tuning parameter
for ii = 1 : length(x)
penal(ii) = lambda*abs(x(ii));
end
figure
plot(x(:), penal(:), 'r');

But now what about the L_0 norm??

Any help will be very appreciated!

score 1 · Accepted Answer · answered Jul 18 '16 at 21:53

1

Replace the line inside the for loop with the following:

penal(ii) = lambda*(x(ii) ~= 0);

This assigns a penalty of lambda for all non-zero values in the vector x.

answered Jul 18 '16 at 21:53

Prakhar

325
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2

BTW, you could avoid `for` loop by using `penal = lambda*(x ~= 0);`, or `penal = lambda*abs(x);`. This would be much more efficient for high dimensional vectors. – Prakhar Jul 18 '16 at 22:15
Thank you so much! – Christina Jul 18 '16 at 22:25

Plot of the L0 norm penalty function in matlab

1 Answers1