How to use PSO (Particle swarm optimization) to optimize objective function containing two terms one of them kmeans clustering?

Hi

I used PSO before to optimize an objective function.Now I have an objective(fitness) function containing two terms; one of them described by k-means clustering ..Euclidean distance?

Answer 1

[Walter Roberson]

You have to pass a function handle as the objective function, but it does not have to be an anonymous function. You can pass the handle to a function that does extensive computation based on the inputs. The only requirement is that the output has to be a scalar.

If you are trying to minimize two distinct things simultaneously then you either need to decide their relative weighting to combine them into a scalar, or else you need to use gamultiobj() to find pareto fronts.

[M.Shaarawy]

[Walter Roberson]

I do not understand that image?

[M.Shaarawy]

You saw what is written in??

[M.Shaarawy]

If you read it

You will see the objective function phi

the first term I made and I want to know how to implement the second term??

If any information you need I will give

[Walter Roberson]

This is what your image looks like at my end:

No phi, no first or second term.

[M.Shaarawy]

This is my objective function : Walter Roberson

[Walter Roberson]

that looks like weighted Euclidean not plain Euclidean .

[M.Shaarawy]

Yes

Now ,how to make as code in MATLAB?

[M.Shaarawy]

Walter Roberson

I have the Wi matrix so how to implement this weighted Euclidean distance?

To get results like these in the images

[M.Shaarawy]

[Walter Roberson]

Use a nested for loop if you need to.

total = 0;
for j = 1 : K
    for i = 1 : N2
        total = total  + sum(sum((W(i) * bsxfun(@minus, V(mu(j)).^i, mu(j)))).^2));
    end
end

Here I assume that V_(mu_j) must indicate a function named V that is being passed a scalar mu(j) and is returning a vector or array -- if V_mu_j is a scalar then it makes less sense to talk about a Euclidean distance. If mu(j) represents a vector or array, or Wi is a vector or array, the code might need to be revised. If we had information about the relative dimensions we might potentially be able to write much more compact code.

[M.Shaarawy]

Wi : is vector

See the attached for more information

[M.Shaarawy]

[M.Shaarawy]

Dear Walter Roberson,

Is there is compact code after the description in the last two images?