X = randi([-9 9], 10, 2)
disp(J(X))
function output = J(X)
L = 0.5;
S = size(X,1);
JA = sum(X.^2,2);
JB = sum(triu(squareform(1./pdist(X, 'squaredeuclidean'))),2);
output = sum(JA + JB)./S;
end
The equation you posted does not include a division by P*(P-1)/2 (for undefined variable P at that.)
The equation you posted is ambiguous about what the upper limit is for j. As s is not defined, it is possible that the size of X is greater than s, so the sum in the second part of the equation might include a potentially large number of terms.
The posted equation has j>=i but when j = i then 
is 0 and the term would be 1/0 which is infinity. That is not a useful equation, so we must suppose that j>i must be true. If s is the number of rows in X then for the last row, i = s, j>i would be empty, which leads to the question of whether adding emptiness should be treated the same as adding 0.
is 0 and the term would be 1/0 which is infinity. That is not a useful equation, so we must suppose that j>i must be true. If s is the number of rows in X then for the last row, i = s, j>i would be empty, which leads to the question of whether adding emptiness should be treated the same as adding 0.
