How can the Neighbourhood function of a Self Organizing map be estimated?

Happy new year :) I would like to write a code for a self organizing map without using the matlab inbuilt SOM function. How can i estimate the neighbourhood function.

h=alpha.*exp(-((ri-rc).^2)/2.*(width).^2);

ri and rc are the vectorial location on the display grid. Alpha and width decreases monotonically with the regression steps. My questions are how do i compute ri, rc and the width so as to get the neighbourhood function?

Any ideas will be appreciated!

x1=signal(1);

x2=signal(2);

x3=signal(3);

x4=signal(4);

x=[x1;x2;x3;x4];

alpha=0.01;

width=2;%%%may be

w=zeros(1,length(x1));

D = sqrt(sum((x1-w).^2));%%%Euclidean Distance

c=min(D);

while max(max(abs(delw)))> 0.00001

for j=1:4

h=alpha.*exp(-((ri-rc).^2)/2.*(width).^2);

deltaw=(h.*(x(:,j)-w));

w=w+delw;

end

alpha=alpha*0.9;

width=width.*0.9;

D = sqrt(sum((x(:,j)-w).^2));%%%Euclidean Distance

c=min(D);

end

This is the idea i have on the SOM script but i am very unssure if it makes any sense. Suggestions please

Answer 1

[Thorsten]

width = 2; % == sigma of Gaussian neighboring function

% change to select size of neighborhood that is about 3 x sigma

b = ceil(3*width); % 99.8% of the Gaussin is in [-3*sigma, 3*sigma];

% BTW: 99.8% is normcdf(3) or 0.5*erfc(-3/sqrt(2))

x = -b:b; y = x; [X Y] = meshgrid(x, y);

G = 1/(2*pi*width^2)*exp(-(X.^2+Y.^2)/(2*width^2)); % 2D Gaussian

G = G/sum(G(:)); % normalize

I = rand(100); % sample input

R = conv2(I, G); % input weighted by neighboring function

subplot(1,3,1), surfl(x, y, G), title('Gaussian neighboring function G')

axis square

subplot(1,3,2), imshow(I, []), title('Input')

subplot(1,3,3), imshow(R, []), title('Input weighted by G')

[Ijeoma Madu]

Thanks but why is y=x? How can i interprete the neighbourhood function you used above with the one below

h=alpha.*exp(-((ri-rc).^2)/2.*(width).^2);

ri and rc are the vector of the coordinates of cells c and i.