Hello, I''m trying to solve the traveling salesman problem, by using a kohonen network. What I did at first, was to change the weight of the neuron winner, and the 2 others wich are near. But in order to improve it, i would like to apply a Mexican hat fonction. But i didn''t find it. I found a function wich is quite similar, but not exactly. This function depends of the distance between the neuron, and the coordonates of the input. D : Distance alpha = 1 / ( 1 + exp(D²/rate)) If you have a better function, please, say me. Cheers

exp(-x^2) ?

Yes, it''s better, but i''m looking for a function....


I''will draw it.

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Pfff the spaces didn''t appair.

I wille explain. Thx a-axis is the distance. I would like that when you are near the 0, the y is high. After, ''y'' decreases, to became neagtive, and then, go upper, to became null with a long distance.

You can enclose text in and tags to make the spaces and stuff appear as written (just don't write the spaces between the [ and ] brackets:

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Edited by - Dactylos on February 11, 2002 4:42:53 PM

It''s not exactly what you want, but how about: e-x^2cos(x)

It has the basic characteristics you want but oscillates about zero as it heads to -ve and +ve infinity.

Timkin

Okay, I found a function that fits the bill!

f(x) = -(x-a)(x+a)e-x^2

If you select a to be close to zero - say a=1 - then you get good results. As a gets larger the brim of the Sombrero disappears and you are left with just the peak. As a gets closer to zero the brim gets deeper so that it is bigger than the peak. Play around with it a little to find the behaviour you want.

If you want to create an asymmetric function, then change one of the constants ''a'' for a different constant ''b''.

Cheers,

Timkin

sin(x)/x ?

Thank you very much Timkin, it was exactly what i was looking for.

Cheers.

What I''m doing, is that during the learning process, the neighborhood became every time smaller. So, I have a rate wich increase during this time.

alpha = -(rate * x² - 1) * exp(-x²)

So, the difference between the neuron winner, and the others, became every time more important.



I think, i will use this one. Thanks for your help.