Assuming that we have a distribution p(ζ)for which a Neural Gas model has to be created. The following parameters are needed for the Algorithm initialization.
λi,λf and Ei,Ef, and tmax
λi,λf are used to set the rate at which learning rate E converges
Ei,Ef are the initial and final learning rate E respectively
tmax is the time till which the process continues.
Step 1. Create a Set A to contain N units each with a vector reference from p(ζ). Also initialize the time parameter to 0.
Step 2. Get a random value from the distribution p(ζ) and call it X.
Step 3. Line up all the elements from A in relation with their nearness to X, with the nearest coming first and the farthest the last.
Thus line up A's vectors such that for Cp,Cm,Co... the corresponding vectors Wp,Wm,Wo,...
||Wp-X|| <=||Wm-X||<=||Wo-X|| holds true
The norm || || usually taken is the square norm.
Step 4. Change the vectors for Cp,Cm,Co...
ΔWi = E(t)*hλ(ki(X,A))*(X-Wi)
λ(t) = λi(λf/λi)(t/tmax)
E(t) = Ei(Ef/Ei)t/tmax
hλ = e(-k/λ(t))
Step 5. Increment t
Step 6. t 2. The neural gas model will require fine tuning of the λ parameters especially to achieve a good convergence rate and stable model.
1. The neural gas model does not delete a node and also does not create new nodes.
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2. The neural gas model will require fine tuning of the λ parameters especially to achieve a good convergence rate and stable model.