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Neural Gas - a biologically inspired adaptive algorithm, coined by Martinetz and Schulten, 1991. It sorts for the input signal according to how far away they are. A certain number of them are selected by distance in order, then the number of adaptation units and strength are decreased according to a fixed schedule.
## Algorithm

The rough steps of the Neural Gas algorithm can be specified as

## Comments

1. The neural gas model does not delete a node and also does not create new nodes.## References & External Links

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.

λ_{i},λ_{f}and E_{i},E_{f}, and t_{max}

λ_{i},λ_{f}are used to set the rate at which learning rate E converges

E_{i},E_{f}are the initial and final learning rate E respectively

t_{max}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.

A={C_{1},C_{2},...C_{N}}

t=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 W_{p},W_{m},W_{o},...

||W_{p}-X|| <=||W_{m}-X||<=||W_{o}-X|| holds true

The norm || || usually taken is the square norm.

Step 4. Change the vectors for Cp,Cm,Co...

ΔWi = E(t)*h_{λ}(k_{i}(X,A))*(X-Wi)

Where,

λ(t) = λi(λ_{f}/λ_{i})^{(t/tmax)}

E(t) = Ei(E_{f}/E_{i})^{t/tmax}

h_{λ}= e^{(-k/λ(t))}

Step 5. Increment t

t=t+1

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.

3. It is topology representing neural network, that is after reaching convergence (>t_{max}), the network node's vector would be representing the distribution being modelled.

- T. M. Martinetz and K. J. Schulten. A ``neural-gas'' network learns topologies. In T. Kohonen, K. Mäkisara, O. Simula, and J. Kangas, editors, Artificial Neural Networks, pages 397-402. North-Holland, Amsterdam, 1991.
- Neural Gas Algorithm
- Java applet. It show evolution of Neural Gas, Growing Neural Gas and several other methods related to competitive learning.
- Growing Neural Gas videos.
- Java Competitve Learning Application A suite of Unsupervised Neural Networks (including Self-organizing map) written in Java. Complete with all source code.

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Last updated on Saturday December 22, 2007 at 17:27:31 PST (GMT -0800)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday December 22, 2007 at 17:27:31 PST (GMT -0800)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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