what is the difference between Self Organizing Maps and neural gas

Question

I am finding it difficult to understand the difference between Self Organizing Maps and neural gas. I read the Wikipedia article and Neural Gas Network Learns topologies article.

The SOM algorithm and Neural Gas algorithm looks so similar. In both it finds the winning neuron and the winning neuron fires and the firing neuron excites the neighbourhood neurons where the neighbourhood is detrmined by a neighbourhood function. In Neural gas the weights are adjusted as
and in SOM weights are adjusted as
.
They both are the same right?

The SOM algorithm is

and the neural gas algorithm is

What is the difference between the two algorithms?

In the article it says

I don't understand what is meant by this. Can some one please help me to understand this.

Answer 1

SOM uses a set of neurons which are arranged in a predefined structure. In SOM neighborhood is defined based on this structure.This picture shows an example of this structure. SOM two dimentional lattice But Neural Gas (NG) defines the neighborhood based on the distance of neurons in the input(feature) space (No structure exists)

In other words, SOM does ordered vector quantization where as NG does unordered vector quantization. It's something like this: In SOM neurons are labeled with numbers at the beginning for example 1,2,3 and so on. the neighborhood is based on this numbers. for example when 1 is the BMU. 2 is a neighboring neuron. In NG when a neuron is selected as BMU. the neurons that have closest weight vectors to BMU are selected as neighbors.