Growing the Network

The new unit must be inserted between um and one of the units to which it is connected because the structure of the network as a series of connected simplexes must be maintained. To determine which of the neighbors this is, the weights at each of the direct neighbors are checked and the one whose weights are most different from the weights at um, as measured by the Euclidean distance between them, is selected. The new node is inserted into the network and joined  

To any other nodes that already have connections to both um and to the neighbor 

Finally, the direct connection between um and its neighbor is removed. 

The reason for selecting the unit that is most unlike um is that we require a wide range of weights vectors across the map if it is to adequately represent the full variety of sample patterns. By choosing to average the weights at the 

If the local error is used instead of the signal counter, it is common to set the initial local error at the new unit to the average of the errors at all units to which it is connected  

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At present, it appears that the most productive types of constructive clustering in the physical and life sciences will be the growing neural gas and the GCS methods in this chapter we focus on the latter. Although this method has notable advantages over the SOM, scientific applications of the GCS have only recently started to appear. There is a little more to the method than a SOM because of the need to grow the network as well as train it, but lack of familiarity with the technique rather than a lack of power explains the present paucity of applications in science because GCSs have nearly all the advantages of the SOM with few of the drawbacks. 

When Co grows, the network volume slightly decreases and the concentration of surfactant q within the network increases. When cjj, exceeds a critical concentration of micelle formation (at this point cq = c, see Figs.14,15), the network collapses because the surfactant molecules aggregated in micelles cease to impose osmotic pressure which causes additional expansion of the network. At relatively small values of the ratio Vf/V, the collapse is continuous (Figs. 14, 15), so that the number of surfactant molecules in micelles increases from zero starting at the concentration c. However, when the ratio Vf/V is sufficiently large, a discrete first-order phase transition takes place. 

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