# Non-Uniform Input-Based Adaptive Growing Neural Gas for Unstructured Environment Map Construction
## 3 Agng-Nu
### Adaptive Adjustment Mechanism of Neuron Parameters  
As the parameters \(eb\) and \(en\) for adjusting the position of the neuron node are fixed values, they cannot be adjusted quickly and reasonably with the positional relationship of the input samples. Therefore, an adaptive adjustment mechanism of neuron parameters is proposed to make the node position more suitable for the environment input description so as to form a more reasonable topology between nodes.  
The degree of parameter dynamic adjustment is related to the cyclic adjustment mean, that is, the sum of the squares of the position differences between the winning node and its neighbors to the actual input sample divided by the total number of nodes. The cyclic adjustment mean value can be determined by Formula (10).  
\[L_{average}=\frac{\sum\limits_{i=1}^{Size of\ Neighborhood}\|S_{1\_Neighbors}(i)-\xi\|^{2}+\|S_{1\_nodes}-\xi\|^{2}}{Size of\ Neighborhood+1} \tag{10}\]where _Size of Neighborhood_ represents the number of nodes with the edge connected to the winning neuron, \(S_{1\_Neighbors}(i)\) represents the \(i\)th neuron connected to the winning neuron, \(S_{1\_nodes}\) represents the winning neuron node, and \(\zeta\) is the actual input sample point.  
```
Input: connecting edge vector \(edges\), connecting edge age vector \(ages\), node position vector \(nodes\), winning node \(s_{1}\), second closest node \(s_{2}\), points \(s_{1\_Neighbors}\) connected with \(s_{1}\) and the number of the points \(Size\)\(Of\)\(Neigh\)\(\_\) Output: connecting edge vector \(edges\)
1: FOR \(1\leq k1\leq SizeOf\)\(Neighbors\) DO
2: \(ages(s_{1\_N}(k1),s_{1})=ages(s_{1\_N}(k1),s_{1})+1\)
3: \(ages(s_{1\_N}(k1))=ages(s_{1\_N}(k1),s_{1})\)
4: END FOR
5: IF \(edges(s_{1},s_{2})=0\) THEN
6: \(edges(s_{1},s_{2})=1\)
7: \(edges(s_{2},s_{1})=1\)
8: \(ages(s_{1},s_{2})=0\)
9: \(ages(s_{2},s_{1})=0\)
10: END IF
11: Calculate \(max\_age_{s_{1}}\) according to Formula (9)
12: FOR \(1\leq k1\leq SizeOf\)\(Neighbors\) DO
13: IF \(ages(s_{1},s_{1\_N}(k1))>max\_age_{s_{1}}\) THEN
14: \(edges(s_{1},s_{1\_N}(k1))=0\)
15: \(edges(s_{1\_N}(k1),s_{1})=0\)
16: \(ages(s_{1\_N}(k1))=\) NaN
17: \(ages(s_{1\_N}(k1),s_{1})=\) NaN
18: END IF
19: END FOR
20: RETURN \(edges\)
```  
**Algorithm 1** Connecting edge adjustment method based on dynamic response deletion mechanism  
In the stage of adaptive adjustment of neuron parameters, the value of the parameter \(eb_{i}\) which used to adjust the winning neuron to move to the actual input sample is determined by the ratio of the position distance between the winning node and the actual input sample point to the cyclic adjustment mean, as shown in Formula (11); the parameter \(en_{j}\), used to adjust neighbor nodes to move to the actual input sample, is determined by the ratio of the distance between the neighbor nodes to the actual input sample to the cyclic adjustment mean, as shown in Formula (12).  
\[eb_{i}=eb\times\alpha^{\frac{\|w_{i}-\zeta\|^{2}}{strong}} \tag{11}\]  
where \(\alpha\) is the adjustment parameter of the winning node, and the value is around \(1\); \(w_{i}\) is the \(i\)th winning neuron node.  
\[en_{j}=en\times\beta^{\frac{\|w_{j}-\zeta\|^{2}}{strong}} \tag{12}\]  
where \(\beta\) is the adjustment parameter of the neighbor node, and the value is around \(1\); \(w_{j}\) is the \(j\)th neighbor node connected to the \(i\)th winning neuron.  
Algorithm 2 demonstrates the neuron coordination and adjustment method based on the adaptive adjustment mechanism of neuron parameters. Lines 1 to 3 show finding the two closest points to the input node and all nodes connected to the winning node, reflecting the coordination mechanism of neurons; lines 4 to 10 show neuron adaptive adjustment method so that the winning node and its topological neighbors adaptively move towards the environment input sample point.