# Non-Uniform Input-Based Adaptive Growing Neural Gas for Unstructured Environment Map Construction
## 4 Simulation Experiments
### Evaluative Indicators  
In the construction of environmental maps, most algorithms are tested based on uniform and randomly distributed input samples. However, in practice, the input sample points in most environments are not uniform, especially for the tunneling section; the density of different sample points can reflect the current state of cutting coal and rock. The dense samples collected indicate that hard points are encountered, and the swing speed of the cutting arm decreases. On the contrary, the sparseness of the collection points indicates that the coal rock has low hardness and is easily cut, and the swing speed of the cutting arm is high.  
In the process of collecting sample points, this kind of non-uniform distribution will be encountered, that is, the environment is unstructured. However, there is no relevant literature that proposes an evaluation index for map construction under non-uniform input environment [8; 24]. Therefore, the evaluation method of map construction is proposed in this paper which is analyzed from the aspects of accuracy and distribution.  
(1) Accuracy  
The accuracy indicator is used to measure the closeness of the current network node to the actual input parameters, and it is evaluated by the mean error of the network. Thesmaller the mean error value, the higher the accuracy of the generated topology network. The calculation formula of accuracy is shown in Formula (13).  
\[RMSE=\frac{\|error\|}{\sqrt{Num\ of\ Nodes}} \tag{13}\]  
where \(RMSE\) is the mean error, \(error\) is the error vector composed by errors of each neuron node, and \(Num\ of\ Nodes\) is the number of network neuron nodes.  
(2) Distribution  
The distribution index is used to evaluate the distribution of the generated network nodes. The denser the environment input is, the more network nodes should be described and the richer the topology structure. Two calculation methods are designed for the distribution index:  
(1) The ratio of the number of connected nodes of each winning neuron node to the total number of points is subtracted from the ratio of the number of input nodes in this area to the total number of input points, and the distribution index is obtained by summing and averaging. The smaller the value, the better the distribution, as shown in Formula (14).  
\[Dist_{1}=\frac{\sum\left|\frac{Size\ of\ Neighborhood\ -\ Size\ of\ Neighborhood\ samples}{max\_nodes}-\frac{Size\ of\ Neighborhood\ samples}{Num\ of\ Samples}\right|}{max\_nodes} \tag{14}\]  
where \(Size\ of\ Neighborhood\) is the number of connected neuron neighbor nodes of the winning neuron node, \(Size\ of\ Neighborhood\ samples\) is the number of input samples in the region, \(\max\_nodes\) is the total number of neuron nodes, and \(Num\ of\ Samples\) is the total number of input samples.  
(2) Divide the overall area into several blocks, calculate the ratio of the number of neuron nodes in this area to its total number, minus the ratio of the number of input nodes in this area to its total number for each block, and the distribution index is obtained by taking the average of the sum. The smaller the value, the better the distribution, as shown in Formula (15).  
\[Dist_{2}=\frac{\sum\left|\frac{Size\ of\ block\ nodes\ -\ Size\ of\ block\ samples}{max\_nodes}-\frac{Size\ of\ \ Number\ of\ Samples}{Num\ of\ Samples}\right|}{max\_block} \tag{15}\]  
where \(Size\ of\ block\ nodes\) is the number of neuron nodes in the divided area, \(Size\ of\ block\ samples\) is the number of input samples in the divided area, \(max\_nodes\) is the maximum number of neuron nodes, \(Num\ of\ Samples\) is the number of input samples, and \(max\_block\) is the number of divided areas.