WSN–SOM results have lower quantization and topographic errors compared with the MATLAB SOM toolbox solutions as shown in Table 5. This means that the WSN–SOM can better represent the original data: weight vectors for BMUs of the WSN–SOM are closer (in the Euclidean distance sense) to the original data patterns than those obtained through the MATLAB SOM toolbox solution. Using the MATLAB SOM toolbox, there are four patterns that are mapped to the same BMU with at least another different pattern, while there is only one such double-representation by a single BMU in the WSN–SOM solution.
4. Complexity and scalability
Attributes of the proposed WSN–ANN architecture with respect to computational and message complexity, and scalability are of interest. Specifically, these attributes include ability of the WSN–ANN to scale with the problem size, the computational complexity in space and time, and the communications or messaging complexity. It is relevant to note that computational complexity aspects of artificial neural networks are an area that is largely incomplete and fragmented although there have been advances during the last decade [58]. One major challenge is the fact that there are too many neural network paradigms, learning algorithms and countless parameters to consider for a unified and coherent treatment of the subject. Therefore computational complexity analysis is only feasible for specific artificial neural network, training algorithm, and problem domain choices. Furthermore, in the case of WSN–SOM realization, various aspects of the sensor network such as the topology, and wireless protocol stack also become relevant factors affecting the complexity aspects of the design.
The SOM neural network algorithm employed in the simulation study is described in Fig. 11 to serve as a reference point for the forthcoming complexity analysis. Next, space, time and communication (messaging) complexity analyses for the WSN–SOM design will be presented, where N (short for NOL), P, and K (=tTE) represent the number of neurons, the number of training patterns, and the number of training iterations or epochs, respectively. This is followed by a discussion on the scalability of the proposed WSN–SOM design.