# Recognition of Stress Activation by Unobtrusive Multi Sensing Setup
## 6 Results
### Self-Organizing Maps  
We have trained a set of two-dimensional SOMs with several units varying from \(3\times 3\) to \(6\times 6\). We did not consider larger maps due the limited dataset size. Maps were trained on the SRAD dataset. For each map size, training was run ten times with random weight initialization. Apart changes in map orientation, no relevant difference was detected inside each run.  
As we are interested in the topographic representation produced by SOMs, we have analyzed each map with respect to the distance between weights of neighboring units (the so-called U-map), and the distribution in the network space of each weight dimension (weight-plane maps). In addition, to explore the semantic role of unit activation we analyzed the distribution of data labels in network space (categorical hit maps). Since the results do not vary significantly with the number of units, to ease readability, we show only data for \(5\times 5\) SOM.  
Map distances in Figure 6 suggest that the units in the right upper corner are rather apart from the other units that tend to be closer each other. This confirms previous data from feature selection and data clustering, and suggests that the data space can be partitioned into two highly structured clusters. It is worth noting that larger maps are expected to capture finer structural details of data as suggested by the comparison of the maps.  
Figure 5: On the **left**: cluster scatter-plot on the SRAD dataset. On the **right**: clustering evaluated on MCA.  
The distribution of SOM weights (Figure 7) provides additional support to distance maps. In particular, spatial arrangement of weights looks consistent among different map sizes. In addition, several components (e.g., those corresponding to median RR, GSR peak number, LF/HF, NN, LF, and HF ) exhibit a well-defined spatial distribution. In particular, some of them such as the weights of median RR and GSR peak number can be related to the partition appearing the left upper part of the map.  
Categorical hit maps (top of Figure 8) for the rest and activation labels of the SRAD dataset show a rather neat distinction among the two categories: only a few units respond simultaneously to both rest and activation data. In the bottom part of Figure 8, we report the hit maps for rest and activation categories of MCA dataset. These maps exhibit a behavior similar to the case of SRAD data.  
Map units can be a posteriori labeled according to several criteria. For example, using the majority-voting scheme as in [46], we obtain the label map in Figure 9. Comparing MCA hits maps with labels we obtain 3 misclassifications (2 false rests and one false activation). It is worth noting that misclassified patterns are next to units that would correctly classify them. It stands to reason that using larger maps trained on extended data could improve labeling result. On the other hand, majority-voting labeling can be sub-optimal and the use of fuzzy labeling [47] should be preferred.  
Figure 6: Maps of distances between the weight of neighboring units for \(5\times 5\) SOM. Darkest colors indicate largest distance while light colors denote smallest ones.  
Figure 8: Map of winning units according to rest and activation labels. **Top**: data from SRAD dataset, **Bottom**: data for MCA dataset.  
Figure 7: Maps of weight components. Darkest colors indicate smallest values while light colors denote largest ones.  
To summarize, results support that SOM has learned a topographic representation of the input space congruous with _a priori_ data labels.