# A Personalised Emotion-Based Model for Relaxation in Virtual Reality
## Experimental Evaluation
### Results
#### 5.2.1 Performance Analysis  
The purpose of this first analysis is to assess the performance of the personalised relaxation model. For this, the default heuristic order configuration (dog, fire, natural lighting, artificial lighting, controlled breathing on, controlled breathing off, music, light colour) is taken and we evaluate the 12 user profiles.  
The evolution of the emotional state in the simulations for the outdoor and indoor environments are shown in Figures 10 and 11 respectively. The plots show the evolution of the different emotional parameters with every adaptation in the environment. The adaptations are shown on the \(x\)-axis while the four emotions are presented on the \(y\)-axis. While the most important emotion is relaxation (which needs to be maximised), the other parameters, fear, stress and arousal are also interesting to the observer as these need to decrease. For some of the users, not all possible adaptations appear. This is due to the profile of these users which prevents these adaptations form being used.  
The initial emotion state is observed at init and is the same for every user. The emotional state at time step start depends on the user itself. At this time step environment is generated and initial values for the adaptations are calculated, these have an impact on the emotional state already as shown in each plot. In the case where the user has the dog adaptation, this will be activated at time step start, this is indicated in the plots as well.  
Figure 10: Plots showing the evolution of the emotional states at each time step for the outdoor environment. The heuristic optimiser applies the adaptations in the same order for each user.  
For every simulated user in the outdoor environment the maximum relaxation of \(1\) is reached. While the stress parameter disappears (value of \(0\)) in every simulation as well, the others, fear and arousal, do not always reach their minimum. Fear never reaches \(-1\). Similarly, arousal is also never completely gone. However, these sub-optimal final emotional parameters do not have an impact on the final relaxation parameter as they are counteracted by the high evaluation of the preference functions.  
In the case of the indoor environments, for every user, the relaxation increases significantly over the duration of the simulation. However, in many cases, the optimal value of \(1\) is not reached. In those cases, the arousal value does not approach \(0\) which could be the reason for the sub-optimal result. In some cases (Users \(2_{in}\), \(3_{in}\), \(4_{in}\) and \(6_{in}\)) fear does not reach its minimal value of \(-1\), however, this does not seem to impact the final relaxation too much either. Finally, the relaxation curve shows slight reductions for users \(3\), \(5\) and \(7\) suggesting relaxation cannot be reached through a greedy approach, in other words, local optima in the curve are not to be considered as a global optimum.  
These simulations indeed show how, even with a fixed order for activating the adaptations, near-optimal relaxation can be researched. Additionally, the heuristic optimiser can find a solution which leads to an acceptable final relaxation. However, it is also clear that maximising relaxation is not sufficient in every case. The other emotions should be minimised as much as possible to reach perfect relaxation. This could potentially be achieved by changing the order of the adaptations.