# Towards Prediction of Immersive Virtual Reality Image Quality of Experience and Quality of Service
## 3 Data Preparation and Evaluation
### Statistical Methods  
We note from the prior Section 2 that subjects \(u\) viewed image \(i\) at different impairment levels \(l\) for a time ranging from \(t_{u}^{s}(i,l)\)-\(t_{u}^{e}(i,l)\). In addition to the media time, EEG data were determined for an individual user's entire session time \(T,t_{u}^{s}\leq t\leq t_{u}^{e}\), which included time before and after the actual media presentation. This approach enables additional evaluation approaches as described in the following for an individual combination of EEG sensor position and a frequency band to maintain clarity in the overall presentation of our approach.  
As the media display invokes EEG potentials trailing between 300 and 500 ms as the result of a stimulus, we initially consider:  
\[\tilde{v}_{u}(i,l)=\frac{\sum_{t=t_{u}^{s}(i,l)}^{t_{u}^{s}(i,l)+500\text{ms} }v(t)}{\sum_{l=t_{u}^{s}(i,l)+500\text{ms}}^{t_{u}^{s}(i,l)+500\text{ms}}\left[ v(1)\
eq 0\right]}. \tag{1}\]  
In other words, we consider the initial 500-ms time from the individual content displays onward by aggregating the individual measurements into a generalized average. The motivation to combine the individual measurement points is provided by the overall setup we employed, which, in its non-clinical approach, is closely aligned with real-world implementation scenarios.  
Figure 3: Overview of the spherical images employed in the SVR scenario. Images were used prior in the evaluation of augmented binocular vision QoE in [2].  
Let \(v^{z}(t)\) denote the generic z-score for a measurement value \(v(t)\) at time \(t\). The z-score is a unit-neutral expression of values in standard deviations from the overall sample mean [28], here for an individual position's single EEG band, as noted above. The z-score, referred to as EEGz, is subsequently determined as:  
\[v^{z}(t)=\frac{v(t)-\bar{v}_{T}}{\sigma(v)}, \tag{2}\]  
whereby \(\bar{v}_{T}\) denotes the overall average for the measurement value (i.e., over \(T\)) and \(\sigma(v)\) denotes its standard deviation.  
We employ logistic regression as the approach underlying the prediction performance evaluation for both QoE and QoS, as both are captured as categorical Likert-type scales in the experimental phase. In our evaluation, we consider the second degree (\(d=2\)) polynomial extension of the original values throughout our prediction efforts, based on our prior findings in [29]. We evaluate different combinations of EEG sensor positions \(p\) as input sources for our evaluations to determine practical device implementation options as follows:  
* All: \(p\in\{1,2,3,4\}\)
* Left: \(p\in\{1,2\}\)
* Right: \(p\in\{3,4\}\)
* Outside: \(p\in\{1,4\}\)
* Inside: \(p\in\{2,3\}\).  
Based on the poor performance of individual measurement points, we found in [2], we here do not consider the individual sensors separately.  
As we perform an evaluation of the possibility to predict the QoE ratings/QoS levels based on the EEG data, let \(\hat{q}^{r}_{u}(i,l)\) denote an estimated QoE rating for an individual image at a specific impairment level presented to the subject under consideration (with the QoS estimation performed similarly). In order to derive a general estimation for the fit of a regression model, a common approach is to consider the \(R^{2}\) coefficient of determination, defined generally here as:  
\[R^{2}=1-\frac{\sum\left(\hat{q}^{r}_{u}(i,l)-q^{r}_{u}(i,l)\right)^{2}}{\sum \left(q^{r}_{u}(i,l)-\bar{q}^{r}_{u}(i,l)\right)^{2}}. \tag{3}\]  
However, the \(R^{2}\) value itself should be put into additional context, such as an evaluation of the actual prediction error. Here, we consider the Mean Absolute Error (MAE). The MAE over a range of sample estimations \(s\) is defined as:  
\[MAE_{u}\left(q^{r}_{u}(i,l),\hat{q}^{r}_{u}(i,l)\right)=\frac{1}{s}\sum\left| q^{r}_{u}(i,l)-\hat{q}^{r}_{u}(i,l)\right|. \tag{4}\]  
Next, we describe how we employ these metrics in our prediction and evaluation approach. We additionally note that this overall process is performed for QoE, QoS and EEG, EEGz combinations in a similar fashion.