# Improving Re-Identification by Estimating and Utilizing Diverse Uncertainty Types for Embeddings
## 4 Experiments
### Simple Score-Level Fusion
#### 4.3.4 Utilizing the Estimated Model Uncertainty to Adjust Feature Vectors  
Adjusting the Feature Vector  
Similarly to the application of data uncertainty in UAL [25], the feature vector can be divided element-wise by the estimated model uncertainty vector. If necessary, a constant \(c\) can be added to the uncertainty vector before it is applied to the feature vector. This is to circumvent the issue of division by small numbers. The adjusted feature vector \(\bar{\mu}^{Q/\mathcal{G}}\) with the model uncertainty employed as standard deviation \(\sqrt{\Sigma^{(M),\mathcal{Q}/\mathcal{G}}}\) is computed as in Equation (31), where \(\odot\) represents the element-wise multiplication. The distance matrix \(D^{\mu,\sqrt{\Sigma^{(M)}}}\) is then computed using the adjusted query feature vectors \(\bar{\mu}^{Q}\) and gallery feature vectors \(\bar{\mu}^{Q}\) as in Equation (32). \[\bar{\mu}^{Q/\mathcal{G}} =\mu^{Q/\mathcal{G}}\odot\frac{1}{\sqrt{\Sigma^{(M),\mathcal{Q}/ \mathcal{G}}}+c} \tag{31}\] \[D^{\mu,\sqrt{\Sigma^{(M)}}} =\mathfrak{d}_{cos}(\bar{\mu}^{Q},\bar{\mu}^{Q}) \tag{32}\]  
In order to find an appropriate value for the constant \(c\), we performed a logarithmic hyperparameter search and selected the value of \(c\) that yielded the best average mAP across all 20 runs. The result achieved with the best identified hyperparameter \(c=0.2435\), is presented in Table 4. We also show the result when the estimated model uncertainty is employed as variance \(D^{\mu,\Sigma^{(M)}}\), which was achieved with the best identified hyperparameter \(c=0.1225\). By employing an appropriate \(c\), identified through hyperparameter search, we observe a notable improvement over UAL [25] for both versions of the estimated model uncertainty used to adjust the feature vector. The performance gain measured by the mAP is 0.44 percentage points on average, which is a greater improvement than UAL [25] achieved over the BOT baseline [66] (0.36 percentage points). Estimating the Hyperparameter \(c\) Based on the Uncertainty Vector  
With the adjustment of the feature vector, we can get a notable improvement in re-identification performance. However, we must perform a hyperparameter search to find an appropriate constant \(c\). Below, we describe how we can compute the value of \(c\) based on the uncertainty vector, in order to eliminate the necessity for a hyperparameter search. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Distance Matrix** & **mAP [\%]** & **rank-1 [\%]** \\ \hline BOT baseline [66] & \(86.41\pm 0.09\) & \(94.42\pm 0.23\) \\ D\({}^{\mu}\) (identical to UAL [25]) & \(86.77\pm 0.14\) & \(94.64\pm 0.21\) \\ D\({}^{\mu,\Sigma^{(M)}}\) & \(87.21\pm 0.17\) & \(94.70\pm 0.17\) \\ D\({}^{\mu,\sqrt{\Sigma^{(M)}}}\) & \(87.20\pm 0.17\) & \(94.70\pm 0.21\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Validation: Can the estimated model uncertainty vector be used to adjust the feature vector? \begin{table}
\begin{tabular}{c c c} \hline \hline
**Distance Matrix** & **mAP [\%]** & **rank-1 [\%]** \\ \hline BOT baseline [66] & \(86.41\pm 0.09\) & \(94.42\pm 0.23\) \\ D\({}^{\mu}\) (identical to UAL [25]) & \(86.77\pm 0.14\) & \(94.64\pm 0.21\) \\ D\({}^{\mu}\)\(\otimes\)M & \(86.80\pm 0.14\) & \(94.72\pm 0.18\) \\ D\({}^{+M}\) & \(86.74\pm 0.14\) & \(94.73\pm 0.18\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Validation: Can simple score-level fusion of the model-uncertainty-based re-identification and feature-vector-based re-identification yield improvements?Furthermore, this offers the advantage, that \(c\) is not required to be a constant, and can rather be computed individually for each input based on the estimated uncertainty. The basic observation that led us towards deriving a formula for calculating \(c\) based on an uncertainty vector was that the best value \(c=0.2435\) for the standard deviation version of the estimated model uncertainty was approximately twice the best value \(c=0.1225\) for the variance version of the estimated model uncertainty.