# CoreTemp: Coreset Sampled Templates for Multimodal Mobile Biometrics
## 5 Experiments
### Ablation Study  
Sampling Ratio  
A core parameter in greedy coreset sampling is the sampling rate, denoted as \(p\) in Section 4.2. The fundamental objective for its employment is to efficiently yet effectively represent the data distribution with a minimal set of representative samples. This is \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline  & & & \multicolumn{2}{c}{**HMOG**} & \multicolumn{2}{c}{**BBMAS**} & \multicolumn{2}{c}{**BBMAS**} \(\rightarrow\) & \multicolumn{2}{c}{**HMOG**} & \multicolumn{2}{c}{**HMOG**} \(\rightarrow\) & \multicolumn{2}{c}{**BBMAS**} \\ \cline{3-11}
**Model** & **Coreset** & **Fast Match** & **Rank1 (\(\uparrow\))** & **Rank5 (\(\uparrow\))** & **Rank1 (\(\uparrow\))** & **Rank5 (\(\uparrow\))** & **Rank1 (\(\uparrow\))** & **Rank5 (\(\uparrow\))** & **Rank1 (\(\uparrow\))** & **Rank5 (\(\uparrow\))** \\ \hline LSTM & ✓ & & & 63.12\({}_{\pm 14.48}\) & 84.01\({}_{\pm 15.87}\) & 75.14\({}_{\pm 14.20}\) & 94.14\({}_{\pm 9.81}\) & 61.37\({}_{\pm 20.57}\) & 82.78\({}_{\pm 21.93}\) & 81.64\({}_{\pm 5.71}\) & 92.07\({}_{\pm 8.14}\) \\  & ✓ & ✓ & & 60.79\({}_{\pm 15.67}\) & 79.85\({}_{\pm 9.96}\) & 72.57\({}_{\pm 4.28}\) & 85.67\({}_{\pm 10.10}\) & 58.38\({}_{\pm 21.74}\) & 78.12\({}_{\pm 21.68}\) & 79.94\({}_{\pm 5.82}\) & 87.05\({}_{\pm 8.45}\) \\ \hline Transformer & ✓ & & & 85.38\({}_{\pm 12.32}\) & 91.06\({}_{\pm 7.37}\) & 89.33\({}_{\pm 7.53}\) & 98.61\({}_{\pm 0.72}\) & 84.85\({}_{\pm 17.60}\) & 90.43\({}_{\pm 10.13}\) & 90.41\({}_{\pm 7.32}\) & 98.75\({}_{\pm 0.60}\) \\  & ✓ & ✓ & & 85.38\({}_{\pm 12.32}\) & 91.06\({}_{\pm 7.37}\) & 89.33\({}_{\pm 7.53}\) & 98.61\({}_{\pm 0.72}\) & 84.43\({}_{\pm 18.29}\) & 90.27\({}_{\pm 9.95}\) & 90.41\({}_{\pm 7.32}\) & 98.75\({}_{\pm 0.60}\) \\ \hline PIEformer & ✓ & & & 87.41\({}_{\pm 11.89}\) & 92.61\({}_{\pm 5.45}\) & 92.23\({}_{\pm 6.33}\) & 98.24\({}_{\pm 0.61}\) & 86.93\({}_{\pm 18.22}\) & 92.08\({}_{\pm 8.26}\) & 94.27\({}_{\pm 7.59}\) & 98.60\({}_{\pm 0.27}\) \\  & ✓ & ✓ & & 87.41\({}_{\pm 11.89}\) & 92.61\({}_{\pm 5.45}\) & 92.23\({}_{\pm 6.33}\) & 98.24\({}_{\pm 0.61}\) & 86.48\({}_{\pm 18.10}\) & 91.94\({}_{\pm 8.69}\) & 94.27\({}_{\pm 7.59}\) & 98.60\({}_{\pm 0.27}\) \\ \hline PIEformer+ & ✓ & & & 88.69\({}_{\pm 11.31}\) & 97.42\({}_{\pm 2.41}\) & 98.03\({}_{\pm 4.72}\) & 98.99\({}_{\pm 0.67}\) & 88.37\({}_{\pm 17.42}\) & 97.22\({}_{\pm 5.38}\) & 98.78\({}_{\pm 5.54}\) & 99.01\({}_{\pm 0.32}\) \\  & ✓ & ✓ & & 88.69\({}_{\pm 11.31}\) & 97.42\({}_{\pm 2.41}\) & 98.03\({}_{\pm 4.72}\) & 98.99\({}_{\pm 0.67}\) & 88.29\({}_{\pm 18.19}\) & 97.19\({}_{\pm 5.64}\) & 98.78\({}_{\pm 5.54}\) & 99.01\({}_{\pm 0.32}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the PIEformer+ with time sequence models for identification, namely, LSTM, Transformer, and PIEformer. Data configurations aligned with notations and explanations in Tables 2 and 3. Figure 4: CMC curve of Transformer, PIEformer, and PIEformer+. Best viewed in color. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & & \multicolumn{2}{c}{**HMOG**} & \multicolumn{2}{c}{**BBMAS**} \\ \cline{3-6}
**Coreset** & **Fast Match** & **Authentication** & **Identification** & **Authentication** & **Identification** \\ \hline  & & 0.54 & - & 0.49 & - \\  & ✓ & 0.07 & 3.68 & 0.04 & 2.07 \\ ✓ & ✓ & 0.02 & 1.92 & 0.02 & 1.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Time required to authenticate a single sample with PIEformer+. Reported in microseconds. achieved by a greedy algorithm that aims to cover the maximum variance of the data with the least redundancy, with detailed steps given in Sections 3.2 and 4.2. Here, we ask the technical question of finding the adequate percentage (\(p\)), where a coreset that is too small risks missing the critical nuances of the data distribution. At the same time, a coreset that is too large unnecessarily increases computation time without substantial gains in performance.