# Metric Embedding Learning on Multi-Directional Projections
## 4 Results
### Discriminative Ability
The effects of multi-class pretraining are shown on the subfigure (a) by visualizing the pretraining loss and the measured loss during metric learning. As clearly visible, all three applied models and inputs, including the projection profile matrices, are showing signs of similar behavior on model fitting. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & **Pretraining** & **Architecture** & **Mining** & \multicolumn{8}{c}{**N-Way**} \\ \cline{4-13}  & & & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \multirow{6}{*}{Original 128 \(\times\) 128} & Yes & Siamese & & 100.0 & 98.3 & 96.4 & 95.6 & 93.7 & 92.2 & 90.9 & 90.4 & 88.8 & 89.9 \\  & Yes & Triplet & Semi-hard & 100.0 & 94.8 & 87.7 & 86.0 & 83.9 & 80.5 & 82.0 & 75.6 & 77.5 & 74.2 \\  & Yes & Triplet & Hardest & 100.0 & 95.7 & 92.5 & 91.1 & 86.7 & 82.4 & 81.0 & 80.2 & 76.9 & 75.3 \\  & No & Siamese & & 100.0 & 98.2 & 97.5 & 94.9 & 94.7 & 92.3 & 93.6 & 90.1 & 87.8 & 89.5 \\  & No & Triplet & Semi-hard & 100.0 & 94.7 & 93.4 & 88.0 & 86.7 & 83.5 & 83.3 & 79.8 & 80.1 & 76.7 \\  & No & Triplet & Hardest & 100.0 & 95.8 & 91.0 & 87.1 & 87.7 & 84.5 & 80.4 & 80.6 & 78.3 & 76.1 \\ \hline \multirow{6}{*}{Highlighted 96 \(\times\) 96} & Yes & Siamese & & 100.0 & 97.5 & 94.7 & 94.0 & 94.5 & 90.5 & 91.6 & 89.7 & 88.0 & 86.5 \\  & Yes & Triplet & Semi-hard & 100.0 & 90.3 & 83.8 & 81.3 & 77.3 & 72.4 & 68.2 & 68.2 & 65.1 & 60.4 \\  & Yes & Triplet & Hardest & 100.0 & 94.1 & 86.3 & 85.9 & 81.2 & 78.1 & 77.6 & 71.7 & 68.1 & 69.8 \\  & No & Siamese & & 100.0 & 94.9 & 92.8 & 91.1 & 88.8 & 84.9 & 83.4 & 84.2 & 79.8 \\  & No & Triplet & Semi-hard & 100.0 & 81.9 & 70.3 & 65.7 & 61.4 & 57.2 & 52.1 & 49.1 & 45.0 & 46.3 \\  & No & Triplet & Hardest & 100.0 & 90.4 & 83.0 & 80.5 & 76.4 & 68.9 & 70.6 & 66.1 & 64.2 & 64.2 \\ \hline \multirow{6}{*}{MDIPFL 50 \(\times\) 37} & Yes & Siamese & & 100.0 & 97.3 & 95.2 & 94.0 & 90.4 & 88.8 & 87.1 & 88.3 & 87.2 & **86.2** \\  & Yes & Triplet & Semi-hard & 100.0 & 92.4 & 87.3 & 86.2 & 81.5 & 77.6 & 75.0 & 76.0 & 69.6 & 70.6 \\ \cline{1-1}  & Yes & Triplet & Hardest & 100.0 & 96.2 & 93.2 & 88.3 & 87.1 & 82.9 & 79.9 & 81.1 & 79.5 & 75.1 \\ \cline{1-1}  & No & Siamese & & 100.0 & 97.7 & 95.1 & 93.9 & 92.7 & 92.2 & 88.0 & 88.1 & 85.9 & **87.3** \\ \cline{1-1}  & No & Triplet & Semi-hard & 100.0 & 80.8 & 72.4 & 66.4 & 61.0 & 54.7 & 54.8 & 50.6 & 45.6 & 42.2 \\ \cline{1-1}  & No & Triplet & Hardest & 100.0 & 94.3 & 91.8 & 87.3 & 83.4 & 80.8 & 79.3 & 77.3 & 77.2 & 75.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The performance of each method for metric learning on the NIST dataset, given by the one-shot classification accuracy on the validation subsets. 1000 classification tasks were evaluated for each measurement. Figure 7: The evolution of loss during different phases of training. Subfigure (**a**) illustrates the measured pretraining loss for the three different inputs and models. (**b**) visualizes the measured loss on Siamese structured training, while (**c,d**) shows the change of triplet loss over training iterations for semi-hard and hardest negative selection, respectively. It is notable, that (**b–d**) use a logarithmic vertical scale for a more detailed representation. Plot (b) of Figure 7 shows the measured loss of Siamese architectured training with and without pretraining for all three inputs. Subfigure (c) and (d) illustrates the same for the Triplet networks, semi-hard and hard negative selections, respectively. In almost all cases, the training of pretrained models is completed in less iterations. Further, convergence of the measured error is smooth, free of outliers. It can be concluded, that pretraining helps to reduce the possibility of volatility during training. The theory is that by learning the basic feature representations of observations and setting the initial parameter values accordingly, the possibility of suboptimal selections are reduced in the embedding learning phase.