# Effect of Probabilistic Similarity Measure on Metric-Based Few-Shot Classification
## 5 Experimental Results
### Multi-PIE Face Recognition  
Figure 5 shows some examples of the Multi-PIE dataset that has been created as a benchmark for facial recognition. A total of 337 subjects participated in data collection, and shooting was conducted in four-time sessions. In the shooting, 20 patterns of lighting effects, 15 poses, and 6 types of emotional expression were mobilized, and over 2000 images were collected per subject in a one-time session. We transform the original data to suit  
\begin{table}
\begin{tabular}{l c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**5-Shot Acc. (\%)**} \\ \cline{2-3}  & **5-Way** & **20-Way** \\ \hline MatchingNet [8] & 98.9 * & 97.0 * \\ RelationNet [10] & 99.6 * & 98.6 * \\ MAML [17] & 99.7 * & 98.7 * \\ ConvNet [19] & 99.6 * & 98.6 * \\ IMP [12] & 99.5 * & 98.6 * \\ ProtoNet [9] & 99.50 ** & 98.40 ** \\ GaussianProtoNet [22] & 99.50 ** & 98.40 ** \\
**Proposed** & **99.71** & **98.71** \\ \hline \hline \end{tabular}
\end{table}
Table 1: The 5-shot classification accuracies on Omniglot data. The values marked with * are quoted from the original works [8; 10; 12; 17; 19], and the ones with ** are measured by experiments using codes provided by the authors [9; 22].  
Figure 4: Change of Classification accuracy on Omniglot data depending on the number of ways (in the case of the Gaussian prototypical network, experiments were possible up to 50 ways with the provided code.).  
the intention of the experiment according to the previous work [32]. The whole image is cropped so that only the face appears as shown in Figure 6. It is then converted to a black and white image and then resized to 28 \(\times\) 28 pixels. The Multi-PIE data have rather simple variations compared to the recent benchmark for face verification. However, considering that this experiment is conducted with the simple convolutional network with the purpose of verifying the effect of the probabilistic similarity, Multi-PIE data are appropriate in the sense that it assorted environmental variations such as illumination, poses, expression, and time sessions.  
The modified dataset consists of a total of 184 classes, and we divide them into 122 training classes and 62 test classes for a few-shot classification problem. The training set contains 600 samples per class, and the test set contains 370 samples per class. For each training episode, 45 queries per class are used. We also should note that each class of Multi-PIE data has much more samples with diverse variations than Omniglot data while only five samples per class are used for support. This may cause some difficulties in estimating the covariance of difference vectors.  
Figure 7 compares the performance of the proposed method using prototypical networks. From the graph, we can see that the proposed method can improve the accuracy by using probabilistic similarity, and the effect of performance improvement appears more clearly as the number of ways increases. This result is consistent with our argument that, as the number of ways increases, the accuracy of the estimation increases and thus more sophisticated classification becomes possible. Recognition performance could be further improved by using a more complex backbone network, but this is somewhat out of the scope of this study. In this experiment, we focused on confirming the effect of probabilistic similarity.  
Figure 5: Original Multi-PIE dataset.  
Figure 6: Modified Multi-PIE image samples used in the experiment.