## 4 Experiments
### Experimental Results  
The training and testing of the models was repeated twenty times, and four performance measures were used for evaluation: Accuracy, Recall, Precision, and F_measurement, calculated on the basis of the confusion matrix \(\mathbf{A}=(a_{ij})_{1\leq i,j\leq 3}\) of the predicted classes of the chunks of the test samples compared to their desired classes as follows. \[\text{Accuracy}=\frac{a_{11}+a_{22}+a_{33}}{\sum_{i=1}^{3}\sum_{j=1}^{3}a_{ij }};\text{Recall}=\frac{1}{3}\sum_{k=1}^{3}\frac{a_{kk}}{\sum_{i=1}^{3}a_{ki}}; \text{Precision}=\frac{1}{3}\sum_{k=1}^{3}\frac{a_{kk}}{\sum_{i=1}^{3}a_{ki}}; \text{F1}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **R + 1** & **R + 3** & **R + 5** & **Total** \\ \hline \multirow{3}{*}{Soundtracks} & Train & 8 & 9 & 10 & 27 \\  & Test & 1 & 1 & 1 & 3 \\  & Total & 9 & 10 & 11 & 30 \\ \hline \multirow{3}{*}{Chunks} & Train & 258 & 268 & 250 & 776 \\  & Test & 19 & 38 & 30 & 87 \\ \cline{1-1}  & Total & 277 & 306 & 280 & 863 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Distribution of soundtracks and chunks by floor. Table 3 presents the Accuracy of the three models learned using the MFCC and the spectrogram of the chunks separately on the training and the test sets. The best performance per modality is shown in bold; \({}^{\downarrow}\) indicates statistically significantly worse performance than the best result according to the Wilcoxon rank-sum test (\(p<0.01\)) [33]. The CNN\({}_{782}\) and CNN\({}_{16384}\) models provide the best results with the Spectogram and MFCC representations, respectively. The CNN\({}_{782}\) model is the second best model when considering the MFCC representation, while CNN\({}_{16384}\) is the worst model with the spectogram representation. The table shows that the CNN\({}_{782}\) model has the best compromise between performance and complexity compared to the two other models. Thus, this model was used in the late fusion approach; two distinct CNN\({}_{782}\) models were trained on the MFCC and spectrogram representations, the outputs of these models were used to represent the sounds, and a third classifier was then trained to combine these predictions for a final classification. This third model used a random forest approach [34], which is one of the most efficient models for classification in cases where the data are represented by vectors. This model learns multiple random trees and combines their results based on majority vote [35]. Table 4 reports the average of the results over twenty training/test runs of this approach. Table 5 presents the confusion matrix of one of these experiments. From these results, it is apparent that the true positives on each diagonal of the confusion matrix are greater than the false positives, meaning that the chunks of the different floors are 100% correctly predicted. This result is the same for the nineteen other experiments, which validates the effectiveness of this approach for automatically determining the floors of a building. Furthermore, these results suggest that by using two views of the sound signal it is possible to combine the outputs of CNN\({}_{782}\) in an efficient manner in order to precisely determine the height of the floors based on their related sound tracks. This paves the way for the use of more elaborate fusion techniques in situations where there are a higher number of floors and a more noisy environment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Accuracy** & **Recall** & **Prec.** & **F1** \\ \hline Random Forest & 0.823 & 0.821 & 0.812 & 0.816 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Late fusion performance on CNN\({}_{782}\) classifier results using MFCC and Spectrograms as two views of sounds.