## 3 Proposed Approach
### Late Fusion  
For the final prediction of our system, late fusion [29] was employed. This technique is mainly used in multi-view learning, and combines information from multiple views of a dataset in order to improve the accuracy of a machine learning model.  
Figure 4: Diagram of the CNN\({}_{782}\) convolutional network used in our experiments, with two successive convolution and max-pooling layers.  
Figure 5: Diagram of the CNN\({}_{392}\) convolutional network used in our experiments.  
Figure 6: Diagram of the CNN\({}_{16384}\) convolutional network used in our experiments.  
In multi-view learning, data are represented by multiple \"views\" or \"modalities\" that contain different information about the same underlying entities. For example, in image classification one view could be the raw pixels of the image, while another view could be a set of hand-crafted features extracted from the image.  
Late fusion involves training separate models on each view of the data, then combining their predictions in a later stage. This can be done using a variety of techniques, such as averaging, voting, or weighted combinations.  
The intuition behind late fusion is that each view contains complementary information about the underlying entities, meaning that combining them can lead to more accurate predictions.  
In our work, the MFCC and the spectogram constitute the two modalities of a sound track, providing complementary information on the characteristics of the latter. Our purpose is to exploit this information by combining the predictions of two models, each operating on one of these modalities. Our approach consists of learning a convolutional model using the MFCC representation of the sounds and another convolutional model using the spectrogram representation of these sounds. After these two models are learned, the sounds in the training set are represented by a vector made up of the outputs of these two models. Each output is a class probability membership corresponding to a floor. Finally, a third model is learned in order to find the association between the predictions of these two initial models and the desired outputs associated with the sounds. This procedure is shown in Figure 7.  
It should be noted that other decision fusion techniques have been proposed recently to combine the decisions made by multiple classifiers. Among them, Alpha integration [30] has been applied to a variety of applications, for example, the classification of archaeological ceramics using ultrasound [31].  
In comparison, late fusion involves independently making decisions with each classifier and then combining them at the end of the classification process, while Alpha integration involves fusing the decisions of the classifiers at an earlier stage by considering the degree of agreement between them. Alpha integration assigns a weight to each classifier based on its performance on the training data and the level of agreement among the classifiers. This weight is then used to combine the decisions of the classifiers, with greater weights assigned to classifiers that are more accurate and have higher agreement with the other classifiers.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **Params** \\ \hline CNN392 & 29 k \\ CNN782 & 227 k \\ CNN16384 & 8 M \\ \hline \hline \end{tabular}
\end{table}
Table 1: The number of parameters of the different models.  
Figure 7: Our strategy of merging the decisions of each convolutional network using the MFCC or Sound Spectrogram representation.  
Alpha integration can lead to better results than late fusion when the classifiers are highly correlated and have high agreement. However, it requires more computation and may be more complex to implement.