## 2 Materials and Methods
### Deep Learning Model for Ambient Sound Recognition of Daily Events
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Network Architecture from Model CNN + MFCC**} \\ \hline Input & \(13\times 130\times 1\) \\ Conv(\(3\times 3\)) & \(11\times 128\times 16\) \\ Conv(\(3\times 3\)) & \(9\times 126\times 16\) \\ Conv(\(3\times 3\)) & \(7\times 124\times 32\) \\ Conv(\(3\times 3\)) & \(5\times 122\times 64\) \\ Conv(\(3\times 3\)) & \(3\times 120\times 128\) \\ Conv(\(3\times 3\)) & \(1\times 118\times 256\) \\ GlobalAvgPool2D & 256 \\ Dense & 1024 \\ Dense & 15 \\ \hline \multicolumn{2}{c}{**Network Architecture from Model CNN + LM**} \\ \hline Input & \(128\times 130\times 1\) \\ Conv(\(2\times 2\)) & \(127\times 129\times 16\) \\ Max-Pool(\(2\times 2\)) & \(63\times 64\times 16\) \\ Conv(\(2\times 2\)) & \(62\times 63\times 32\) \\ Max-Pool(\(2\times 2\)) & \(31\times 31\times 32\) \\ Conv(\(2\times 2\)) & \(30\times 30\times 64\) \\ Max-Pool(\(2\times 2\)) & \(15\times 15\times 64\) \\ Conv(\(2\times 2\)) & \(14\times 14\times 128\) \\ Conv(\(2\times 2\)) & \(13\times 13\times 128\) \\ Flatten & 21,632 \\ Dense & 1024 \\ Dense & 1024 \\ Dense & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Network Architecture from models CNN + MFCC and CNN + LM. Figure 3: Example of raw audio signals at 44.1 kHz, log-Mel spectrogram (LM), and Mel-frequency cepstral coefficient (MFCC) of the ambient audio events: cutlery, blind, alarm clock, and door bell. of audio classification in real-time conditions in order to provide temporal restrictions and criteria to identify a given event. The stream of audio recognition from a smart audio sensor \(s^{j}\) is composed of a set of predictions \(s^{j}=\{m_{i}^{j}\}\), where each prediction is represented by \(m_{i}^{j}=\{v_{i}^{j},t_{i}^{j}\}\), where \(v_{i}^{j}\) represents a given audio from a recognised event, and \(t_{i}^{j}\) the time-stamp for the sensor \(j\) in a given time \(t_{i}\). From the sensor streams, we defined _protoforms_ which integrate an interpretable, rich, and expressive approach that models the expert knowledge in the stream linguistically. The protoform is in the shape of the following:  
\[Q_{k}V_{r}T_{j}\]  
where are \(Q_{k}\ V_{r}\ T_{j}\) are identifiers of the following linguistic terms:  
* \(V_{r}\) defines a crisp term, whose value is directly related to a recognised event \(r\). * \(T_{j}\) defines a fuzzy temporal window (FTW) \(j\) where the audio event \(V_{r}\) is aggregated. The FTWs are described according to the distance from the current time \(t^{*}\) to a given timestamp \(t_{i}\) as \(\Delta t_{i}=t^{*}-t_{i}\) using the membership function \(\mu_{T_{j}(\Delta t_{i})}\), which defines a degree of relevance between \([0,1]\) for the time elapsed \(\Delta t_{i}\) between the point of time \(t_{i}\) current time \(t^{*}\). * We defined an aggregation function of \(V_{r}\) over \(T_{j}\) which computes a unique aggregation degree of the occurrence of the event \(V_{r}\) within a temporal window \(T_{j}\). Therefore, the following \(t\)-norm and \(t\)-conorm are defined to aggregate a linguistic term and temporal window: \[V_{r}\cap T_{j}(\tilde{s}_{i}^{j}) =V_{r}(\tilde{s}_{i}^{j})\cap T_{j}(\Delta t_{i})\in[0,1]\] \[V_{r}\cup T_{j}(\tilde{s}_{i}^{j}) =\bigcup_{\tilde{s}_{i}^{j}\subset S^{j}}V_{r}\cap T_{j}(\tilde{s }_{i}^{j})\in[0,1]\] where we use Fuzzy weighted average (FWA) [55] to compute the degree of the linguistic term in the temporal window. In this way, the \(t\)-norm computes the temporal degree for each point of time of the temporal window, and the co-norm aggregates these computed degrees in the whole temporal window in a unique representative degree. * \(Q_{k}\) is a fuzzy quantifier \(k\) that filters and transforms the aggregation degree of the audio event \(V_{r}\) within the FTW \(T_{j}\). The set of quantifiers defined in this domain are represented by the fuzzy sets shown [56]. The quantifier applies a transformation \(\mu_{Q_{k}}:[0,1]\rightarrow[0,1]\) to the aggregated degree of \(\mu_{Q_{k}}(A_{k}\cup T_{j}(S^{r}))\)[57].