## 3 Supervised Learning of Inter-Floor Noises
### Network Architecture  
Figure 4 shows the architecture of the inter-floor noise type/position classifier. The classifier maps an inter-floor noise to a type/position through (1) conversion of an inter-floor noise into a log-scaled Mel-spectrogram, (2) input channels, (3) CNN, (4) adaptation layer, and (5) softmax classifier. In [25], state-of-the-art CNNs for image classification in ILSVRC are examined and applied to audio classification. The models employed in the paper are AlexNet [26], VGGNet [27], and ResNet [28]. AlexNet was the first CNN-based winner in ILSVRC. VGGNet showed better image classification performance with the ImageNet dataset than AlexNet in ILSVRC 2014. ResNet was the winner of ILSVRC 2015 and showed better image classification performance than the other two models. VGGNet and ResNet can be classified based on the number of layers (depth) of their neural networks. VGG16 and ResNet V1 50, which are considered basic models from each group, were used in this study. The inter-floor noises are converted to log-scaled Mel-spectrograms using LibROSA [29] to represent audio samples in 2 dimensions with size of \(H\times W\), where \(H\) and \(W\) denote the height and the width, respectively. In the literature [20; 21; 25; 30; 31; 32], a spectrogram, log-scaled Mel-spectrogram, and Mel-frequency cepstral coefficient are used as input features in ASC. They represent a signal in the TF domain and are acceptable CNN inputs. In our previous study [13], using a log-scaled Mel-spectrogram provided the best performance with the inter-floor noise dataset. Thus, we used a log-scaled Mel-spectrogram in this study. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & **1F0m** & **1F6m** & **1F12m** & **2F0m** & **2F6m** & **2F12m** & **3F0m** & **3F6m** & **3F12m** \\ \hline MB & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 \\ HD & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 \\ HH & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 \\ CD & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 \\ VC & & & & 50 & 50 & 50 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The number of data in the inter-floor noise dataset for 5 types and 9 positions. Figure 4: Architecture of the inter-floor noise type/position classifier. A log-scaled Mel-spectrogram **P** is obtained through the following steps. First, a signal \(\textbf{s}\ \in\ \mathbb{R}^{l}\) is extracted from an audio clip in the inter-floor noise dataset. The sample length \(l\) is set to \(132,300\) samples (3 s in length). Second, **s** is converted to a magnitude of short time Fourier transforms \(\textbf{S}\in\mathbb{R}^{1025\times W}\) using a 2048 points fast Fourier transform with window size of \(\lceil l/W\rceil\) and the same hop size, where \(\lceil\cdot\rceil\) rounds to the next largest integer. Third, a Mel-spectrogram is obtained using  
\[\textbf{M}=\textbf{FS}, \tag{1}\]  
where \(\textbf{F}\in\mathbb{R}^{H\times 1025}\) is a Mel-filter bank with frequency range of \([0,f_{s}/2]\). This converts frequency scale of **S** to the Mel-scale. Finally, **M** is converted to a log-scaled Mel-spectrogram  
\[\textbf{P}=10\log\left(\textbf{M}/m\right), \tag{2}\]  
where \(m\) is the largest element in **M**. \(H\times W\) is given from the input size \(W\times H\times 3\) for a CNN. For example, VGG16 has input size of \(224\times 224\times 3\). Since the three CNNs (AlexNet, VGG16, and ResNet V1 50) are designed for image classification, they have 3 input channels (BGR). To take advantage of the knowledge learned from a large dataset, the weights between the three input channels and the following layer are preserved instead of modifying the input channels to a single channel. Consequently, **P** is supplied to all the channels. Potential of this method against the inter-floor noise dataset was shown in [13] via performance comparison between a CNN with one input channel and VGG16 without knowledge transfer. The three CNNs contain millions of learnable weights.