## 3 Inter-Floor Noise Classification
### Convolutional Neural Network-Based Classifier
(**a**) A signal from a detected onset position (\(\triangle\)) \(\mathbf{s}\) is converted to a log-scaled Mel-spectrogram \(\mathbf{P}\). \(\mathbf{P}\) is provided to the three input channel of the feature extractor \(f_{\mathbf{\Theta}}(\cdot)\) then pseudo probabilities of categories in a label space for a given input \(\mathbf{\hat{y}}\) are predicted. (**b**) The one-dimensional CNN computes one-dimensional convolution directly on \(\mathbf{s}\) and summarizes the signal. where \(\mathbf{F}\) is a Mel-filterbank, which changes the scale of frequency to the Mel-scale. The maximum frequency of the filterbank is set as \(5\) kHz, because most of the signals in the dataset exist below this frequency, and other inter-floor noise studies deal with frequency ranges below \(5\) kHz [57; 58]. The scale of the entries of \(\mathbf{M}\) is also rescaled to obtain a log-scaled Mel-spectrogram, as follows:  
\[\mathbf{P}=10\log\bigl{(}\mathbf{M}/\max\bigl{(}\mathbf{M}_{ij}\bigr{)}\bigr{)}. \tag{8}\]  
VGG16, the two-dimensional convolutional layers and fully connected layers employed in this work, was originally designed for image-recognition tasks. It has three input channels for the reception of a batch of color images, followed by 13 convolutional layers and three fully connected layers. Because a single two-dimensional feature is obtained via conversion of an inter-floor noise event to \(\mathbf{P}\), the feature is given to all channels to train the weights \(\mathbf{\Theta}\) of the CNN and to test a trained CNN. As described in Section 2, the datasets obtained in this study are sparse compared to those adopted in other data-driven approaches. The \(\mathbf{\Theta}\) was initialized with weights pre-trained on a large-scale dataset (ImageNet) [59] to mitigate the problems originating from data sparsity. This can be viewed as transfer learning [60], which has already demonstrated its effectiveness in the image domain [61], as well as for inter-floor noise classification [9; 10]. The image and the sound representations of the inter-floor noise data are considered different. However, the inter-floor noise events are converted to image-like representations \(\mathbf{P}\) and used. Although the datasets are from different domains, low-level notions such as edges and shapes can be shared to learn distribution of a new task [48]. ImageNet is a large-scale dataset and adopted in transfer learning studies. Knowledge obtained from a large dataset has a higher chance to have sharable low-level notions than that via learning from scratch on a sparse dataset. In addition, it can prevent the over-fitting and contribute to the generalization. Use of low-level notions from a totally different domain knowledge and their performance improvements were presented [61; 62]. In addition, use of a large-scale dataset also studied in low-shot learning [63]. This learns the metric using a large dataset and test it against unseen data. The output size of VGG16 is already given as 1000 by the source task, which is classification of ImageNet. It needs to be reduced to the size of the label space of a target \(\text{Dim}(\mathcal{Y}_{T})\). This was realized by adopting an additional fully connected layer, called the adaptation layer, with a reduced number of nodes \(n=\text{Dim}(\mathcal{Y}_{T})\). The weights between the last layer of VGG16 and the adaptation layer \(\theta\in\mathbb{R}^{1000\times n}\) were initialized as random numbers following a normal distribution with a standard deviation of 0.01 [50; 51; 64]. The bias of the adaptation layer is initialized as \(1\)[50]. The pseudo-probability of \(n\) categories \(y_{i}\in\mathcal{Y}_{T}\), \((i=1,\cdots,n)\) for a given input \(\mathbf{P}\) is represented as \(\hat{\mathbf{y}}\in\mathbb{R}^{n}\).