# Sound Event Detection Using Derivative Features in Deep Neural Networks
## 1 Introduction  
Humans can obtain information about their surroundings from nearby sounds. Accordingly, sound signal analysis, whereby information may be automatically extracted from audio data, has attracted considerable attention. The Detection and Classification of Acoustic Scenes and Events (DCASE) 2013-2020 challenges have greatly contributed to increasing the interest in this area, and several competition tasks have been defined. Among these tasks, sound event detection (SED) is aimed at identifying both the existence and occurrence times of the various sounds in our daily lives [1]. It has several applications, such as surveillance [2; 3], urban sound analysis [4], information retrieval from multimedia content [5], health care monitoring [6], and bird call detection [7]. Recently, deep neural networks (DNNs) have demonstrated superior performance to that of conventional machine learning techniques in image classification [8], speech recognition [9], and machine translation [10]. In [11; 12; 13], it was demonstrated that the feedforward neural networks (FNNs) outperformed the traditional Gaussian mixture model and support vector machines in SED. Therefore, current studies on SED primarily focus on DNN-based approaches. Owing to their fixed interlayer connections, FNNs (which are the basic architecture of DNNs) cannot effectively handle signal distortions in image classification. The same phenomenon may occur in SED, which generally uses a two-dimensional time-frequency spectrogram as input to the FNN. Moreover, FNNs have limitations in modeling the long-term time-correlation of the sound signal samples. Accordingly, FNNs are not widely used in SED. Convolutional neural networks (CNNs) have exhibited superior performance to that of FNNs in various recognition tasks, including SED [11]. By using two-dimensional filters, the parameters of which are shared along the time and frequency shift, CNNs can efficiently handle audio signal distortions in the time-frequency domain [12]. However, CNNs are not suitable for modeling the time correlations of audio signals. Recurrent neural networks (RNNs), such as gated recurrent neural networks (GRUs) and long short-term memory, have been successfully used in speech recognition [14]. They can efficiently model the long-term time-correlations in time-series signals, and thus they are expected to facilitate SED. The recently proposed convolutional recurrent neural networks (CRNNs), which combine CNNs and RNNs, have exhibited satisfactory classification performance in SED [11]. They are currently recognized as a highly effective deep neural network architecture in SED and have been widely used in the DCASE challenge since 2018. As SED becomes more demanding, larger amounts of training data are required. However, owing to the high cost of gathering strongly labeled data, weakly labeled data are widely used instead. In recent DCASE challenges, weakly labeled and unlabeled data were provided as the training data for CRNNs. Although CRNNs perform quite well in SED, they generally assume strongly labeled training data and are not robust against weakly labeled and unlabeled training data. Recently, attention-based neural networks have been widely used in speech recognition, vision classification and machine translation [15; 16; 17; 18]. In some studies, improved sound classification results have been obtained by using an attention mechanism in the deep neural network. In [19], an attention scheme was incorporated into a deep CRNN, and improved performance was exhibited on a weakly labeled SED task. The attention method was effective in identifying sound events from audio recordings, including noisy sounds. Owing to their availability, unlabeled data are critical for improved SED. In [20], for efficient use of unlabeled training data, a mean-teacher model based on an attention-based CRNN was proposed for SED and it showed the best performance in DCASE challenge 2018. The architecture and training method of this model is designed to be suitable for unlabeled training data [21].