# Augmentation Embedded Deep Convolutional Neural Network for Predominant Instrument Recognition
## 3 The Proposed AEDCN Methods
### AEDCN Model Details  
The proposed AEDCN consists of two main components:  
1. Multi-task deep instrument recognition backbone neural network: The backbone deep neural network contains multiple convolutional layers, pooling layers, two fully connected layers, and an output layer for classification. To introduce label augmentation, an auxiliary classifier is integrated into the backbone neural network. This involves adding an extra classification layer to the network that predicts auxiliary labels. The purpose is to recognize augmented labels during training, which in turn enhances the model's generalization capability. The input of the multi-task deep instrument recognition backbone neural network is the concatenated two-channel spectrogram, the structure of this network is shown in Table 1.  
In this backbone, we use filters with a 3 \(\times\) 3 receptive field, with a fixed stride size of 1, and spatial abstraction is conducted by max-pooling with a size of 3 \(\times\) 3. In Table 1, we list the detailed network structure. It should be pointed out that the input for each convolution layer is zero-padded with 1 \(\times\) 1 to preserve the spatial resolution regardless of input window size. To effectively train the backbone neural network and maximize the inter class distance between features as much as possible, we introduce a center loss as a regularization term to the loss function. The loss function of the backbone neural network is written as:  
\[Loss=Loss_{pricipal}+Loss_{auxiliary}+Loss_{ACEVAE}+\alpha(Loss_{center\_ loss1}+Loss_{center\_ loss2}) \tag{1}\]  
\(Loss_{pricipal}\) and \(Loss_{auxiliary}\) are the classification loss, they are expressed as cross entropy functions. \(Loss_{center\_loss1}\) is a center loss function of the first fully connected layer, which has been used in the CNN [10], and \(Loss_{center\_loss2}\) is a center loss function of the second fully connected layer. \(\alpha\) is a hyper-parameter (0.01 in this paper). Using the center loss to encourage feature separation in the first fully connected layer can be beneficial when training ACEVAE. The center loss aims to minimize the intra-class variations and maximize the inter-class distances of the learned features. By leveraging the center loss, the features corresponding to different types of instruments in the first fully connected layer become more discriminative and separated. This separation allows ACEVAE to generate more diverse and distinct augmented samples for each instrument class. ACEVAE takes these feature vectors as inputs to learn the underlying distribution of instrument features and generate augmented samples that align with the desired instrument classes. This approach helps to enhance the quality and diversity of the generated samples, leading to improved instrument recognition performance. Embedded data augmentation method ACEVAE:  
The second part of the AEDCN is the designed ACEVAE. The ACEVAE is a special type of Variational AutoEncoder that is capable of generating specific types of instrument features based on designated labels and an adversarial loss.