# Improved Broad Learning System for Birdsong Recognition
## 4 Methods
### Improved Broad Learning System
#### 4.2.2 Improved BLS Based on Residual Block and Mutual Similarity Criterion (RMSC-BLS)  
In this paper, we introduce two modules, residual block and MSC (Mutual similarity criterion) layer, into the BLS to form an improved BLS, named RMSC-BLS. The structure of the model is shown in Figure 4.  
The design of residual block  
The residual block allows the network to learn residual information of the differences between feature nodes and enhancement nodes during the training process by introducing  
Figure 4: The improved BLS model with residual block and MSC.  
Figure 3: Construction of \(d_{square}\) feature.  
skip connections. In this way, the network can adjust the expression of the original features by learning residuals, rather than directly learning the features themselves. The design of the residual module is mainly used between feature nodes (\(Z\)) and enhancement nodes (\(H\)) of BLS, as shown in Formula (8).  
\[NL=(Z\oplus H)|Z \tag{8}\]  
where \(\oplus\) represents residual connection. After obtaining the residual block, the residual block is linearly concatenated with \(Z\) to obtain the Nodes Layer (\(NL\)).  
* Mutual similarity criterion (MSC)  
Nodes in BLS have a direct impact on the network. Through the correlation between the nodes and the class, the features irrelevant to the output are removed, so that the BLS can effectively carry out feature learning. This improves the generalization ability of the model. According to the nodes and class \(c\) combined with the cosine similarity, it is called MSC (Mutual similarity criterion), and can be expressed as:  
\[\cos\left(F^{i},c\right)=\frac{F^{i}\cdot c}{\left|F^{i}\right||c|}=\frac{F^{i }\cdot c}{\left\|F^{i}\right\|_{2}\left\|c\right\|_{2}} \tag{9}\]  
where \(F^{i}\) represents the \(i\)-th node in Nodes layer, \(c\) is the sample class. \(\cos\left(F^{i},c\right)\) refers to the cosine similarity between each node and class. \(\left\|\cdot\right\|_{2}\) is the Frobenius norm of the matrix. Due to \(cos\left(F^{i},c\right)\in[-1,1]\), the closer the cosine values of \(F^{i}\) and \(c\) are to 1, the higher the correlation between the nodes and \(c\). During the node selection process, the correlation between \(F^{i}\) and \(c\) is computed using the cosine theorem, and the correlations are ranked. Subsequently, the top \(k\) nodes are chosen from MSC layer to form the node subset (\(Ns\)). This obtained node subset is then entered into the output layer of BLS to establish a birdsong classification model. The major steps of the proposed RMSC-BLS are summarized in Algorithm 1.  
```
Input: training set [X, Y], number of feature nodes \(n\), number of enhancement nodes \(m\), node subset \(Ns=\varnothing\). Output: Classification result \(\hat{Y}\)
1. for\(i=1;i\leq n\)do
2. Randomly generate \(W_{ei}\) and \(\beta_{ei}\);
3. Calculate \(Z_{i}\) by Formula (1);
4. end // Obtained the feature nodes \(Z\).
5. for\(j=1;j\leq m\)do
6. Randomly generate \(W_{hi}\) and \(\beta_{hi}\);
7. Calculate \(H_{j}\) by Formula (2);
8. end // Obtained the enhancement nodes \(H\).
9. Obtain Nodes Layer (\(NL\)) according to the Formula (8);
10. Calculate correlation for each node in \(NL\) according to the Formula (9);
11. Sort the correlation and select the top \(k\) nodes as nodes subset \(Ns\);
12. Set the input \(A=[Ns|W]\) for BLS;
13. Calculate \(A^{+}\) with Formula (6);
14. Calculate the weight matrix \(W\) with Formula (5);
15. Obtained \(\hat{Y}\) with Formula (3);
16. Output \(\hat{Y}\).
```  
**Algorithm 1**The procedure of RMSC-BLS