# Cucumber Leaf Diseases Recognition Using Multi Level Deep Entropy-ELM Feature Selection
## 2 Proposed Methodology
### Entropy-ELM Based Features Selection and Parallel Fusion  
Feature selection is an important and hot research topic nowadays [32]. The main purpose of feature selection is to increase the system accuracy and minimize the computational time by focusing on the selection of the most important features [33]. In this work, a new technique is proposed named Entropy-ELM for the best feature selection. This proposed technique worked in the following steps: (i) compute the entropy of input vector; (ii) based on the entropy value, a threshold function is employed that return two vectors--fulfill the threshold value (selected) and not-selected; (iii) ELM [34] employed as a fitness function and selected threshold passed features are utilized as an input. Mathematically, the entropy formulation is defined as follows:  
\[H_{1}=-\sum_{k=1}^{G}P_{k}ld(P_{k}) \tag{9}\]  
Figure 3: Transfer learning-based training of deep models for cucumber leaf diseases recognition.  
\[H_{diff,1}=-\int\limits_{0}^{1}h_{1}(w)1d[h_{1}(w)]dw. \tag{10}\]  
\[H_{1}=H_{diff,1}+\text{Id}(\text{G})=\ H_{diff,1}+H_{1,max} \tag{11}\]  
\[\iint\limits_{whole\ image}[\Delta w(w,y)]^{k}dxdy\propto\int_{-1}^{1}{(\Delta w )^{k}h_{d}(\Delta w)d\Delta w}=M_{k} \tag{12}\]  
\[T=\ \left\{\begin{array}{ll}\ Sel(k)&for\ Features(i)\ \geq H_{1}\\ NotSelect(l)&for\ Features(i)\ <H_{1}\end{array}\right. \tag{13}\]  
The detail of this selection process is given in Algorithm 2.  
```
Step 1: Input Feature Vector \(N\times K\) // \(K\) is the length of features Step 2: For i = 1 to N Step 3: Computer Entropy through Equations (9)-(12) Step 4: Define Threshold Function as Equation (13) Step 5: Check Fitness through ELM Step 6: Evaluate the Accuracy Step 7: Repeat Step 2-6, until accuracy on the top side End Selected Feature Vector
```  
**Algorithm 2**(Entropy-ELM)  
Finally, the parallel fusion approach is opted to get the fused feature vector. This approach is based on the following three steps. In the first step, get the maximum length feature vector. As we have two feature vectors \(X\) and \(X_{1}\), where the length of vectors is \(N\times K\) and \(N\times K_{1}\), respectively. In the second step, compute the entropy value and perform padding for the lower size feature vector. In the third step, correlation is computed among \(K\) and \(K_{1}\) features for the final fusion. The fused vector is finally utilized for the classification through supervised learning classifiers.  
\[Fusion=\psi(K,K_{1}) \tag{14}\]  
where \(K\) and \(K_{1}\in X\) and \(X_{1}\)  
**3. Experimental Results**  
The proposed framework is evaluated on the selected cucumber dataset having a ratio of 70:15:15 which means that 70% of the images are utilized to train the model, whereas the 15% for testing and 15% for validation. We combined the testing and validation images and performed testing (30%). All the experimental results are computed with K-Fold cross-validation, whereas the value of K is 10. Several classifiers are implemented as discussed in Table 1. The performance of each classifier is computed through several measures such as recall rate, precision rate, F1-Score, accuracy, and time. The entire framework simulations are conducted on Simulink MATLAB2021a using a Personal Desktop.