## 3 Class Imbalance Problem
### Genetic Algorithm Architecture for Class Imbalance Problem
#### 3.4.2 Genetic Operators
```
0: Positive set \(\mid d\mid^{+}\), negative set \(\mid d\mid^{-}\), weak classifier \(I_{1,2}\) (SVM), \(I_{3}\) (neural networks), integer \(T_{a,b,c}=1\) (number of generated classifiers) and the test sample \(x\)
0: Classifier \(C^{*}\)
1: % asymmetric bagging with elite parents for the SVM
2:for\(i\gets 1\) to \(T\)do
3:\(\Theta^{+}\leftarrow\) Genetic Algorithm(\(\mid d\mid^{+}\)) with Elite parents
4:\(\Theta^{+}\leftarrow\) bootstrap samples from \(\mid d\mid^{+}\)
5:\(\Theta^{-}\leftarrow\mid d\mid^{-}\)
6:\(C_{i}=I(\Theta^{+},\Theta^{-})\)
7:endfor
8: % bagging based on tournament selection for SVM
9:for\(j\gets 1\) to \(T_{b}\)do
10:\(\Theta^{+}\leftarrow\) Genetic Algorithm(\(\mid d\mid^{+}\)) with Elite parents \(\mid d\mid^{+}\)
11:\(\Theta^{+}\leftarrow\) bootstrap samples from \(\mid d\mid^{+}\)
12:\(\Theta^{-}\leftarrow\) bootstrap samples from \(\mid d\mid^{-}\)
13:\(C_{j}=I(\Theta^{+},\Theta^{-})\)
14:endfor
15: % asymmetric bagging using the neural networks
16:for\(k\gets k,T_{c}\)do
17:\(S_{k}^{-}\leftarrow\) bootstrap samples from \(\mid d\mid^{-}\)
18:
19:\(\mid d\mid^{+}\leftarrow\mid d\mid^{+}\)
20:
21:\(C_{k}=I(S_{k}^{+},S_{k}^{-})\)
22:endfor
23:\(C^{*}(x)=aggregation\{C_{i,j,k}(x,S_{i,j,k}^{+},S_{i,j,k}^{-}),1\leq i,j,k\leq T _{a,b,c}\}\)
24: % generate the output, and repeat the process in all feedback iterations
```

**Algorithm 5** The relevance feedback algorithm. ### Experimental Details

In our experiments, 300 images are randomly selected and then relevance feedback is automatically performed by the computer. All query relevant images (i.e., images with the same concept as the query) are marked as positive feedback samples and all the other images are marked as negative feedback samples. The current system is tested on top 30 and top 60 images with nine iterations, where the zeroth iteration returns the initial output through a distance measure. The average precision of the 300 query images is used to measure the performance of the RF based image retrieval that can be defined as the ratio of relevant images with respect to the retrieval rate. The proposed RF method is compared against genetically optimized support vector machines (GOSVM) [27], generalized biased discriminant analysis (GBDA) [55], biased discriminant euclideanembedding (BDEE) [4], and direct kernel biased discriminant analysis (DKBDA) [56]. From the results presented in Figures 11 and 12, we can easily observe that the proposed system has outperformed the comparative systems in terms of precision of output, and most importantly the convergence of the proposed method in earlier iterations is far better then the comparative methods, that clearly means that the user will have a better system experience and need to pass from a few feedback rounds to achieve the desired output. ### Genetic Algorithm Evaluation

The objective function used in Equation (18) ensures that the GA receives good features in every generation that results in the form of improved classification performance. In order to justify this argument, we have designed an experiment where we compare the classification performance of the proposed method over COIL and Caltech-101 datasets with and without objective function. In the case when the objective function is not used, then we generate a single chromosome population instead of \(\alpha\) chromosome populations. From the results presented in Figure 13, we can observe that the objective function with \(\alpha\) chromosome populations significantly improves the classification performance. The foremost reason

Figure 11: Comparison of the proposed method in terms of precision on top 30 retrievals against genetically optimized support vector machines (GOSVM), generalized biased discriminant analysis (GBDA), biased discriminant euclidean embedding (BDEE) and direct kernel biased discriminant analysis (DKBDA). Figure 8:0 Comparison of the proposed method in terms of precision on top 60 retrievals against GOSVM, GBDA, BDEE and direct kernel biased discriminant analysis (DKBDA).