## 3 Class Imbalance Problem
### Genetic Algorithm Architecture for Class Imbalance Problem
#### 3.4.2 Genetic Operators
The confusion matrix is used in binary classification problems to record the results of correct and incorrect recognitions for a particular classifier through accuracy measure. However, when the data-sets are highly imbalanced the accuracy measure cannot be tuned to verify the performance of a classifier, as it is unable to distinguish the number of correct classifications between the examples of different classes

Figure 8: False positive comparison against ANN and SVM classifiers in terms of false positive rates. Figure 7: Image retrieval comparison against artificial neural networks (ANN) and support vector machines (SVM) classifiers in terms of precision. [14]. Therefore, in the imbalanced domain there are some other appropriate matrices that can be considered to measure the classification performance, i.e., [14]:

\[TP_{rate}=\frac{TP}{TP\ +\ FN},\]

\[TN_{rate}=\frac{TN}{TP\ +\ TN},\]

\[FP_{rate}=\frac{FP}{FP\ +\ TN},\]

\[FN_{rate}=\frac{FN}{TP\ +\ FN},\]

where the \(TP_{rate}\) is the true positive rate (also known as sensitivity) that describes the percentage of the positive instances that are classified correctly, \(TN_{rate}\) is the true negative rate is the percentage of the negative instances correctly classified, \(FP_{rate}\) is the false positive rate (one-specificity) is the number of negative instances misclassified, and similarly \(FN_{rate}\) is the false negative rate is the number of positive instances that are misclassified. As the classification is applied with an intention to improve the results, none of the measures mentioned above are appropriate to measure the classification performance individually. One way to generate the combination of these measures is through the receiver operating characteristic (ROC) curves [14], that allows to view the trade-off between the benefits (\(TP_{rate}\)) and cost (\(FP_{rate}\)). As in our implementation we are performing the image classification by mapping the multi-class problem in the form of multiple binary classification problems, therefore, we have also evaluated the classification performance through the ROC measure. Classification rates of the proposed method are compared against several existing systems of CBIR in terms of area under the ROC curve (AUC). The comparative methods are those of [PERSON] et al. [49], [PERSON] et al. [54], and Ensemble based SVM [42]. Classification performance in terms of ROC curves are plotted in Figures 9 and 10. From the results it can be observed that the classification results of the proposed method are far better then the comparative methods, that clearly shows its reliability and effectiveness. Figure 9: Comparison of average precision versus rate of returned images. ### Relevance Feedback

Relevance feedback (RF) that is incorporated in our system generates the initial output against a query image on the basis of distance. The user gives the initial feedback by selecting only the relevant or the positive images in the returned output, and the remaining images are considered as negative feedbacks. Asymmetric bagging and symmetric bagging procedures as already described

Figure 10: Performance evaluation of the proposed method with other standard content-based image retrieval (CBIR) systems [PERSON] et al. [49], [PERSON] et al. [54], and Ensemble based SVM (EMSVM) [42] using the receiver operating characteristic (ROC) curves. are applied on the positive samples to return genetically diverse chromosomes against the positive samples. Negative samples are considered as the chromosomes that are not diverse and after few generations/iterations they are intended to die. The support vector machines and artificial neural networks are trained on both classes of chromosomes and output is generated. The user iteratively provides the feedback on the output until the desired results are achieved. The complete process of the relevance feedback is provided in Algorithm 5.