# A Review of Fuzzy and Pattern-Based Approaches for Class Imbalance Problems
## 3 Pattern and Fuzzy Approaches for Imbalance Problems
### Algorithm Level  
In this subsection, we present the most recent algorithm-level approaches presented for imbalance problems that use patterns and fuzzy logic. In 2011, [PERSON] et al. [20] proposed a fuzzy emerging pattern technique that overcomes the problem presented with continuous attributes using fuzzy discretization. To extract the fuzzy patterns, they used several fuzzy decision trees. For the induction procedure, they implemented linguistic hedges that solved the problem of the initial fuzzy discretization of continuous attributes. They created a way to test the discriminability of a fuzzy pattern named Trust. Finally, they proposed a new classifier (FEPC) that uses a graph-based strategy for pattern organization. The results outperform popular crisp classifiers such as bagging [88], boosting [88], c4.5 [52], random forest [89], and SJEP [90]; however, the results were similar compared to kNN and SVM, which were tested on 16 databases from the UCI repository [54]. In 2014, [PERSON] et al. [91] proposed K-Contractive Map (K-CM), which is a neural network that uses the variable connection weights to obtain the z-transforms. Then, they combined k-NN classifiers, which are used for class evaluation, and the connection weights are given by the Learning of the Auto-Contractive Map (Auto-CM) strategy [92]. The authors mentioned how K-CM helps bottom-up algorithms to provide a symbolic explanation of their learning. They also claimed that K-CM is not prone to over-fitting because it works with a complex minimization of the energy function with parallel constraints that includes all the input variable. The experiments were performed in 10 databases. Overall, K-CM showed the best performance when it was compared against k-NN [18], RF [93], PLS-DA [94], MLP [95], CART [96], Logistic [97], LDA [98], and SMO [99]. However, it has a similar performance with k-NN because it has the same modeling principles. In 2016, [PERSON] et al. [100] reviewed evolutionary fuzzy systems (EFSs) for imbalance problems. They introduce some concepts about linguistic fuzzy rules systems. They presented a taxonomy of the methodologies of that moment. Then, they present the most popular methods, until that year, to solve the imbalance problem (i.e., data level, algorithm level, cost-sensitive, and methods embedded into ensemble learning). Finally, to demonstrate the performance of EFSs, they implemented the GP-COACH-H [101] algorithm. The evaluation metric was G-mean and they compared their results against crisp C4.5 with SMOTE + ENN [77]. They used 44 databases from the KEEL repository [55]. In the end, the results are favorable for the EFSs and it outperforms the results of the SMOTE + ENN + C4.5. In 2016, [PERSON] et al. [102] proposed a fuzzy membership evaluation that assigns the membership value according to the class certainty. Their method is EFSVM and is inspired by FSVM [103]. The method is going to pay more attention to the minority class due to the entropy levels. Their method has three main steps: first, the entropy of the samples in the majority class is calculated. Then, the majority class is divided into subsets. Finally, each sample in the minority class is assigned to a larger fuzzy membership to guarantee the importance of the class. They compared their method, in three synthetic databases, against SVM [104] and the fuzzy method FSVM. Then, they compared their method on 64 real-world databases from the KEEL repository [55], against FSVM, SVM-SMOTE, SVM-OSS- SVM-RUS, EasyEnsemble [105], AdaBoost [106], and 1-NN. The results showed that EFSVM has better results than the compared algorithms in terms of AUC. In 2017, [PERSON] et al. [107] introduced KRNN (k rare-class nearest neighbour), which is a modification of the k nearest neighbour (kNN) classifier [18]. KRNN creates groups of objects from the minority class and tries to adjust the induction bias of kNN in correspondence to the size and the distribution of the groups. kRNN also uses the Laplace estimate to adjust the posterior probability estimation for query objects.