# A New Under-Sampling Method to Face Class Overlap and Imbalance
## 6 Conclusions  
In this work, we have proposed a new under-sampling method called DBMIST-US to face class overlap and class imbalance through the combination of the DBSCAN clustering algorithm with the generation of an MST. The goal of the technique proposed here is to handle both data complexities simultaneously using a two-stage algorithm. In the first stage, the decision boundary is cleaned by removing negative instances that have been considered as noise, whereas the second stage is in charge of balancing the classes by selecting representative instances from the majority class according to a maximum imbalance ratio predefined by the user.  
As already introduced in Section 3.3, several differences between DBMIST-US and some recent related under-sampling algorithms can be highlighted: (i) DBMIST-US faces class overlap and class imbalance simultaneously, whereas other methods are designed to tackle these data complexities separately or by applying a series of techniques in a sequential manner, (ii) the baseline clustering-based under-sampling approaches are based on the classical \(K\)-means algorithm, whereas our proposal combines DBSCAN with MST, and (iii) the algorithms that rest upon the use of DBSCAN are primarily developed for over-sampling the minority class instead of under-sampling the majority class.  
We carried out a set of experiments to validate the performance of the DBMIST-US method against 12 state-of-the-art under-sampling algorithms using three supervised classifiers (1 NN, J48, and SVM), tested on both real-life data sets and synthetic data sets with an imbalance ratio ranging from 7 to 82. The results have shown that the method here proposed performs well with noisy and borderline problems and better than the remaining algorithms when applied on heavily imbalanced data sets, especially using the SVM classification model. Another research question that has properly been answered in the experimental study refers to robustness, showing that DBMIST-US is high robust to the use of classifiers of different nature. It is also worth noting the percentage of average reduction of the imbalance ratio achieved by DBMIST-US, which was comparable to the reduction produced by the best reference algorithms.  
The promising results of the DBMIST-US algorithm encourage us to examine some directions for future research. The most immediate issue relates to the generalization of DBMIST-US for handling the multi-class imbalance problem, which emerges as a more challenging situation in many practical applications. A second subject that deserves further research is the multi-label classification of imbalanced data where the classes are not mutually exclusive, which represents a much more complex classification task because an instance may belong to more than one class. However, another avenue for investigation is to analyze how the DBMIST-US algorithm can be used on large-scale data and data streams.  
[PERSON], [PERSON], and [PERSON] designed the study; [PERSON] implemented the algorithms and carried out the experiments; [PERSON] and [PERSON] performed the analysis; [PERSON] wrote the manuscript; [PERSON] and [PERSON] revised and validated the manuscript. All authors have read and agreed to the published version of the manuscript.  
This work was partially supported by the Universitat Jaume I under grant [UJI-B2018-49], the 5046/2020 CIC UAEM project and the Mexican Science and Technology Council (CONACYT) under scholarship [702275].  
The authors declare no conflict of interests.