# An Oversampling Method for Class Imbalance Problems on Large Datasets
## 5 Conclusions  
In this paper, we introduced Fast-SMOTE, a fast oversampling method non based on the \(k\)-nearest neighbors search that is the most time-expensive step of SMOTE-based methods. For each feature, the proposed method uses the value that appears most often in the minority class (the mode) jointly with the minimum and maximum values (all three can be quickly computed), in an appropriate manner, for the generation of synthetic objects around the mode in the region of the minority class defined by the minimum and maximum values. This allowed us to obtain a linear complexity oversampling method that is much faster than SMOTE-based methods, which complexity is at least quadratic. Moreover, the proposed method has a complexity similar to the complexity of NDO, which is the only oversampling method reported in the literature that is not based on the \(k\)-nearest neighbors, however according to our experiments, the proposed method scales better when the number of objects and features increases.  
Comparing the synthetic objects generated by the proposed method against those generated by SMOTE and NDO, we have shown that similar to SMOTE and NDO, Fast-SMOTE generate synthetic objects close to the objects of the minority class and near the decision region between the classes.  
In small unbalanced datasets where state-of-the-art oversampling methods can oversample the minority class in a short time, the proposed method obtains an oversampling quality similar to these method but it is found to be the fastest method.  
Our comparison between Fast-SMOTE and NDO for large datasets with regard to runtime and _AUC_ shows that Fast-SMOTE produces oversampled datasets that allow training supervised classifiers to obtain classification results that are statistically similar to those classification results obtained by training the classifiers with datasets oversampled by NDO, but in much less runtime. From all of these experiments, we can conclude that Fast-SMOTE is the best method for oversampling large datasets with imbalanced classes.  
As mentioned above, the development of oversampling methods not based on the search for nearest neighbors is a poorly explored research direction. Hence, in future work, we propose to continue developing oversampling methods following this approach. In particular, we are interested in developing oversampling methods that can work on large mixed datasets with imbalanced classes. Additionally, the implementation and development of oversampling methods on GPU, parallel CPU or distributed computing [58; 59; 60; 61; 62] is an active research area. Thus, in future work, we will develop an implementation of our oversampling method on these platforms to improve its runtime further. Also, we will face the imbalance problem with other problems in supervised classification as noise, missing data, or multiple minority class groups.  
Writing--original draft preparation, F.R.-T.; writing--review and editing, F.R.-T., J.F.M.-T. and J.A.C.-O.; supervision, J.F.M.-T. and J.A.C.-O. All authors have read and agreed to the published version of the manuscript.  
This research was partly funded by the National Council of Science and Technology of Mexico.  
Not applicable.  
The first author gratefully acknowledges the National Council of Science and Technology of Mexico (CONACyT) for his Ph.D. fellowship through a scholarship.  
The authors declare no conflict of interest.