The challenge of learning from rare cases

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An important challenge is learning from domains that do not have the same proportion of classes, that is, learning from problems that contain class imbalances (Orriols-Puig, 2008). Figure 1 shows a toy example of this issue. Notwithstanding, it is challenging because (1) in many real-world problems we cannot assume a balanced distribution of classes and (2) traditional machine learning algorithms cannot induce accurate models in such domains. Oftentimes it happens that the key knowledge to solve a problem that previously eluded solution is hidden in patterns that are rare. To tackle this issue, practitioners rely on re-sampling techniques, that is, algorithms that pre-process the data sets and either (1) add synthetic instances of the minority pattern to the original data or (2) eliminate instances from the majority class. The first type is called over-sampling and the later, under-sampling. 
Figure 1. Our unbalanced data set. Black dots are the majority class (0) and red dots the minority (1). It has an imbalance ratio of 11.25, where the majority class correspods to the 91.8367% of the data, and the minority to the 8.1633%

In this post I will present the most successful over-sampling technique, the so called Synthetic Minority Over-sampling Technique (SMOTE), which was introduced by Chawla et al. (2002). It works in a very simple manner: it generates new samples out of the minority class by seeking the nearest neighbors of these. Figure 2 shows the results of applying this method to our toy problem.

Figure 2. The SMOTEd version of the data set (see Figure 1). Now we have a much more balanced domain (almost 50% of the instances are in each class)

In the following I provide the R code. In it one can select the requested number of samples to generate, the number of k-neighbors for the data generation and the distance metric used (one of the following two: the Euclidean distance or the Mahalanobis distance).
 

References

A. Orriols-Puig. New Challenges in Learning Classifier Systems: Mining Rarities and Evolving Fuzzy Models. PhD thesis, Universitat Ramon Llull, Barcelona (Spain). 2008. 

 N. Chawla, K. Bowyer, L. Hall, and W. Kegelmeyer. SMOTE: Synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 16:321–357, 2002.

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