# Handling unbalanced data using SMOTE - no big difference?

I have a classification problem with 2 classes. I have nearly 5000 samples, each of which is represented as vector with 570 features. The positive class samples are nearly 600. Meaning, I have a 1:8 ratio of positive and negative samples in the dataset. This imbalance in the dataset is mitigated using SMOTE. Subsequently, classification with 10 fold CV is performed. I get a f-measure of 0.91.

To study the effect of imbalance in the dataset, I tried using the data with imbalance itself (i.e. without SMOTE). This time around, I observed a f-measure of 0.92. I understand the difference is using accuracy and f-measure to interpret the classifier predictions and since I have an unbalanced dataset, I chose to use f-measure.

There seems to be no big difference in the end result whether or not I have an imbalance in the dataset in my case. In this context, I have the following questions:

• Why there seems to be no big difference in the f-measure in both the cases?
• It could be noted that, after I used SMOTE to mitigate the imbalance, the dataset becomes balanced and still I use f-measure to evaluate the classification results. Is it right to use f-measure in this case or should I use accuracy?
• SMOTE does oversampling of the minority class. Similarly, down sampling (or undersampling) the majority class could also rectify the imbalance. Why this methods is not preferred (If I may say so)? What effect does under sampling have on the classifier subjected to training and accuracy compared to oversampling.

SMOTE isn't really about changing f-measure or accuracy... it's about the trade-off between precision vs. recall.

By using SMOTE you can increase recall at the cost of precision, if that's something you want. Just look at Figure 2 in the SMOTE paper about how SMOTE affects classifier performance.

Undersampling the minority class gets you less data, and most classifiers' performance suffers with less data.

An alternative, if your classifier allows it, is to reweight the data, giving a higher weight to the minority class and lower weight to the majority class.

So why use something like SMOTE? Usually if the class you're interested in is rare, like finding defaults if predicting a credit score, a classifier giving 0-1 scores will say everyone doesn't default. Often in practice, one would rather have a classifier that returns the vast majority of the defaults, even if precision is less than 50%, as these can be examined by a human, or you can direct deeper, more expensive, data collection efforts towards these cases. If you use a classifier with a more continuous score, you can just lower the threshold to get more recall - i.e. for a logistic regression, start treating $X^T w > -2$ as positive, but this usually results in getting lower f-measure, since it's not the "fulcrum point" of where the model is being trained.

By reweighting the proportion of the classes, you make your model be trained at the precision/recall tradeoff you prefer, which means you end up with both being slightly better than if you just lowered the threshold.

• SMOTE isn't really about changing f-measure or accuracy - Yes, I get it. But After applying SMOTE, the dataset becomes balanced and there is no reason why we should not use accuracy instead? Putting it simply, what measure should I use to evaluate the classifier predictions on a dataset that is artificially balanced (using a technique like SMOTE)? – Annamalai N May 13 '14 at 18:48
• If your dataset is balanced, and the output of the model still ends up as balanced (which in most cases I think it would), then of course there's not anything bad with accuracy. But it's always good to report something like f-measure so people don't have to read the fine print of your methods to convince themselves you don't have an issue with imbalanced data. – Joe May 13 '14 at 18:56

I would like to bring to your attention also that in the original SMOTE paper, the good results were based on both combining SMOTE and random under-sampling. This is because applying SMOTE to achieve an equal balance with the majority class is not necessarily the best case for the classifier and as your results show. Thus, you may under-sample the majority to different percentages of the original majority class and then (say 25%, 50%, 75%) , apply SMOTE to minority samples with different numbers of synthetically generated samples (say 2, 3, 4). You end up with a combination of cases and you may choose the one showing better cross-validated results.

Let's say your classes are split as 0: 10,000 and 1: 100. So, even if you model is predicting ALL 1's incorrectly, your model would be 99% accurate. Is that a good model to predict 1's accurately? No. Hence, SMOTE*. Even if accuracy of the new model is 96%

*stands true for both accuracy and f-measure