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I am working on multi-class classification problem on an image dataset. There is one class with 80% of the images and rest 20% is divided into rest 6 remaining classes. If I have to apply the image-augmentation technique, what ratio of count of images between each class I have to maintain?

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I think that you first need to consider what are the class proportions in the data that you are going to eventually use the model for. It is important to have a test set that comes from the same data generating distribution as the real data. Now, in case the proportions in this data are the same as you wrote than it is actually a good thing to have more examples for the classes that are more common. It allows your model to give those classes a bigger prior and focus more on those classes, extract more features relevant to those classes particularly.

In case you'd like to reduce this skew (for example because the proportions in the real data are different or the imbalance is so big that your model learns to assign always just the most common class and ignores others) you can use resampling: define what class proportions would suit you and randomly sample examples using those ratios.

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