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I am currently working on a project that not only is imbalanced but has a lot of overlap between the data points from the two classes. I am not quite sure how to go about solving this problem.

What I am looking for is any documentation for either R or Python for packages that handle this type of data and anyone experience tackling such a problem themselves.

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I'm haven't been working with very complicated problems of classification (prefer regression modeling), but I can recommend 2 techniques, which handle the most complicated decision boundaries for classification: neural networks and k nearest neighbors analysis. I'm not sure about Python and R, but MATLAB definitely has very good libraries for neural networks; k nearest neighbors analysis isn't very complicated and can be coded easily in any language. You can also try adaptive nearest neighbor metric for the boundaries to stretch in one direction.

You may also try using Gaussian methods such as naïve Bayes classifier using Gaussian density (smooth Parzen estimate). Hope you will solve your problem effectively!

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