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Let's say in machine learning the test cases are biased towards one or more options.

For example when there are 100 (just an example) test cases in total and every test case has a color to be suggested:

60 => blue
30 => green
9 => red
1 => yellow

Most machine learning techniques will suggest blue just for probability reasons. To avoid this some write you should use the same amount of test cases for every answer. But that way I only have 4 test cases.

Also when principal component analysis does not bring any insights, what can be done to help machine learning algorithms like neural networks or genetic algorithms to avoid the sampling bias towards the given training data?

Would it help to create/train one for each color? Or what would you do?

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Weighting, boosting, re-sampling, balancing are some ideas for unbalanced samples when using Neural Networks.

An idea for PCA+MLPs is found in this paper.

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