I have a question regarding classification in general. Let $f$ be a classifier, which outputs a set of probabilities given some data D. Normally, one would say: well, if $P(c|D) > 0.5$, we will assign a class 1, otherwise 0 (let this be a binary classification).
My question is, what if I find out, that if I classify the class as 1 also when the probabilities are larger than, for instance 0.2, and the classifier performs better. Is it legitimate to then use this new threshold when doing classification?
I would interpret the necessity for lower classification bound in the context of the data emitting a smaller signal; yet still significant for the classification problem.
I realize this is one way to do it. However, if this is not correct thinking of reducing the threshold, what would be some data transformations, which emphasize individual features in a similar manner, so that the threshold can remain at 0.5?