In generative classification you build a model of each class. Then for new instances, for each model, you assume the instance belongs to that class and then finally classify it as the class of the most probable model.
My question is this: If you are doing PCA as a preprocess, say for dimensionality reduction, does it ever make sense to make a PCA mapping for each class (seeing how you assume that the instance already belongs to a given models class). Obviously you can't do this for discriminative classification.
My guess is this is bad idea and that you should always be finding a single pca mapping based on data from all classes, but I can't think of a good argument on why this would be a bad idea.
I guess this applies to other forms of unsupervised preprocessing methods than just PCA. Would you ever do this for other methods, like say simple zscore normalization?
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