I'm doing basic classification and I'd like to make my training data as similar as possible to my testing data. The idea being that I would transform my training data and train my classifier on the transformed data and then predict on data that was similarly transformed. A thought I had, which may or may not make sense when you get down to the details, was to perform CCA on the covariance matrices of my training and testing data and then generate new data according to the result of my CCA which I'd like to interpret as a covariance matrix which maximizes the correlation between the training and testing data. There are several potential problems with this, but I figured I'd ask here before trying to find the answers in the mathematics myself. However, here are some things I think may be a problem:
It's quite likely that the CCA projection of two symmetric matrices is not symmetric itself and thus I wouldn't be able to interpret the result as a covariance matrix. Also, how should I use the covariance matrix to modify my training data? Would it even be meaningful/helpful to do so?
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