I use ANN and ELM for a regression problem.I normalize inputs with minmax normalization at [-1,1]. Currently I apply normalization separately to the train and test set. However this should result in difficulties as far as regression is concerned if the train and test set have min and max values that differ. Would it be better to normalize th train and test set using the same normalization paramters (min and max value in this case)?
Yes. Normally the training and testing data sets are taken out from the same data set. 70 ~ 80 % data to training and 30 ~ 20% of data to test the data set. Therefore the training and testing data should have the same normalization parameters.
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you must use the normalization deduced from the training set **only** for both the train, validation and test sets
for input values at test time, there is no problem : if a value in the test set is larger than the max seen on the training set (this may happen but should not happen too often as your training set is supposed statistically representative !), just let your system generalize (alternatively, you can clip the normalized value to 1 ...)
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The underlying assumption of all learning algorithms including ANN and ELM is that all data (test,train, validation) come from the same distribution.You must normalization vyiur training dats first and then use the normalization oarameters to nomalize the test data. In case, you have the data points in the test data which are lager than maximum value of your training data points ( or smaller than min value of your traning data point), you can consider to normalize your training data in the [-0.9, 0.9] rather than [-1,1].
"for input values at test time, there is no problem : if a value in the test set is larger than the max seen on the training set (this may happen but should not happen too often as your training set is supposed statistically representative !), just let your system generalize (alternatively, you can clip the normalized value to 1 ...) "
Well, that is my main worry since for regression problems NN are not designed to extrapolate , so if a test sample is beyond the range of the training test the regression will most likely work in unpredictable ways for this sample. Clipping the values seems like a good idea although still I think it will not help a lot as far as extrapolation is concerned.
For the biggest part the test set is within the range of the train set, except for a few values at the lower and upper limits of the functions...
""Perhaps you can consider to normalize your training in the [-0.9, 0.9] rather than [-1,1] to reduce number of the test data points."
I am sorry but I don't see how reducing the normalization range reduces the number of test data points - the dimensionality of the test set remains the same. Can you elaborate a bit on this?
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