I am thinking of preprocessing techniques for the input data to a convolutional neural network (CNN) using sparse datasets and trained with SGD. In Andrew Ng's coursera course, Machine Learning, he states that it is important to preprocess the data so it fits into the interval $ \left[ 3, 3 \right] $ when using SGD. However, the most common preprocessing technique is to standardize each feature so $ \mu = 0 $ and $ \sigma = 1 $. When standardizing a highly sparse dataset many of the values will not end up in the interval.
I am therefore curious - would it be better to aim for e.g. $ \mu = 0 $ and $ \sigma = 0.5 $ in order for the values be closer to the interval $ \left[ 3, 3 \right] $? Could anyone argue based on a knowledge of SGD on whether it is most important to aim for $ \mu = 0 $ and $ \sigma = 1 $ or $ \left[ 3, 3 \right] $?