When and why do we need data normalization?

We do data normalization when seeking for relations. Some people do this methods, unfortunately, in experimental designs, which is not correct except if the variable is a transformed one, and all the data needs the same normalization method, such as pH in sum agricultural studies. Normalization in experimental designs are meaningless because we can't compare the mean of, for instance, a treatment with the mean of another treatment logarithmically normalized. In regression and multivariate analysis which the relationships are of interest, however, we can do the normalization to reach a linear, more robust relationship. Commonly when the relationship between two dataset is non-linear we transform data to reach a linear relationship. Here, normalization doesn't mean normalizing data, it means normalizing residuals by transforming data. So normalization of data implies to normalize residuals using the methods of transformation.

In ANN and other data mining approaches we need to normalize the inputs, otherwise the network will be ill-conditioned. In essence, normalization is done to have the same range of values for each of the inputs to the ANN model. This can guarantee stable convergence of weight and biases.