Data normalization in machine learning

I wrote about cluster analysis in the previous article (Clustering: concepts, tools and algorithms), where I had a short discussion on data normalization. I touched upon how data normalization impacts clustering, and unsupervised algorithms generally. But I felt that I missed the opportunity to go into more details. But of course, that wasn't the focus of that article, so today I want to pick up on that. Let's first define what exactly is normalization.