As far as you know, how popular is this method in user research? What do you think of this method? Normally who are doing this job? People from UX team or other teams? What tools do they usually use for data mining?
Some tools allow you to view a Heat Map of where people click on your pages over time (e.g. Google Analytics or CrazyEgg). You can analyse to see where people are clicking on your pages based on installing the analytics. You could also use your logs if you can back-correlate to screen positions.
A/B testing allows you to show different versions to different people. You can record which they view and then datamine the results.
You can go beyond to testing a whole range of options. For example Google conducted a link color experiment. I recall reading a rant by an ex-google UI designer about how they weren't willing to take risks, but I can't find the link. Instead read this 37Signals explanation of how they test.