I'm performing dimension reduction on some data sets and would like to evaluate how has a particular dimension reduction algorithm performed in terms of how much data is lost. If we are given 1000 dimensions, and we reduce it to 2, then how effective is it? I'm trying to figure till what should you do DR such that your results don't go bad? Is there a metric which does this? I'm using PCA.
Can I use some distance metric to do the evaulation?