Some Tutorial Notes on Dimension Reduction

The problem of dimension reduction has inspired many different methods over the years in the statistics and machine learning communities. However, as often seems the case, the efforts in these two communities seem largely disconnected. In this talk I will review some old statistical techniques that do not appear to be widely known in the machine learning community – estimating the Correlation Dimension, Sliced Inverse Regression, and Sliced Average Variance Estimation. I’ll put these algorithms through their paces on several toy data sets to gain intuition, and also see how they do on a large web ranking data set. I’ll end by giving a pointer to more recent work developing these ideas.