Dimension reduction is the mapping of data to a lower dimensional space such that uninformative variance in the data is discarded, or such that a subspace in which the data lives is detected. Dimension reduction has a long history as a method for data visualization, and for extracting key low dimensional features (for example, the two-dimensional orientation of an object, from its high dimensional image representation). In some cases the desired low dimensional features depend on the task at hand. Apart from teaching us about the data, dimension reduction can lead us to better models for...