Dimension Reduction: A Guided Tour

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 inference. Dimension Reduction: A Guided Tour covers many well-known, and some less well-known, methods for dimension reduction for which the inferred variables are continuous. It describes the mathematics and key ideas underlying the methods, and provides some links to the literature for those interested in pursuing a topic further.