  I consider unsupervised extensions of the fast stepwise linear regression
algorithm \cite{efroymson1960multiple}. These extensions allow one to
efficiently identify highly-representative feature variable subsets within a
given set of jointly distributed variables. This in turn allows for the
efficient dimensional reduction of large data sets via the removal of redundant
features. Fast search is effected here through the avoidance of repeat
computations across trial fits, allowing for a full representative-importance
ranking of a set of feature variables to be carried out in $O(n^2 m)$ time,
where $n$ is the number of variables and $m$ is the number of data samples
available. This runtime complexity matches that needed to carry out a single
regression and is $O(n^2)$ faster than that of naive implementations. I present
pseudocode suitable for efficient forward, reverse, and forward-reverse
unsupervised feature selection. To illustrate the algorithm's application, I
apply it to the problem of identifying representative stocks within a given
financial market index -- a challenge relevant to the design of Exchange Traded
Funds (ETFs). I also characterize the growth of numerical error with iteration
step in these algorithms, and finally demonstrate and rationalize the
observation that the forward and reverse algorithms return exactly inverted
feature orderings in the weakly-correlated feature set regime.
