A Fast Iterative Algorithm for Improved Unsupervised Feature Selection

Dimensionality reduction is often a crucial step for the successful application of machine learning and data mining methods. One way to achieve said reduction is feature selection. Due to the impossibility of labelling many data sets, unsupervised approaches are frequently the only option. The column subset selection problem translates naturally to this purpose, and has received consider able attention over the last few years, as it provides simple linear models for data reconstruction. Existing methods, however, often achieve approximation errors that are far from the optimum. In this paper we present a novel algorithm for column subset selection that consistently outperforms state-of-the-art methods in approximation error. We present a series of key derivations that allow an efficient implementation, making it comparable in speed and in some cases faster than other algorithms. We also prove results that make it possible to deal with huge matrices, which has strong implications for other algorithms of this type in the big data field. We validate our claimsthrough experiments on a wide variety of well-known data sets.