Feature selection for unsupervised learning via comparison of distance matrices

Feature selection for unsupervised learning is generally harder than for supervised learning, because the former lacks the class information of the latter, and thus an obvious way by which to measure the quality of a feature subset. In this paper, we propose a new method based on representing data sets by their distance matrices, and judging feature combinations by how well the distance matrix using only these features resembles the distance matrix of the full data set. Using articial data for which the relevant features were known, we observed that the results depend on the data dimensionality, the fraction of relevant features, the overlap between clusters in the relevant feature subspaces, and how to measure the similarity of distance matrices. Our method consistently achieved higher than 80% detection rates of relevant features for a wide variety of experimental configurations.