Rethinking Embedded Unsupervised Feature Selection: A Simple Joint Approach

Recently, various embedded methods for unsupervised feature selection have been put forward. However, most of them adopt a two-step strategy, i.e., selecting
$k$
top-ranked dimensions according to a learned order of all features, then conducting K-means clustering for evaluation. This commonly used strategy usually results in a group of sub-optimal features, because the selected
$k$
top-ranked features are seldom the desired top-
$k$
dimensions. To address this problem, we rethink the two steps in a joint manner and propose a simple yet effective approach called
U
nsupervised
F
eature
S
election with
S
eparability (
UFS$^{\mathbf{2}}$2
) to simultaneously select features and cluster data. More specifically, a binary vector is seamlessly integrated into K-means to select an exact number of features for clustering. Different from previous embedded methods involving
$l_{2,1}$
-norm, our joint model explicitly uses the parameter
$k$
(i.e., the number of selected features). Afterwards, a customized term for the binary vector is designed to maximize the separability among selected feature dimensions. In order to solve the formulated 0-1 integer programming problem, an iterative algorithm is developed. Finally, we evaluate the proposed approach extensively on different datasets. Despite the relative simplicity, UFS
$^{2}$
remarkably and generally outperforms state-of-the-art baselines.