  Extracting an understanding of the underlying system from high dimensional
data is a growing problem in science. Discovering informative and meaningful
features is crucial for clustering, classification, and low dimensional data
embedding. Here we propose to construct features based on their ability to
discriminate between clusters of the data points. We define a class of problems
in which linear separability of clusters is hidden in a low dimensional space.
We propose an unsupervised method to identify the subset of features that
define a low dimensional subspace in which clustering can be conducted. This is
achieved by averaging over discriminators trained on an ensemble of proposed
cluster configurations. We then apply our method to single cell RNA-seq data
from mouse gastrulation, and identify 27 key transcription factors (out of 409
total), 18 of which are known to define cell states through their expression
levels. In this inferred subspace, we find clear signatures of known cell types
that eluded classification prior to discovery of the correct low dimensional
subspace.
