  The scale and complexity of modern data sets and the limitations associated
with testing large numbers of hypotheses underline the need for feature
selection methods. Spectral techniques rank features according to their degree
of consistency with an underlying metric structure, but their current
graph-based formulation restricts their applicability to point features. We
extend spectral methods for feature selection to abstract simplicial complexes
and present a general framework which can be applied to 2-point and
higher-order features. Combinatorial Laplacian scores take into account the
topology spanned by the data and reduce to the ordinary Laplacian score in the
case of point features. We demonstrate the utility of spectral simplicial
methods for feature selection with several examples of application to the
analysis of gene expression and multi-modal genomic data. Our results provide a
unifying perspective on topological data analysis and manifold learning
approaches.
