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Feature ranking has been widely adopted in machine learning applications suchas high-throughput biology and social sciences. The approaches of the popularRelief family of algorithms assign importances to features by iterativelyaccounting for nearest relevant and irrelevant instances. Despite their highutility, these algorithms can be computationally expensive and not-well suitedfor high-dimensional sparse input spaces. In contrast, recent embedding-basedmethods learn compact, low-dimensional representations, potentiallyfacilitating down-stream learning capabilities of conventional learners. Thispaper explores how the Relief branch of algorithms can be adapted to benefitfrom (Riemannian) manifold-based embeddings of instance and target spaces,where a given embedding's dimensionality is intrinsic to the dimensionality ofthe considered data set. The developed ReliefE algorithm is faster and canresult in better feature rankings, as shown by our evaluation on 20 real-lifedata sets for multi-class and multi-label classification tasks. The utility ofReliefE for high-dimensional data sets is ensured by its implementation thatutilizes sparse matrix algebraic operations. Finally, the relation of ReliefEto other ranking algorithms is studied via the Fuzzy Jaccard Index.

ReliefE: Feature Ranking in High-dimensional Spaces via Manifold Embeddings