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Real-world datasets are often of high dimension and effected by the curse ofdimensionality. This hinders their comprehensibility and interpretability. Toreduce the complexity feature selection aims to identify features that arecrucial to learn from said data. While measures of relevance and pairwisesimilarities are commonly used, the curse of dimensionality is rarelyincorporated into the process of selecting features. Here we step in with anovel method that identifies the features that allow to discriminate datasubsets of different sizes. By adapting recent work on computing intrinsicdimensionalities, our method is able to select the features that candiscriminate data and thus weaken the curse of dimensionality. Our experimentsshow that our method is competitive and commonly outperforms establishedfeature selection methods. Furthermore, we propose an approximation that allowsour method to scale to datasets consisting of millions of data points. Ourfindings suggest that features that discriminate data and are connected to alow intrinsic dimensionality are meaningful for learning procedures.

Selecting Features by their Resilience to the Curse of Dimensionality