Real-world datasets are often of high dimension and effected by the curse of dimensionality. This hinders their comprehensibility and interpretability. To reduce the complexity feature selection aims to identify features that are crucial to learn from said data. While measures of relevance and pairwise similarities are commonly used, the curse of dimensionality is rarely incorporated into the process of selecting features. Here we step in with a novel method that identifies the features that allow to discriminate data subsets of different sizes. By adapting recent work on computing intrinsic dimensionalities, our method is able to select the features that can discriminate data and thus weaken the curse of dimensionality. Our experiments show that our method is competitive and commonly outperforms established feature selection methods. Furthermore, we propose an approximation that allows our method to scale to datasets consisting of millions of data points. Our findings suggest that features that discriminate data and are connected to a low intrinsic dimensionality are meaningful for learning procedures.

翻译：现实世界的数据集通常具有高维特性，并受到维度灾难的影响，这阻碍了其可理解性与可解释性。为降低复杂性，特征选择旨在识别从该数据中学习的关键特征。尽管相关性度量与成对相似性方法被广泛使用，但维度灾难很少被纳入特征选择过程。本文提出一种新方法，通过识别能够区分不同规模数据子集的特征来应对这一挑战。通过改进近期关于内在维度计算的研究成果，我们的方法能够筛选出具有数据区分能力的特征，从而削弱维度灾难的影响。实验表明，该方法与现有特征选择方法相比具有竞争力，且通常表现更优。此外，我们提出一种近似策略，使该方法可扩展至包含数百万个数据点的数据集。研究结果表明，具有数据区分能力且与低内在维度相关联的特征对学习过程具有实际意义。