Local intrinsic dimensionality estimators based on concentration of measure
arXiv:2001.11739
Abstract
Intrinsic dimensionality (ID) is one of the most fundamental characteristics of multi-dimensional data point clouds. Knowing ID is crucial to choose the appropriate machine learning approach as well as to understand its behavior and validate it. ID can be computed globally for the whole data point distribution, or computed locally in different regions of the data space. In this paper, we introduce new local estimators of ID based on linear separability of multi-dimensional data point clouds, which is one of the manifestations of concentration of measure. We empirically study the properties of these estimators and compare them with other recently introduced ID estimators exploiting various effects of measure concentration. Observed differences between estimators can be used to anticipate their behaviour in practical applications.
arXiv commentto be published in the International Joint Conference On Neural Networks (IJCNN) held as part of the IEEE World Congress On Computational Intelligence (WCCI), July 2020
References in corpus (9)
- Estimating the intrinsic dimension of datasets by a minimal neighborhood information
- To Trust Or Not To Trust A Classifier
- Adversarial vulnerability for any classifier
- Approximation with Random Bases: Pro et Contra
- Correction of AI systems by linear discriminants: Probabilistic foundations
- Lower Bounds on Adversarial Robustness from Optimal Transport
- Intrinsic dimension estimation of data by principal component analysis
- Symphony of high-dimensional brain
- Empirically Measuring Concentration: Fundamental Limits on Intrinsic Robustness