  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.
