Intrinsic dimensionality (ID) is one of the most fundamental characteristics\nof multi-dimensional data point clouds. Knowing ID is crucial to choose the\nappropriate machine learning approach as well as to understand its behavior and\nvalidate it. ID can be computed globally for the whole data point distribution,\nor computed locally in different regions of the data space. In this paper, we\nintroduce new local estimators of ID based on linear separability of\nmulti-dimensional data point clouds, which is one of the manifestations of\nconcentration of measure. We empirically study the properties of these\nestimators and compare them with other recently introduced ID estimators\nexploiting various effects of measure concentration. Observed differences\nbetween estimators can be used to anticipate their behaviour in practical\napplications.\n