  The existing approaches to intrinsic dimension estimation usually are not
reliable when the data are nonlinearly embedded in the high dimensional space.
In this work, we show that the explicit accounting to geometric properties of
unknown support leads to the polynomial correction to the standard maximum
likelihood estimate of intrinsic dimension for flat manifolds. The proposed
algorithm (GeoMLE) realizes the correction by regression of standard MLEs based
on distances to nearest neighbors for different sizes of neighborhoods.
Moreover, the proposed approach also efficiently handles the case of nonuniform
sampling of the manifold. We perform numerous experiments on different
synthetic and real-world datasets. The results show that our algorithm achieves
state-of-the-art performance, while also being computationally efficient and
robust to noise in the data.
