The problem of estimating the intrinsic dimension of a set of points in high dimensional space is a critical issue for a wide range of disciplines, including genomics, finance, and networking. Current estimation techniques are dependent on either the ambient or intrinsic dimension in terms of computational complexity, which may cause these methods to become intractable for large data sets. In this paper, we present a clustering-based methodology that exploits the inherent self-similarity of data to efficiently estimate the intrinsic dimension of a set of points. When the data satisfies a specified general clustering condition, we prove that the estimated dimension approaches the true Hausdorff dimension. Experiments show that the clustering-based approach allows for more efficient and accurate intrinsic dimension estimation compared with all prior techniques, even when the data does not conform to obvious self-similarity structure. Finally, we present empirical results which show the clustering-based estimation allows for a natural partitioning of the data points that lie on separate manifolds of varying intrinsic dimension
