In this paper we propose a novel clustering algorithm that uses local affine/convex hulls for high-dimensional data clustering. In high-dimensional spaces, the sparse and irregular distributions make the nearest-neighbor distances unreliable (hole artifact), and this deteriorates the clustering performance. Therefore, there is a need to fill in these gaps between the nearest samples. To this end, we use local affine/convex hulls of the nearest neighbors of a given sample to fill in the holes, and this greatly improves the Euclidean distance metric and the clustering accuracy. The proposed method can also be seen as the local extension of the well-known iterative subspace clustering algorithms in which the entire cluster is approximated with a single linear/affine subspace. Experimental results show that the proposed method is efficient and it outperforms other subspace clustering algorithms on a wide range of datasets. (C) 2019 Elsevier B.V. All rights reserved.