Summary: We develop and analyze a method to reduce the size of a very large set of data points in a high-dimensional Euclidean space \(\mathbb{R}^d\) to a small set of weighted points such that the result of a predetermined data analysis task on the reduced set is approximately the same as that for the original point set. For example, computing the first \(k\) principal components of the reduced set will return approximately the first \(k\) principal components of the original set or computing the centers of a \(k\)-means clustering on the reduced set will return an approximation for the original set. Such a reduced set is also known as a coreset. The main new feature of our construction is that the cardinality of the reduced set is independent of the dimension \(d\) of the input space and that the sets are mergeable [P. K. Agarwal et al., ACM Trans. Database Syst. 38, No. 4, Article No. 26, 28 p. (2013; Zbl 1321.68238)]. The latter property means that the union of two reduced sets is a reduced set for the union of the two original sets. It allows us to turn our methods into streaming or distributed algorithms using standard approaches. For problems such as \(k\)-means and subspace approximation the coreset sizes are also independent of the number of input points. Our method is based on data-dependently projecting the points on a low-dimensional subspace and reducing the cardinality of the points inside this subspace using known methods. The proposed approach works for a wide range of data analysis techniques including \(k\)-means clustering, principal component analysis, and subspace clustering. The main conceptual contribution is a new coreset definition that allows charging costs that appear for every solution to an additive constant.