We present a novel method for clustering data drawn from a union of arbitrary dimensional subspaces, called Discriminative Subspace Clustering (DiSC). DiSC solves the subspace clustering problem by using a quadratic classifier trained from unlabeled data (clustering by classification). We generate labels by exploiting the locality of points from the same subspace and a basic affinity criterion. A number of classifiers are then diversely trained from different partitions of the data, and their results are combined together in an ensemble, in order to obtain the final clustering result. We have tested our method with 4 challenging datasets and compared against 8 state-of-the-art methods from literature. Our results show that DiSC is a very strong performer in both accuracy and robustness, and also of low computational complexity.