In this paper we present a framework for spectral clustering based on the following simple scheme: sample a subset of the input points, compute the clusters for the sampled subset using weighted kernel k-means (Dhillon et al. 2004) and use the resulting centers to compute a clustering for the remaining data points. For the case where the points are sampled uniformly at random without replacement, we show that the number of samples required depends mainly on the number of clusters and the diameter of the set of points in the kernel space. Experiments show that the proposed framework outperforms the approaches based on the Nystrom approximation both in terms of accuracy and computation time.