Before revision:  2) Each cluster is modeled as a  ball in \mathbb{R}^d  . 3) Each cluster contains a \frac{n{m}, k-dimensional affine subspaces . 4) All k-dimensional affine subspaces, which belong in the same cluster, are intersected with the ball of the cluster.
After revision:  2) Each cluster is modeled as a set of disjoint ball in \mathbb{R}^d . 3) Each cluster contains a \frac{n{m}, k-dimensional affine subspaces . 4) All k-dimensional affine subspaces, which belong in the same cluster, are intersected with the ball of the cluster.