  We propose a method to reconstruct and cluster incomplete high-dimensional
data lying in a union of low-dimensional subspaces. Exploring the sparse
representation model, we jointly estimate the missing data while imposing the
intrinsic subspace structure. Since we have a non-convex problem, we propose an
iterative method to reconstruct the data and provide a sparse similarity
affinity matrix. This method is robust to initialization and achieves greater
reconstruction accuracy than current methods, which dramatically improves
clustering performance. Extensive experiments with synthetic and real data show
that our approach leads to significant improvements in the reconstruction and
segmentation, outperforming current state of the art for both low and high-rank
data.
