  We describe the Fast Greedy Sparse Subspace Clustering (FGSSC) algorithm
providing an efficient method for clustering data belonging to a few
low-dimensional linear or affine subspaces. The main difference of our
algorithm from predecessors is its ability to work with noisy data having a
high rate of erasures (missed entries with the known coordinates) and errors
(corrupted entries with unknown coordinates). We discuss here how to implement
the fast version of the greedy algorithm with the maximum efficiency whose
greedy strategy is incorporated into iterations of the basic algorithm.
  We provide numerical evidences that, in the subspace clustering capability,
the fast greedy algorithm outperforms not only the existing state-of-the art
SSC algorithm taken by the authors as a basic algorithm but also the recent
GSSC algorithm. At the same time, its computational cost is only slightly
higher than the cost of SSC.
  The numerical evidence of the algorithm significant advantage is presented
for a few synthetic models as well as for the Extended Yale B dataset of facial
images. In particular, the face recognition misclassification rate turned out
to be 6-20 times lower than for the SSC algorithm. We provide also the
numerical evidence that the FGSSC algorithm is able to perform clustering of
corrupted data efficiently even when the sum of subspace dimensions
significantly exceeds the dimension of the ambient space.
