  Sparse subspace clustering (SSC) using greedy-based neighbor selection, such
as matching pursuit (MP) and orthogonal matching pursuit (OMP), has been known
as a popular computationally-efficient alternative to the conventional
L1-minimization based methods. Under deterministic bounded noise corruption, in
this paper we derive coherence-based sufficient conditions guaranteeing correct
neighbor identification using MP/OMP. Our analyses exploit the maximum/minimum
inner product between two noisy data points subject to a known upper bound on
the noise level. The obtained sufficient condition clearly reveals the impact
of noise on greedy-based neighbor recovery. Specifically, it asserts that, as
long as noise is sufficiently small so that the resultant perturbed residual
vectors stay close to the desired subspace, both MP and OMP succeed in
returning a correct neighbor subset. A striking finding is that, when the
ground truth subspaces are well-separated from each other and noise is not
large, MP-based iterations, while enjoying lower algorithmic complexity, yield
smaller perturbation of residuals, thereby better able to identify correct
neighbors and, in turn, achieving higher global data clustering accuracy.
Extensive numerical experiments are used to corroborate our theoretical study.
