1 research outputs found
Fast Robust Subspace Tracking via PCA in Sparse Data-Dependent Noise
This work studies the robust subspace tracking (ST) problem. Robust ST can be
simply understood as a (slow) time-varying subspace extension of robust PCA. It
assumes that the true data lies in a low-dimensional subspace that is either
fixed or changes slowly with time. The goal is to track the changing subspaces
over time in the presence of additive sparse outliers and to do this quickly
(with a short delay). We introduce a "fast" mini-batch robust ST solution that
is provably correct under mild assumptions. Here "fast" means two things: (i)
the subspace changes can be detected and the subspaces can be tracked with
near-optimal delay, and (ii) the time complexity of doing this is the same as
that of simple (non-robust) PCA. Our main result assumes piecewise constant
subspaces (needed for identifiability), but we also provide a corollary for the
case when there is a little change at each time.
A second contribution is a novel non-asymptotic guarantee for PCA in linearly
data-dependent noise. An important setting where this is useful is for linearly
data dependent noise that is sparse with support that changes enough over time.
The analysis of the subspace update step of our proposed robust ST solution
uses this result.Comment: To appear in IEEE Journal of Special Areas in Information Theor