This talk is about a curious phenomenon. Suppose we have a data
matrix, which is the sum of a low-rank component and a sparse
component. Can we recover each component individually? We prove
that under some suitable assumptions, it is possible to recover
both the low-rank and the sparse components exactly by solving a
very convenient convex program. This suggests the possibility of
a principled approach to robust principal component analysis
since our methodology and results assert that one can recover the
principal components of a data matrix even though a positive
fraction of its entries are corrupted. This extends to the
situation where a fraction of the entries are missing as well. We
present applications in the area of video surveillance, where our
methodology allows for the detection of objects in a cluttered
background, and in the area of face recognition.
Joint work with X. Li, Y. Ma and J. Wright.
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