4,301 research outputs found
Stable Principal Component Pursuit
In this paper, we study the problem of recovering a low-rank matrix (the
principal components) from a high-dimensional data matrix despite both small
entry-wise noise and gross sparse errors. Recently, it has been shown that a
convex program, named Principal Component Pursuit (PCP), can recover the
low-rank matrix when the data matrix is corrupted by gross sparse errors. We
further prove that the solution to a related convex program (a relaxed PCP)
gives an estimate of the low-rank matrix that is simultaneously stable to small
entrywise noise and robust to gross sparse errors. More precisely, our result
shows that the proposed convex program recovers the low-rank matrix even though
a positive fraction of its entries are arbitrarily corrupted, with an error
bound proportional to the noise level. We present simulation results to support
our result and demonstrate that the new convex program accurately recovers the
principal components (the low-rank matrix) under quite broad conditions. To our
knowledge, this is the first result that shows the classical Principal
Component Analysis (PCA), optimal for small i.i.d. noise, can be made robust to
gross sparse errors; or the first that shows the newly proposed PCP can be made
stable to small entry-wise perturbations.Comment: 5-page paper submitted to ISIT 201
Structural Analysis of Network Traffic Matrix via Relaxed Principal Component Pursuit
The network traffic matrix is widely used in network operation and
management. It is therefore of crucial importance to analyze the components and
the structure of the network traffic matrix, for which several mathematical
approaches such as Principal Component Analysis (PCA) were proposed. In this
paper, we first argue that PCA performs poorly for analyzing traffic matrix
that is polluted by large volume anomalies, and then propose a new
decomposition model for the network traffic matrix. According to this model, we
carry out the structural analysis by decomposing the network traffic matrix
into three sub-matrices, namely, the deterministic traffic, the anomaly traffic
and the noise traffic matrix, which is similar to the Robust Principal
Component Analysis (RPCA) problem previously studied in [13]. Based on the
Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated
Proximal Gradient (APG) algorithm, we present an iterative approach for
decomposing a traffic matrix, and demonstrate its efficiency and flexibility by
experimental results. Finally, we further discuss several features of the
deterministic and noise traffic. Our study develops a novel method for the
problem of structural analysis of the traffic matrix, which is robust against
pollution of large volume anomalies.Comment: Accepted to Elsevier Computer Network
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