559 research outputs found
Recovery of Low-Rank Plus Compressed Sparse Matrices with Application to Unveiling Traffic Anomalies
Given the superposition of a low-rank matrix plus the product of a known fat
compression matrix times a sparse matrix, the goal of this paper is to
establish deterministic conditions under which exact recovery of the low-rank
and sparse components becomes possible. This fundamental identifiability issue
arises with traffic anomaly detection in backbone networks, and subsumes
compressed sensing as well as the timely low-rank plus sparse matrix recovery
tasks encountered in matrix decomposition problems. Leveraging the ability of
- and nuclear norms to recover sparse and low-rank matrices, a convex
program is formulated to estimate the unknowns. Analysis and simulations
confirm that the said convex program can recover the unknowns for sufficiently
low-rank and sparse enough components, along with a compression matrix
possessing an isometry property when restricted to operate on sparse vectors.
When the low-rank, sparse, and compression matrices are drawn from certain
random ensembles, it is established that exact recovery is possible with high
probability. First-order algorithms are developed to solve the nonsmooth convex
optimization problem with provable iteration complexity guarantees. Insightful
tests with synthetic and real network data corroborate the effectiveness of the
novel approach in unveiling traffic anomalies across flows and time, and its
ability to outperform existing alternatives.Comment: 38 pages, submitted to the IEEE Transactions on Information Theor
Link Delay Estimation via Expander Graphs
One of the purposes of network tomography is to infer the status of
parameters (e.g., delay) for the links inside a network through end-to-end
probing between (external) boundary nodes along predetermined routes. In this
work, we apply concepts from compressed sensing and expander graphs to the
delay estimation problem. We first show that a relative majority of network
topologies are not expanders for existing expansion criteria. Motivated by this
challenge, we then relax such criteria, enabling us to acquire simulation
evidence that link delays can be estimated for 30% more networks. That is, our
relaxation expands the list of identifiable networks with bounded estimation
error by 30%. We conduct a simulation performance analysis of delay estimation
and congestion detection on the basis of l1 minimization, demonstrating that
accurate estimation is feasible for an increasing proportion of networks
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