425 research outputs found
Binary Independent Component Analysis with OR Mixtures
Independent component analysis (ICA) is a computational method for separating
a multivariate signal into subcomponents assuming the mutual statistical
independence of the non-Gaussian source signals. The classical Independent
Components Analysis (ICA) framework usually assumes linear combinations of
independent sources over the field of realvalued numbers R. In this paper, we
investigate binary ICA for OR mixtures (bICA), which can find applications in
many domains including medical diagnosis, multi-cluster assignment, Internet
tomography and network resource management. We prove that bICA is uniquely
identifiable under the disjunctive generation model, and propose a
deterministic iterative algorithm to determine the distribution of the latent
random variables and the mixing matrix. The inverse problem concerning
inferring the values of latent variables are also considered along with noisy
measurements. We conduct an extensive simulation study to verify the
effectiveness of the propose algorithm and present examples of real-world
applications where bICA can be applied.Comment: Manuscript submitted to IEEE Transactions on Signal Processin
Topology Discovery of Sparse Random Graphs With Few Participants
We consider the task of topology discovery of sparse random graphs using
end-to-end random measurements (e.g., delay) between a subset of nodes,
referred to as the participants. The rest of the nodes are hidden, and do not
provide any information for topology discovery. We consider topology discovery
under two routing models: (a) the participants exchange messages along the
shortest paths and obtain end-to-end measurements, and (b) additionally, the
participants exchange messages along the second shortest path. For scenario
(a), our proposed algorithm results in a sub-linear edit-distance guarantee
using a sub-linear number of uniformly selected participants. For scenario (b),
we obtain a much stronger result, and show that we can achieve consistent
reconstruction when a sub-linear number of uniformly selected nodes
participate. This implies that accurate discovery of sparse random graphs is
tractable using an extremely small number of participants. We finally obtain a
lower bound on the number of participants required by any algorithm to
reconstruct the original random graph up to a given edit distance. We also
demonstrate that while consistent discovery is tractable for sparse random
graphs using a small number of participants, in general, there are graphs which
cannot be discovered by any algorithm even with a significant number of
participants, and with the availability of end-to-end information along all the
paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is
scheduled to appear in J. on Random Structures and Algorithm
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Diagnostic Applications for Micro-Synchrophasor Measurements
This report articulates and justifies the preliminary selection of diagnostic applications for data from micro-synchrophasors (µPMUs) in electric power distribution systems that will be further studied and developed within the scope of the three-year ARPA-e award titled Micro-synchrophasors for Distribution Systems
Estimating Dynamic Traffic Matrices by using Viable Routing Changes
Abstract: In this paper we propose a new approach for dealing with the ill-posed nature of traffic matrix estimation. We present three solution enhancers: an algorithm for deliberately changing link weights to obtain additional information that can make the underlying linear system full rank; a cyclo-stationary model to capture both long-term and short-term traffic variability, and a method for estimating the variance of origin-destination (OD) flows. We show how these three elements can be combined into a comprehensive traffic matrix estimation procedure that dramatically reduces the errors compared to existing methods. We demonstrate that our variance estimates can be used to identify the elephant OD flows, and we thus propose a variant of our algorithm that addresses the problem of estimating only the heavy flows in a traffic matrix. One of our key findings is that by focusing only on heavy flows, we can simplify the measurement and estimation procedure so as to render it more practical. Although there is a tradeoff between practicality and accuracy, we find that increasing the rank is so helpful that we can nevertheless keep the average errors consistently below the 10% carrier target error rate. We validate the effectiveness of our methodology and the intuition behind it using commercial traffic matrix data from Sprint's Tier-1 backbon
Node Failure Localization via Network Tomography
We investigate the problem of localizing node failures in a communication network from end-to-end path measure-ments, under the assumption that a path behaves normally if and only if it does not contain any failed nodes. To uniquely localize node failures, the measurement paths must show dif-ferent symptoms under different failure events, i.e., for any two distinct sets of failed nodes, there must be a measure-ment path traversing one and only one of them. This condi-tion is, however, impractical to test for large networks. Our first contribution is a characterization of this condition in terms of easily verifiable conditions on the network topol-ogy with given monitor placements under three families of probing mechanisms, which differ in whether measurement paths are (i) arbitrarily controllable, (ii) controllable but cycle-free, or (iii) uncontrollable (i.e., determined by the de-fault routing protocol). Our second contribution is a char-acterization of the maximum identifiability of node failures, measured by the maximum number of simultaneous failures that can always be uniquely localized. Specifically, we bound the maximal identifiability from both the upper and the lower bounds which differ by at most one, and show that these bounds can be evaluated in polynomial time. Finally, we quantify the impact of the probing mechanism on the capability of node failure localization under different prob-ing mechanisms on both random and real network topolo-gies. We observe that despite a higher implementation cost, probing along controllable paths can significantly improve a network’s capability to localize simultaneous node failures
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