The Experts below are selected from a list of 41328 Experts worldwide ranked by ideXlab platform
Georgios B Giannakis - One of the best experts on this subject based on the ideXlab platform.
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efficient and stable graph scattering transforms via pruning
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020Co-Authors: Vassilis N Ioannidis, Siheng Chen, Georgios B GiannakisAbstract:Graph convolutional networks (GCNs) have well-documented performance in various graph learning tasks, but their analysis is still at its infancy. Graph scattering transforms (GSTs) offer training-free deep GCN models, and are amenable to generalization and stability analyses. The price paid by GSTs is Exponential Complexity that increases with the number of layers. This discourages deployment of GSTs when a deep architecture is needed. The present work addresses the Complexity limitation of GSTs by introducing an efficient so-termed pruned (p)GST approach. The resultant pruning algorithm is guided by a graph-spectrum-inspired criterion, and retains informative scattering features on-the-fly while bypassing the Exponential Complexity associated with GSTs. Stability of the novel pGSTs is established when the input graph data or the network structure are perturbed. Furthermore, the sensitivity of pGST to random and localized signal perturbations is investigated analytically and experimentally. Numerical tests showcase that pGST performs comparably to the baseline GST at considerable computational savings. Furthermore, pGST achieves comparable performance to state-of-the-art GCNs in graph and 3D point cloud classification tasks. Upon analyzing the pGST pruning patterns, graph data in different domains call for different network architectures, and the pruning algorithm may guide the design choices for contemporary GCNs.
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efficient and stable graph scattering transforms via pruning
arXiv: Signal Processing, 2020Co-Authors: Vassilis N Ioannidis, Siheng Chen, Georgios B GiannakisAbstract:Graph convolutional networks (GCNs) have well-documented performance in various graph learning tasks, but their analysis is still at its infancy. Graph scattering transforms (GSTs) offer training-free deep GCN models that extract features from graph data, and are amenable to generalization and stability analyses. The price paid by GSTs is Exponential Complexity in space and time that increases with the number of layers. This discourages deployment of GSTs when a deep architecture is needed. The present work addresses the Complexity limitation of GSTs by introducing an efficient so-termed pruned (p)GST approach. The resultant pruning algorithm is guided by a graph-spectrum-inspired criterion, and retains informative scattering features on-the-fly while bypassing the Exponential Complexity associated with GSTs. Stability of the novel pGSTs is also established when the input graph data or the network structure are perturbed. Furthermore, the sensitivity of pGST to random and localized signal perturbations is investigated analytically and experimentally. Numerical tests showcase that pGST performs comparably to the baseline GST at considerable computational savings. Furthermore, pGST achieves comparable performance to state-of-the-art GCNs in graph and 3D point cloud classification tasks. Upon analyzing the pGST pruning patterns, it is shown that graph data in different domains call for different network architectures, and that the pruning algorithm may be employed to guide the design choices for contemporary GCNs.
J Baillieul - One of the best experts on this subject based on the ideXlab platform.
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remarks on a simple control law for point robot formations with Exponential Complexity
Conference on Decision and Control, 2006Co-Authors: J BaillieulAbstract:This paper considers a simple decentralized control law which stabilizes rigid formations of point robots in a way that is consistent with recent work B.D.O. Anderson and a number of others. The feedback law is simple in that it is shown to make parsimonious use of feedback information in a sense that will be made precise, and it is also simple in that it is the obvious one would try to control the relative positions of a group of robots. The law is Exponentially complex, however, in the sense that the number of stable equilibria grows Exponentially as a function of the number of point robots involved in the formation. Assuming only one formation of the Exponentially many possibilities is of interest, we discuss the problem of achieving the desired formation using the feedback law. The paper will also discuss the combinatorial problem of determining all possible formation topologies as well as the critical point theory of the proposed control law.
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CDC - Remarks on a Simple Control Law for Point Robot Formations with Exponential Complexity
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: J BaillieulAbstract:This paper considers a simple decentralized control law which stabilizes rigid formations of point robots in a way that is consistent with recent work B.D.O. Anderson and a number of others. The feedback law is simple in that it is shown to make parsimonious use of feedback information in a sense that will be made precise, and it is also simple in that it is the obvious one would try to control the relative positions of a group of robots. The law is Exponentially complex, however, in the sense that the number of stable equilibria grows Exponentially as a function of the number of point robots involved in the formation. Assuming only one formation of the Exponentially many possibilities is of interest, we discuss the problem of achieving the desired formation using the feedback law. The paper will also discuss the combinatorial problem of determining all possible formation topologies as well as the critical point theory of the proposed control law.
Vassilis N Ioannidis - One of the best experts on this subject based on the ideXlab platform.
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efficient and stable graph scattering transforms via pruning
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020Co-Authors: Vassilis N Ioannidis, Siheng Chen, Georgios B GiannakisAbstract:Graph convolutional networks (GCNs) have well-documented performance in various graph learning tasks, but their analysis is still at its infancy. Graph scattering transforms (GSTs) offer training-free deep GCN models, and are amenable to generalization and stability analyses. The price paid by GSTs is Exponential Complexity that increases with the number of layers. This discourages deployment of GSTs when a deep architecture is needed. The present work addresses the Complexity limitation of GSTs by introducing an efficient so-termed pruned (p)GST approach. The resultant pruning algorithm is guided by a graph-spectrum-inspired criterion, and retains informative scattering features on-the-fly while bypassing the Exponential Complexity associated with GSTs. Stability of the novel pGSTs is established when the input graph data or the network structure are perturbed. Furthermore, the sensitivity of pGST to random and localized signal perturbations is investigated analytically and experimentally. Numerical tests showcase that pGST performs comparably to the baseline GST at considerable computational savings. Furthermore, pGST achieves comparable performance to state-of-the-art GCNs in graph and 3D point cloud classification tasks. Upon analyzing the pGST pruning patterns, graph data in different domains call for different network architectures, and the pruning algorithm may guide the design choices for contemporary GCNs.
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efficient and stable graph scattering transforms via pruning
arXiv: Signal Processing, 2020Co-Authors: Vassilis N Ioannidis, Siheng Chen, Georgios B GiannakisAbstract:Graph convolutional networks (GCNs) have well-documented performance in various graph learning tasks, but their analysis is still at its infancy. Graph scattering transforms (GSTs) offer training-free deep GCN models that extract features from graph data, and are amenable to generalization and stability analyses. The price paid by GSTs is Exponential Complexity in space and time that increases with the number of layers. This discourages deployment of GSTs when a deep architecture is needed. The present work addresses the Complexity limitation of GSTs by introducing an efficient so-termed pruned (p)GST approach. The resultant pruning algorithm is guided by a graph-spectrum-inspired criterion, and retains informative scattering features on-the-fly while bypassing the Exponential Complexity associated with GSTs. Stability of the novel pGSTs is also established when the input graph data or the network structure are perturbed. Furthermore, the sensitivity of pGST to random and localized signal perturbations is investigated analytically and experimentally. Numerical tests showcase that pGST performs comparably to the baseline GST at considerable computational savings. Furthermore, pGST achieves comparable performance to state-of-the-art GCNs in graph and 3D point cloud classification tasks. Upon analyzing the pGST pruning patterns, it is shown that graph data in different domains call for different network architectures, and that the pruning algorithm may be employed to guide the design choices for contemporary GCNs.
Alexander Wolpert - One of the best experts on this subject based on the ideXlab platform.
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Exponential Complexity of satisfiability testing for linear size boolean formulas
International Conference on Algorithms and Complexity, 2013Co-Authors: Evgeny Dantsin, Alexander WolpertAbstract:The Exponential Complexity of the satisfiability problem for a given class of Boolean circuits is defined to be the infimum of constants α such that the problem can be solved in time poly(m) 2 αn , where m is the circuit size and n is the number of input variables [IP01]. We consider satisfiability of linear Boolean formula over the full binary basis and we show that the corresponding Exponential complexities are “interwoven” with those of k-\(\textsf{CNF} \; \textsf{SAT}\) in the following sense. For any constant c, let f c be the Exponential Complexity of the satisfiability problem for Boolean formulas of size at most cn. Similarly, let s k be the Exponential Complexity of k-\(\textsf{CNF} \; \textsf{SAT}\). We prove that for any c, there exists a k such that f c ≤ s k . Since the Sparsification Lemma [IPZ01] implies that for any k, there exists a c such that s k ≤ f c , we have sup c {f c } = sup k {s k }. (In fact, we prove this equality for a larger class of linear-size circuits that includes Boolean formulas.) Our work is partly motivated by two recent results. The first one is about a similar “interweaving” between linear-size circuits of constant depth and k-CNFs [SS12]. The second one is that satisfiability of linear-size Boolean formulas can be tested Exponentially faster than in O(2 n ) time [San10, ST12].
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CIAC - Exponential Complexity of Satisfiability Testing for Linear-Size Boolean Formulas
Lecture Notes in Computer Science, 2013Co-Authors: Evgeny Dantsin, Alexander WolpertAbstract:The Exponential Complexity of the satisfiability problem for a given class of Boolean circuits is defined to be the infimum of constants α such that the problem can be solved in time poly(m) 2 αn , where m is the circuit size and n is the number of input variables [IP01]. We consider satisfiability of linear Boolean formula over the full binary basis and we show that the corresponding Exponential complexities are “interwoven” with those of k-\(\textsf{CNF} \; \textsf{SAT}\) in the following sense. For any constant c, let f c be the Exponential Complexity of the satisfiability problem for Boolean formulas of size at most cn. Similarly, let s k be the Exponential Complexity of k-\(\textsf{CNF} \; \textsf{SAT}\). We prove that for any c, there exists a k such that f c ≤ s k . Since the Sparsification Lemma [IPZ01] implies that for any k, there exists a c such that s k ≤ f c , we have sup c {f c } = sup k {s k }. (In fact, we prove this equality for a larger class of linear-size circuits that includes Boolean formulas.) Our work is partly motivated by two recent results. The first one is about a similar “interweaving” between linear-size circuits of constant depth and k-CNFs [SS12]. The second one is that satisfiability of linear-size Boolean formulas can be tested Exponentially faster than in O(2 n ) time [San10, ST12].
Ali Zolghadri - One of the best experts on this subject based on the ideXlab platform.
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Set Adaptive Observers for Linear Parameter-Varying Systems: Application to Fault Detection
Journal of Dynamic Systems Measurement and Control, 2013Co-Authors: Denis Efimov, Tarek Raïssi, Ali ZolghadriAbstract:This paper deals with the problem of joint state and parameter estimation based on a set adaptive observer design. The problem is formulated and solved for an LPV (linear parameter-varying) system. The resolution methodology avoids the Exponential Complexity obstruction usually encountered in the set-membership parameter estimation. A simulation example is presented to illustrate the efficiency of the proposed approach.
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SET ADAPTIVE OBSERVERS FOR LPV SYSTEMS: APPLICATION TO FAULT DETECTION
Journal of Dynamic Systems Measurement and Control-transactions of The Asme, 2013Co-Authors: Denis Efimov, Tarek Raïssi, Ali ZolghadriAbstract:This paper deals with the problem of joint state and parameter estimation based on a set adaptive observer design. The problem is formulated and solved for an LPV (Linear Parameter-Varying) system. The resolution methodology avoids the Exponential Complexity obstruction usually encountered in the set-membership parameter estimation. A simulation example is presented to illustrate the efficiency of the proposed approach.
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Robust State and Parameter Estimation for Nonlinear Continuous-Time Systems in a Set-Membership Context
Modeling Design and Simulation of Systems with Uncertainties, 2011Co-Authors: Denis Efimov, Tarek Raässi, Ali ZolghadriAbstract:This chapter deals with joint state and parameter estimation for nonlinear continuous-time systems. Based on an appropriate LPV approximation, the problem is formulated in terms of a set adaptive observer design problem which can be efficiently solved. The resolution methodology avoids the Exponential Complexity obstruction often met in set-membership parameter estimation. The efficacy of the proposed set adaptive observers is demonstrated on several examples.
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Adaptive Set Observers Design for Nonlinear Continuous-Time Systems: Application to Fault Detection and Diagnosis
arXiv: Systems and Control, 2010Co-Authors: Denis Efimov, Tarek Raïssi, Ali ZolghadriAbstract:The paper deals with joint state and parameter estimation for nonlinear continuous-time systems. Based on a guaranteed LPV approximation, the set adaptive observers design problem is solved avoiding the Exponential Complexity obstruction usually met in the set-membership parameter estimation. Potential application to fault diagnosis is considered. The efficacy of the proposed set adaptive observers is demonstrated on several examples.
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MONOTONE ADAPTIVE SET OBSERVERS FOR NONLINEAR CONTINUOUS-TIME SYSTEMS
IFAC Proceedings Volumes, 2010Co-Authors: Denis Efimov, Tarek Raïssi, Ali ZolghadriAbstract:The paper deals with joint state and parameter estimation for nonlinear continuous-time systems. Based on a guaranteed LPV approximation, the problem of set observers design is recasted into more general adaptive observers design problem in order to avoid the Exponential Complexity obstruction usually met in the set-membership nonlinear estimation. The efficacy of the proposed set adaptive observer is demonstrated on a bioreactor example.
