Subspace Selection for Projection Maximization With Matroid Constraints

Zhang, Zhenliang; Wang, Yuan; Chong, Edwin K. P.; Pezeshki, Ali

doi:10.1109/tsp.2016.2634544

Cited by 3 publications

(1 citation statement)

References 41 publications

(30 reference statements)

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“…This inequality characterizes the submodularity, which is the quantitative measure of the diminishing-return property [34]. It is analogous to concavity of continuous functions, wherein the increment of adding a new component v ∈ V \T to the set S, is larger than or equal to the set T .…”

Section: Submodularitymentioning

confidence: 99%

Leader Selection in Multi-Agent Networks with Switching Topologies via Submodular Optimization

Chen¹,

He²,

Tang³

et al. 2019

Preprint

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In leader-follower multi-agent networks with switching topologies, choosing a subset of agents as leaders is a critical step to achieve desired performances. In this paper, we concentrate on the problem of selecting a minimum-size set of leaders that ensure the tracking of a reference signal in a highorder linear multi-agent network with a set of given topologydependent dwell time (TDDT). First, we derive a sufficient condition that guarantees the states of all agents converging to an expected state trajectory. Second, by exploiting submodular optimization method, we formulate the problem of identifying a minimal leader set which satisfies the proposed sufficient condition. Third, we present an algorithm with the provable optimality bound to solve the formulated problem. Finally, several numerical examples are provided to verify the effectiveness of the designed selection scheme.

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Section: Submodularitymentioning

confidence: 99%

Leader Selection in Multi-Agent Networks with Switching Topologies via Submodular Optimization

Chen¹,

He²,

Tang³

et al. 2019

Preprint

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Controlled Islanding via Weak Submodularity

Liu

Clark

Bushnell

et al. 2019

IEEE Trans. Power Syst.

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Cascading failures typically occur following a large disturbance in power systems, such as tripping of a generating unit or a transmission line. Such failures can propagate and destabilize the entire power system, potentially leading to widespread outages. One approach to mitigate impending cascading failures is through controlled islanding, in which a set of transmission lines is deliberately tripped to partition the unstable system into several disjoint, internally stable islands. Selecting such a set of transmission lines is inherently a combinatorial optimization problem. Current approaches address this problem in two steps: first classify coherent generators into groups and then separate generator groups into different islands with minimal load-generation imbalance. These methods, however, are based on computationally expensive heuristics that do not provide optimality guarantees. In this paper, we propose a novel approach to controlled islanding based on weak submodularity. Our formulation jointly captures the minimal generator non-coherency and minimal load-generation imbalance in one objective function. We relax the problem to a formulation with bounded submodularity ratio and a matroid constraint, and propose an approximation algorithm which achieves a provable optimality bound on non-coherency and load-generation imbalance. The proposed framework is tested on IEEE 39-bus and 118-bus power systems.

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On the Vulnerability of Graph Learning-based Collaborative Filtering

et al. 2023

ACM Trans. Inf. Syst.

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Graph learning based collaborative filtering (GLCF), which is built upon the message passing mechanism of graph neural networks (GNNs), has received great recent attention and exhibited superior performance in recommender systems. However, although GNNs can be easily compromised by adversarial attacks as shown by the prior work, little attention has been paid to the vulnerability of GLCF. Questions like can GLCF models be easily fooled just as GNNs remain largely unexplored. In this article, we propose to study the vulnerability of GLCF. Specifically, we first propose an adversarial attack against CLCF. Considering the unique challenges of attacking GLCF, we propose to adopt the greedy strategy in searching for the local optimal perturbations, and design a reasonable attacking utility function to handle the non-differentiable ranking-oriented metrics. Next, we propose a defense to robustify GCLF. The defense is based on the observation that attacks usually introduce suspicious interactions into the graph so as to manipulate the message passing process. We then propose to measure the suspicious score of each interaction and further reduce the message weight of suspicious interactions. We also give a theoretical guarantee of its robustness. Experimental results on three benchmark datasets show the effectiveness of both our attack and defense.

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Subspace Selection for Projection Maximization With Matroid Constraints

Cited by 3 publications

References 41 publications

Leader Selection in Multi-Agent Networks with Switching Topologies via Submodular Optimization

Leader Selection in Multi-Agent Networks with Switching Topologies via Submodular Optimization

Controlled Islanding via Weak Submodularity

On the Vulnerability of Graph Learning-based Collaborative Filtering

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