General Iterative Framework Research Articles

Identifying influential nodes on directed networks

Identifying influential nodes on directed networks is a challenging and widely studied task that keeps drawing extensive attention from both academia and industry. The simultaneous consideration of both local and global structural information has demonstrated its effectiveness in identifying influential nodes on un-directed networks. Nevertheless, how to better utilize these two types of information on directed networks remains a challenge. In this paper, we address the influential nodes identification problem for directed networks where a node can directly affect its in-neighbors, like the social network of Twitter. We present a general iterative framework that integrates both local structural information and global influence. The global influence exerted by the target node is determined as the cumulative sum of the global influences originating from its in-neighbors, achieved through an iterative procedure. Meanwhile, the in-degree of the target node is leveraged to capture local structural information, which is consistently reinforced throughout the iterative process to prevent the attenuation of its significance over successive iterations. Our algorithm demonstrates significant performance improvement, averaging 21.61% in Kendall's τ and 23.43% in precision@0.05 over the 8 benchmarks across 15 real networks. Moreover, it outperforms the benchmarks on artificial networks, and can effectively identify fast influencers.

A compass-based hyper-heuristic for multi-objective optimization problems

Multi-objective selection hyper-heuristics have attracted more attention of researchers because of their cross-domain ability. However, for multi-objective optimization problems (MOPs), obtaining a manageable number of solutions that are well distributed and converged in the objective space is still a challenge, especially when solving high-dimensional MOPs. In order to solve this problem, this paper proposes a compass-based hyper-heuristics(COHH), which is a general iterative framework that learns and selects from a set of meta-heuristics or components (named low-level heuristics, LLHs). The selected LLH is applied to solve the given MOP at the current iteration. In order to learn the potential of LLHs, the impact of the diversity of the current solution set on the final performance is studied. Then a new compass-based indicator is defined to evaluate the current solution sets. The learning strategy with new indicator can bias to diversity by adjusting the angle of a reference vector. After learning, the adaptive two-stage selection strategy triggered by the quality of the current solution set is used to choose LLH. Experiments are conducted on DTLZ, MaOP, WFG, and MaF test suites, as well as several real-world constrained test problems. Experimental results show that COHH is competitive in performance and cross-domain capability when compared with popular meta-heuristics and hyper-heuristics.

The minimum cost network upgrade problem with maximum robustness to multiple node failures

The design of networks which are robust to multiple failures is gaining increasing attention in areas such as telecommunications. In this paper, we consider the problem of upgrading an existent network in order to enhance its robustness to events involving multiple node failures. This problem is modeled as a bi-objective mixed linear integer formulation considering both the minimization of the cost of the added edges and the maximization of the robustness of the resulting upgraded network. As the robustness metric of the network, we consider the value of the Critical Node Detection (CND) problem variant which provides the minimum pairwise connectivity between all node pairs when a set of c critical nodes are removed from the network. We present a general iterative framework to obtain the complete Pareto frontier that alternates between the minimum cost edge selection problem and the CND problem. Two different approaches based on a cover model are introduced for the edge selection problem. Computational results conducted on different network topologies show that the proposed methodology based on the cover model is effective in computing Pareto solutions for graphs with up to 100 nodes, which includes four commonly used telecommunication networks.

AdaPT: An Interactive Procedure for Multiple Testing with Side Information

SummaryWe consider the problem of multiple-hypothesis testing with generic side information: for each hypothesis Hi we observe both a p-value pi and some predictor xi encoding contextual information about the hypothesis. For large-scale problems, adaptively focusing power on the more promising hypotheses (those more likely to yield discoveries) can lead to much more powerful multiple-testing procedures. We propose a general iterative framework for this problem, the adaptive p-value thresholding procedure which we call AdaPT, which adaptively estimates a Bayes optimal p-value rejection threshold and controls the false discovery rate in finite samples. At each iteration of the procedure, the analyst proposes a rejection threshold and observes partially censored p-values, estimates the false discovery proportion below the threshold and proposes another threshold, until the estimated false discovery proportion is below α. Our procedure is adaptive in an unusually strong sense, permitting the analyst to use any statistical or machine learning method she chooses to estimate the optimal threshold, and to switch between different models at each iteration as information accrues. We demonstrate the favourable performance of AdaPT by comparing it with state of the art methods in five real applications and two simulation studies.

An iterative framework for sparse signal reconstruction algorithms

It has been shown that iterative re-weighted strategies will often improve the performance of many sparse reconstruction algorithms. However, these strategies are algorithm dependent and cannot be easily extended for an arbitrary sparse reconstruction algorithm. In this paper, we propose a general iterative framework and a novel algorithm which iteratively enhance the performance of any given arbitrary sparse reconstruction algorithm. We theoretically analyze the proposed method using restricted isometry property and derive sufficient conditions for convergence and performance improvement. We also evaluate the performance of the proposed method using numerical experiments with both synthetic and real-world data.

A framework for iterative analysis of non-classically damped dynamical systems

In this paper, we propose a general iterative framework to solve the dynamic problem for linear systems with non-classical viscous damping. A systematic approach is used to derive families of stationary iterative schemes that, as an instance of particular interest, decouple the equations of motion for numerical study of the system response. For such schemes, we present a detailed convergence analysis and propose several solution strategies suitable for a broad class of systems. These techniques are based on spectral analysis of particular iteration matrices arising in the derivation and aim at optimizing the convergence performance of the method. We demonstrate that the proposed systematic framework, based on a novel application of the homotopy analysis method, generalizes iterative schemes previously reported in the literature and, importantly, provides a unified perspective for the study of iterative solutions of dynamic problems. Further, we establish a connection between our results and the theory of iterative schemes for algebraic linear systems, thus providing insights on convergence results and applicability of the method. Numerical examples illustrate the effectiveness of the approach and indicate future research directions.

Dynamical backreaction of relic gravitons

The dynamical effects of the tensor modes of the geometry are investigated in the context of curvature bounces. Since the bouncing behaviour implies sharp deviations from a radiation-dominated evolution, significant back-reaction effects of relic gravitons may be expected at short wavelengths. After developing a general iterative framework for the calculation of dynamical back-reaction effects, explicit analytical and numerical examples are investigated for different parametrizations of the energy-momentum pseudo-tensor(s) of the produced gravitons. The reported results suggest that dynamical back-reaction effects are a necessary ingredient for a consistent description of bouncing models at late times.

Globally convergent iterative numerical schemes for nonlinear variational image smoothing and segmentation on a multiprocessor machine

We investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel. A general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown. We characterize various edge-preserving regularization methods from the image processing literature involving auxiliary variables as special cases of this general framework. As a by-product, global convergence can be proven under conditions slightly weaker than these stated in the literature. Efficient Krylov subspace solvers for the linear parts of these schemes have been implemented on a multiprocessor machine. The performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed-up factors are reported.

Precision Requirements for Closed-Loop Kinematic Robotic Control Using Linear Local Mappings

Neural networks are approximation techniques that can be characterized by adaptability rather than by precision. For feedback systems, high precision can still be acquired in presence of errors. Within a general iterative framework of closed-loop kinematic robotic control using linear local modeling, the inverse Jacobian matrix error and the maximum length of the displacement for which the linear model is valid are computed. They guarantee convergence of the feedback loop. The error bounds are computed for our manipulator. The theoretical results are validated by simulation.