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Distributed non-negative matrix factorization with determination of the number of latent features

The holistic analysis and understanding of the latent (that is, not directly observable) variables and patterns buried in large datasets is crucial for data-driven science, decision making and emergency response. Such exploratory analyses require devising unsupervised learning methods for data mining and extraction of the latent features, and non-negative matrix factorization (NMF) is one of the prominent such methods. NMF is based on compute-intense non-convex constrained minimization, which, for large datasets requires fast and distributed algorithms. However, current parallel implementations of NMF fail to estimate the number of latent features. In practice, identifying these features is both difficult and significant for pattern recognition and latent feature analysis, especially for large dense matrices. Here, we introduce a distributed NMF algorithm coupled with distributed custom clustering followed by a stability analysis on dense data, which we call DnMFk, to determine the number of latent variables. The results on synthetic data and the classical Swimmer data set demonstrate the accuracy of model determination while scaling nearly linearly across multiple processors for large data. Further, we employ DnMFk to determine the number of hidden features from a terabyte matrix.

97 MATHEMATICS AND COMPUTING↗

Generating Dominating Sets Using Locally Defined Centrality Measures

The dominating set problem has many practical applications but is well-known to be NP-hard. Therefore, there is a need for efficient heuristic algorithms, especially in applications such as ad hoc wireless networks. Most distributed algorithms proposed in the literature assume that each node has knowledge of the network structure. We propose a distributed heuristic algorithm that uses two rounds of communication, and where each node has only local information, both in terms of network structure and dominating set assignment. First, each node calculates a local centrality measure to determine whether it is part of the dominating set D. The second round guarantees D is a dominating set by adding any non-dominated nodes. We compare several centrality measures and show that the Shapley centrality, derived from the Shapley value in game theory, is theoretically motivated and performs well in practice on several synthetic and real-world networks.

Network↗

Efficient Parallel Algorithm For Direct Numerical Simulation of Turbulent Flows

A distributed algorithm for a high-order-accurate finite-difference approach to the direct numerical simulation (DNS) of transition and turbulence in compressible flows is described. This work has two major objectives. The first objective is to demonstrate that parallel and distributed-memory machines can be successfully and efficiently used to solve computationally intensive and input/output intensive algorithms of the DNS class. The second objective is to show that the computational complexity involved in solving the tridiagonal systems inherent in the DNS algorithm can be reduced by algorithm innovations that obviate the need to use a parallelized tridiagonal solver.

Moitra, Stuti↗

Stochastic Gradient-Based Distributed Bayesian Estimation in Cooperative Sensor Networks

Distributed Bayesian inference provides a full quantification of uncertainty offering numerous advantages over point estimates that autonomous sensor networks are able to exploit. However, fully-decentralized Bayesian inference often requires large communication overheads and low network latency, resources that are not typically available in practical applications. In this paper, we propose a decentralized Bayesian inference approach based on stochastic gradient Langevin dynamics, which produces full posterior distributions at each of the nodes with significantly lower communication overhead. We provide analytical results on convergence of the proposed distributed algorithm to the centralized posterior, under typical network constraints. Finally, we also provide extensive simulation results to demonstrate the validity of the proposed approach.

42 ENGINEERING↗

Distributed Automatic Differentiation for Ptychography

Synchrotron radiation light source facilities are leading the way to ultrahigh resolution X-ray imaging. High resolution imaging is essential to understanding the fundamental structure and interaction of materials at the smallest length scale possible. Diffraction based methods achieve nanoscale imaging by replacing traditional objective lenses by pixelated area detectors and computational image reconstruction. Among these methods, ptychography is quickly becoming the standard for sub-30 nanometer imaging of extended samples, but at the expense of increasingly high data rates and volumes. This paper presents a new distributed algorithm for solving the ptychographic image reconstruction problem based on automatic differentiation. Input datasets are subdivided between multiple graphics processing units (GPUs); each subset of the problem is then solved either entirely independent of other subsets (asynchronously) or through sharing gradient information with other GPUs (synchronously). The algorithm was evaluated on simulated and real data acquired at the Advanced Photon Source, scaling up to 192 GPUs. The synchronous variant of our method outperformed an existing multi-GPU implementation in terms of accuracy while running at a comparable execution time.

distributed algorithms↗

A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems

Historically, centrally computed algorithms have been the primary means of power system optimization and control. With increasing penetrations of distributed energy resources requiring optimization and control of power systems with many controllable devices, distributed algorithms have been the subject of significant research interest. Here, this paper surveys the literature of distributed algorithms with applications to optimization and control of power systems. In particular, this paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Distributed state-space generation of discrete-state stochastic models

High-level formalisms such as stochastic Petri nets can be used to model complex systems. Analysis of logical and numerical properties of these models of ten requires the generation and storage of the entire underlying state space. This imposes practical limitations on the types of systems which can be modeled. Because of the vast amount of memory consumed, we investigate distributed algorithms for the generation of state space graphs. The distributed construction allows us to take advantage of the combined memory readily available on a network of workstations. The key technical problem is to find effective methods for on-the-fly partitioning, so that the state space is evenly distributed among processors. In this paper we report on the implementation of a distributed state-space generator that may be linked to a number of existing system modeling tools. We discuss partitioning strategies in the context of Petri net models, and report on performance observed on a network of workstations, as well as on a distributed memory multi-computer.

Ciardo, Gianfranco↗

Improving Search Algorithms by Using Intelligent Coordinates

We consider algorithms that maximize a global function G in a distributed manner, using a different adaptive computational agent to set each variable of the underlying space. Each agent eta is self-interested; it sets its variable to maximize its own function g (sub eta). Three factors govern such a distributed algorithm's performance, related to exploration/exploitation, game theory, and machine learning. We demonstrate how to exploit alI three factors by modifying a search algorithm's exploration stage: rather than random exploration, each coordinate of the search space is now controlled by a separate machine-learning-based player engaged in a noncooperative game. Experiments demonstrate that this modification improves simulated annealing (SA) by up to an order of magnitude for bin packing and for a model of an economic process run over an underlying network. These experiments also reveal interesting small-world phenomena.

Wolpert, David H.↗

Fast and Scalable Implementations of Influence Maximization Algorithms

The Influence Maximization problem has been extensively studied in the past decade because of its practical applications in finding the key influencers in social networks. Due to the hardness of the underlying problem, existing algorithms have tried to trade off practical efficiency with approximation guarantees. However, even such approximate solutions take several hours of compute time on modest sized real world inputs. On the other hand, there is a lack of effective parallel and distributed algorithms to solve this problem. In this paper, we present efficient parallel algorithms for multithreaded and distributed systems to solve the influence maximization with approximation guarantee. Our algorithms extend state-of-the-art sequential approach based on computing reverse reachability sets. We present a detailed experimental evaluation, and analyze their performance and their sensitivity to input parameters, using real world inputs. Our experimental results demonstrate significant speedup on parallel architectures. We further show a speedup of up to 586X relative to the state-of-the-art sequential baseline using 1024 nodes of a supercomputer at far greater accuracy and twice the seed set size. To the best of our knowledge, this is the first effort in parallelizing the influence maximization operation at scale.

Minutoli, Marco↗

Distributed Detection of Malicious Attacks on Consensus Algorithms with Applications in Power Networks

Consensus-based distributed algorithms are well suited for coordination among agents in a cyber-physical system. These distributed schemes, however, suffer from their vulnerability to cyber attacks that are aimed at manipulating data and control ow. In this article, we present a novel distributed method for detecting the presence of such intrusions for a distributed multi-agent system following ratio consensus. We employ a Max-Min protocol to develop low cost, easy to implement detection strategies where each participating node detects the intrusion independently, eliminating the need for a trusted certifying agent in the network. The effectiveness of the detection method is demonstrated by numerical simulations on a 1000 node network to demonstrate the efficacy and simplicity of implementation.

27 ARPA - Advanced Research Projects Agency-Energy↗

Building Large-Scale U.S. Synthetic Electric Distribution System Models

Rapid increases in distributed energy resources on distribution systems are prompting research efforts to improve and evaluate electric power distribution algorithms; however, there is a shortage of realistic, large-scale, U.S.-style test systems for the evaluation of such advanced algorithms. Some available tools to build large-scale test systems are of European style, and their application to studies focused on the United States might not be desirable given very different characteristics between the European and U.S. distribution designs. Motivated by this need, this paper develops detailed algorithms to build large-scale U.S. distribution systems and incorporates them in a new Reference Network Model, RNM-US. The approach starts with information from street maps and a catalog with electric equipment that includes power lines, transformers, voltage regulators, capacitors, and switching devices. The paper presents the algorithms through an illustrative case study of the different steps that comprise the process of building a synthetic distribution grid. Finally, the paper presents a medium- and a large-scale data set covering 10 million electrical nodes and 120,000 km of power lines, demonstrating the applicability of the proposed method to build very large-scale synthetic distribution systems.

27 ARPA - Advanced Research Projects Agency-Energy↗

Distributed Energy Management for Networked Microgrids Using Online ADMM With Regret

We propose a distributed algorithm for online energy management in networked microgrids with a high penetration of distributed energy resources (DERs). A high penetration of DERs introduces high uncertainty of power generation to the microgrids. In general, the state-of-the-art forecasting for non-dispatchable DERs such as solar energy is not sufficiently accurate, which results in inaccurate energy scheduling. To address the high uncertainty issue in the networked microgrids, we propose an online energy management based on the online alternating direction method of multipliers algorithm with the past power generation information from the DERs. The online algorithm provides less conservative schedule than the robust optimization-based approach. The effectiveness of the proposed algorithm is verified by various numerical examples.

alternating direction method of multipliers↗

Impacts of Distributed Speed Harmonization and Optimal Maneuver Planning on Multi-Lane Roads

A commonly proposed method for improving traffic flow on freeways is speed harmonization. The effectiveness of current speed harmonization approaches, such as variable speed limits, is extremely reliant on human driver compliance. Connected and automated vehicles (CAVs) are expected to come to market within this decade, offering the opportunity to eliminate or reduce the reliance on human compliance. However, extending current roadside infrastructure-based approaches of assigning centrally computed harmonization speeds to individual vehicles is, costly. An alternative approach is to have individual vehicles estimate the traffic state on-board and make distributed decisions to achieve the harmonization goal autonomously. In this work, we present a distributed algorithm for estimating the current average speed of traffic. We couple this with a distributed 2D maneuver planning approach. Then, we study the impact on traffic efficiency in terms of energy consumption and travel time at varying CAV penetration rates.

Goulet, Nathan↗

Distributed Augmentation, Hypersweeps, and Branch Decomposition of Contour Trees for Scientific Exploration

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale using highperformance computing. To address this challenge, recent work has introduced distributed hierarchical contour trees for distributed computation and storage of contour trees. However, effective use of these distributed structures in analysis and visualization requires subsequent computation of geometric properties and branch decomposition to support contour extraction and exploration. In this work, we introduce distributed algorithms for augmentation, hypersweeps, and branch decomposition that enable parallel computation of geometric properties, and support the use of distributed contour trees as query structures for scientific exploration. Finally, we evaluate the parallel performance of these algorithms and apply them to identify and extract important contours for scientific visualization.

97 MATHEMATICS AND COMPUTING↗

Distributed Optimal Dispatch of Distributed Energy Resources Over Lossy Communication Networks

In this paper, we consider the economic dispatch problem (EDP), where a cost function that is assumed to be strictly convex is assigned to each of distributed energy resources (DERs), over packet dropping networks. The goal of a standard EDP is to minimize the total generation cost while meeting total demand and satisfying individual generator output limit. We propose a distributed algorithm for solving the EDP over networks. The proposed algorithm is resilient against packet drops over communication links. Under the assumption that the underlying communication network is strongly connected with a positive probability and the packet drops are independent and identically distributed (i.i.d.), we show that the proposed algorithm is able to solve the EDP. Numerical simulation results are used to validate and illustrate the main results of the paper.

97 MATHEMATICS AND COMPUTING↗

Distributed topology control algorithm for multihop wireless netoworks

We present a network initialization algorithmfor wireless networks with distributed intelligence. Each node (agent) has only local, incomplete knowledge and it must make local decisions to meet a predefined global objective. Our objective is to use power control to establish a topology based onthe relative neighborhood graph which has good overall performance in terms of power usage, low interference, and reliability.

topology control distributed algorithm wireless ne↗

Digital image centering. II

Digital image centering algorithms were compared in a test involving microdensitometer raster scans of a refractor parallax series consisting of 22 stars on 26 plates. The highest accuracy in determining stellar image positions was provided by an algorithm which involved fitting of a symmetric Gaussian curve and a flat background to the image marginal density distributions. Algorithms involving transmission marginals instead of density marginals were found to be less accurate. The repeatability and computational efficiency of the digital image centering technique were also studied.

Auer, L. H.↗