The $25,000,000,000 Eigenvector: The Linear Algebra behind Google

Bryan, Kurt; Leise, Tanya

doi:10.1137/050623280

Cited by 215 publications

(151 citation statements)

References 9 publications

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“…This metric has been generalized to metapopulations by Ovaskainen and Hanski (35) and Jacobi and Jonsson (36), and it identifies the contribution of an individual subpopulation to the growth rate of the entire metapopulation. This metric is otherwise known as "eigenvector centrality" in network theory and has been used to identify keystone species in food webs (36) and important Web pages by the Google search algorithm (54). Here, eigenvector centrality is calculated as the left eigenvector associated with the leading eigenvalue of the realized connectivity matrix (R ij ) and identifies subpopulations that are hubs of realized connectivity.…”

Section: Methodsmentioning

confidence: 99%

Identifying critical regions in small-world marine metapopulations

Watson

Siegel

Kendall³

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

111

118

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The precarious state of many nearshore marine ecosystems has prompted the use of marine protected areas as a tool for management and conservation. However, there remains substantial debate over their design and, in particular, how to best account for the spatial dynamics of nearshore marine species. Many commercially important nearshore marine species are sedentary as adults, with limited home ranges. It is as larvae that they disperse greater distances, traveling with ocean currents sometimes hundreds of kilometers. As a result, these species exist in spatially complex systems of connected subpopulations. Here, we explicitly account for the mutual dependence of subpopulations and approach protected area design in terms of network robustness. Our goal is to characterize the topology of nearshore metapopulation networks and their response to perturbation, and to identify critical subpopulations whose protection would reduce the risk for stock collapse. We define metapopulation networks using realistic estimates of larval dispersal generated from ocean circulation simulations and spatially explicit metapopulation models, and we then explore their robustness using node-removal simulation experiments. Nearshore metapopulations show small-world network properties, and we identify a set of highly connected hub subpopulations whose removal maximally disrupts the metapopulation network. Protecting these subpopulations reduces the risk for systemic failure and stock collapse. Our focus on catastrophe avoidance provides a unique perspective for spatial marine planning and the design of marine protected areas.connectivity | larval dispersal | protected area design | network theory | Lagrangian simulations N earshore marine ecosystems are some of the most productive and diverse environments on earth, maintaining a wide variety of organisms and providing essential food and services to the global population. Unfortunately, they are also under increasing stress from perturbations, such as oil spills, climate change, and overfishing, and are at risk for losing their productive output (1, 2). Mitigating the impacts of these perturbations is difficult because most nearshore marine species exist in a spatially complex system of connected subpopulations; stress placed at one location may detrimentally reduce stock levels at many others (3, 4). Quantifying patterns of connectivity is crucial to our ability to manage these systems effectively. For example, marine protected areas (MPAs) have emerged as an important tool for conservation and fisheries managers tasked with maintaining nearshore systems and accounting for the mutual demographic dependence of populations (3-9). Current approaches to their design center on either protecting essential habitats (5, 6, 9) or maximizing economic goals (10, 11). We provide an alternative and consider the design of MPAs as a problem of metapopulation network robustness, here defined as the ability of a system to withstand perturbation (12). Our goal is to account for patterns of connectivity and...

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Section: Methodsmentioning

confidence: 99%

Identifying critical regions in small-world marine metapopulations

Watson

Siegel

Kendall³

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

111

118

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“…A benefit of this approach is that as additional data are included, the analyses become repetitive, more refined, and thus more efficient. For example, Google originally used PageRank to prune and order search queries; new search algorithms, however became even ''smarter'' as the number and types of searches increased over time, and more and better information was included in the query algorithms (Bryan and Leise 2006). Now, power users can direct the analyses and develop products and tools based on correlations that are then accessed by the user community for more specific applications (Garrett et al 2006, Delaney andBarga 2009).…”

Section: Current Approaches To the Data Delugementioning

confidence: 99%

“…Alternatively, data-intensive approaches using machine learning developed in other fields, for example to provide information retrieval, support business decision-making, and improve overall user experience on the Internet (Bryan andLeise 2006, Ginsberg et al 2009), can explain patterns in ecological data. However, these correlation analyses of large quantities of mixed quality data, and numerous queries and analyses have limited direct application to scientific research where understanding underlying processes is paramount to knowledge discovery and problem solving (http://nyti.ms/1kgErs2).…”

Section: Introductionmentioning

confidence: 99%

“…In order to scale the scientific method to allow ecologists to take advantage of the data deluge, what is needed is a knowledge-driven, open access system that ''learns'' and becomes more efficient and easier to use as streams of data, and the number and types of user interactions, increase-similar to how internet searches and recommender systems work (Bryan and Leise 2006;http://microsoft.com). Science is on the verge of a revolution, but for this to occur, scientists must radically change their way of thinking and their way of doing science to take advantage of the deluge of data and its global accessibility (Friedman 2005, Tolle et al 2011.…”

Section: Introductionmentioning

confidence: 99%

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Harnessing the power of big data: infusing the scientific method with machine learning to transform ecology

Peters¹,

Havstad²,

Cushing³

et al. 2014

Ecosphere

135

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Abstract. Most efforts to harness the power of big data for ecology and environmental sciences focus on data and metadata sharing, standardization, and accuracy. However, many scientists have not accepted the data deluge as an integral part of their research because the current scientific method is not scalable to large, complex datasets. Here, we explain how integrating a data-intensive, machine learning approach with a hypothesis-driven, mechanistic approach can lead to a novel knowledge, learning, analysis system (KLAS) for discovery and problem solving. Machine learning leads to more efficient, user-friendly analytics as the streams of data increase while hypothesis-driven decisions lead to the strategic design of experiments to fill knowledge gaps and to elucidate mechanisms. KLAS will transform ecology and environmental sciences by shortening the time lag between individual discoveries and leaps in knowledge by the scientific community, and will lead to paradigm shifts predicated on open access data and analytics in a machine learning environment.

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“…, λ m , then [Haveliwala & Kamvar (2003); Langville & Meyer (2005)]: (7.12) Then, Equation 7.12 guarantees convergence, with the appropriate accuracy, of this power method. Another works introduce alternatives to approach the PageRank vector; among them Bryan & Leise (2006), Langville & Meyer (2006) and Pedroche (2007). Chung & Zhao (2008) proposed a generalisation of the PageRank algorithm to establish an ordering of the vertices in a graph.…”

Section: Computation Of Pagerank Vectormentioning

confidence: 99%

Improving water network management by efficient division into supply clusters

Herrera¹,

Manuel²

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Water is a scarce resource and must be efficiently managed. One of the purposes of efficient management should be reducing water losses and increasing supply performance in the networks through a profound knowledge of water supply networks (WSN). Obtaining this knowledge in real networks is a complex task because distribution systems may consist of thousands of consumption nodes interconnected by thousands of lines and the necessary elements to feed the network. These networks are not usually the outcome of a single process of design and are the consequence of years of anarchic responses to continually rising new demands. As a result, layouts lack a clear structure from a topological point of view.The division of a water supply network into supply clusters enables sufficient hydraulic knowledge to be gathered to carry out maintenance tasks and guarantee quantity and regularity to the final consumer. This approach divides large and highly interconnected distribution networks into smaller sub-networks. These smaller networks are virtually independent and fed by a prefixed number of sources. Independence can be physically enforced in a number of ways. For instance, by closing valves in existing pipes, by sectioning existing pipes, or by introducing new pipes to redistribute the flow. Each supply cluster inlet must be equipped with at least one flowmeter to accurately measure and record consumption in short time periods.However, gauges and meters must also be placed to measure and control pressure, chlorine concentrations, and other supply parameters.Water network division into supply clusters should not be understood only in network configuration terms, but also as a permanent method of management. It is essential to provide the system with a main centre that can receive and sort daily data, as well as analyse other information (such as financial, climatological, inventory, and maintenance data). In this way, we can establish the real performance of sectors and take appropriate decisions regarding both operational maintenance and investment. From a classical perspective, the division of a water supply network into sectors is used with the aim of controlling leaks, since it helps maintain a permanent pressure control system. Nevertheless, this target has recently become more ambitious and incorporates new operational and management tasks.This thesis proposes a suitable framework to establish efficient methods to divide the network into sectors and manage a WSN by taking advantage of this structure. These tasks will be addressed using kernel methods and multi-agent systems. Spectral clustering and semi-supervised learning have been shown to behave well when defining a sectorised network with a minimum number of cut-off valves. However, their algorithms are slow (and sometimes infeasible) when tackling divisions in a large WSN. The multi-agent system approach, firstly created as an alternative solution, is an excellent complementary tool for clustering kernel methods that use a boosting methodology. It is ther...

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The $25,000,000,000 Eigenvector: The Linear Algebra behind Google

Cited by 215 publications

References 9 publications

Identifying critical regions in small-world marine metapopulations

Identifying critical regions in small-world marine metapopulations

Harnessing the power of big data: infusing the scientific method with machine learning to transform ecology

Improving water network management by efficient division into supply clusters

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