Learning in Single Hidden-Layer Feedforward Network Models: Backpropagation in a Spatial Interaction Modeling Context

Learning in neural networks has attracted considerable interest in recent years. Our focus is on learning in single hidden-layer feedforward networks which is posed as a search in the network parameter space for a network that minimizes an additive error function of statistically independent examples. We review first the class of single hidden-layer feedforward networks and characterize the learning process in such networks from a statistical point of view. Then we describe the backpropagation procedure, the leading case of gradient descent learning algorithms for the class of networks considered here, as well as an efficient heuristic modification. Finally, we analyze the applicability of these learning methods to the problem of predicting interregional telecommunication flows. Particular emphasis is laid on the engineering judgment, first, in choosing appropriate values for the tunable parameters, second, on the decision whether to train the network by epoch or by pattern (random approximation), and, third, on the overfitting problem. In addition, the analysis shows that the neural network model whether using either epoch-based or pattern-based stochastic approximation outperforms the classical regression approach to modeling telecommunication flows.     

Dispersion of Nodes Added to a Network

For location problems in which optimal locations can be at nodes or along arcs but no finite dominating set has been identified, researchers may desire a method for dispersing p additional discrete candidate sites along the m arcs of a network. This article develops and tests minimax and maximin models for solving this continuous network location problem, which we call the added-node dispersion problem (ANDP). Adding nodes to an arc subdivides it into subarcs. The minimax model minimizes the maximum subarc length, while the maximin model maximizes the minimum subarc length. Like most worst-case objectives, the minimax and maximin objectives are plagued by poorly behaved alternate optima. Therefore, a secondary MinSumMax objective is used to select the best-dispersed alternate optima. We prove that equal spacing of added nodes along arcs is optimal to the MinSumMax objective. Using this fact we develop greedy heuristic algorithms that are simple, optimal, and efficient (O( mp )). Empirical results show how the maximum subarc, minimum subarc, and sum of longest subarcs change as the number of added nodes increases. Further empirical results show how using the ANDP to locate additional nodes can improve the solutions of another location problem. Using the p-dispersion problem as a case study, we show how much adding ANDP sites to the network vertices improves the p-dispersion objective function compared with (a) network vertices only and (b) vertices plus randomly added nodes. The ANDP can also be used by itself to disperse facilities such as stores, refueling stations, cell phone towers, or relay facilities along the arcs of a network, assuming that such facilities already exist at all nodes of the network.     

A Computational Method for Market Area Analysis on a Network

This paper shows a computational method for market area analysis assuming that stores and consumers are distributed over a network and the distance between two points on the network is given by the route distance. First, we consider five basic questions often raised in market area analysis, and show a general method, called the network transformation method, that gives an intuitive way of looking at computational methods for solving these questions. Second, assuming that consumers follow the Huff model, we consider four questions concerning market area delineation and market potential often discussed in market area analysis in practice. We show that the network transformation method is also useful to develop computational methods for solving these questions. One of the notable results is that market area delineation of the Huff model (which is analytically difficult to obtain on a plane) can be exactly obtained on a network.     

To binarize or not to binarize: relational data and the construction of archaeological networks

Over the last several years, network methods and models from the social and physical sciences have gained considerable popularity in archaeology. Many of the most common network methods begin with the creation of binary networks where links among some set of actors are defined as either present or absent. In most archaeological cases, however, the presence or absence of a specific kind of relationship between actors is not straightforward as we must rely on material proxies for assessing connections. A common approach in recent studies has been to define some threshold for the presence of a tie by partitioning continuous relational data among sites (e.g., artifact frequency or similarity data). In this article, using an example from the U.S. Southwest, we present a sensitivity analysis focused on the potential effects of defining binary networks from continuous relational data. We show that many key network properties that are often afforded social interpretations are fundamentally influenced by the assumptions used to define connections. We suggest that, although network graphs provide powerful visualizations of network data, methods for creating and analyzing weighted (non-binarized) networks often provide a better characterization of specific network properties.     

ARTIFICIAL NEURAL NETWORKS: A NEW APPROACH TO MODELING INTERREGIONAL TELECOMMUNICATION FLOWS*

ABSTRACT. During the last thirty years there has been much research effort in regional science devoted to modeling interactions over geographic space. Theoretical approaches for studying these phenomena have been modified considerably. This paper suggests a new modeling approach, based upon a general nested sigmoid neural network model. Its feasibility is illustrated in the context of modeling interregional telecommunication traffic in Austria, and its performance is evaluated in comparison with the classical regression approach of the gravity type. The application of this neural network approach may be viewed as a three-stage process. The first stage refers to the identification of an appropriate network from the family of two-layered feedforward networks with 3 input nodes, one layer of (sigmoidal) intermediate nodes and one (sigmoidal) output node (logistic activation function). There is no general procedure to address this problem. We solved this issue experimentally. The input-output dimensions have been chosen in order to make the comparison with the gravity model as close as possible. The second stage involves the estimation of the network parameters of the selected neural network model. This is performed via the adaptive setting of the network parameters (training, estimation) by means of the application of a least mean squared error goal and the error back propagating technique, a recursive learning procedure using a gradient search to minimize the error goal. Particular emphasis is laid on the sensitivity of the network performance to the choice of the initial network parameters, as well as on the problem of overfitting. The final stage of applying the neural network approach refers to the testing of the interregional teletraffic flows predicted. Prediction quality is analyzed by means of two performance measures, average relative variance and the coefficient of determination, as well as by the use of residual analysis. The analysis shows that the neural network model approach outperforms the classical regression approach to modeling telecommunication traffic in Austria.     

Micro‐Level Interpretation of Exponential Random Graph Models with Application to Estuary Networks

The exponential random graph model (ERGM) is an increasingly popular method for the statistical analysis of networks that can be used to flexibly analyze the processes by which policy actors organize into a network. Often times, interpretation of ERGM results is conducted at the network level, such that effects are related to overall frequencies of network structures (e.g., the number of closed triangles in a network). This limits the utility of the ERGM because there is often interest, particularly in political and policy sciences, in network dynamics at the actor or relationship levels. Micro‐level interpretation of the ERGM has been employed in varied applications in sociology and statistics. We present a comprehensive framework for interpretation of the ERGM at all levels of analysis, which casts network formation as block‐wise updating of a network. These blocks can represent, for example, each potential link, each dyad, the out‐ or in‐going ties of each actor, or the entire network. We contrast this interpretive framework with the stochastic actor‐based model (SABM) of network dynamics. We present the theoretical differences between the ERGM and the SABM and introduce an approach to comparing the models when theory is not sufficiently strong to make the selection a priori. The alternative models we discuss and the interpretation methods we propose are illustrated on previously published data on estuary policy and governance networks.     

The Probabilistic Minisum Flow Interception Problem: Minimizing the Expected Travel Distance until Intercept under Probabilistic Interception

We develop a variant of the flow interception problem (FIP) in which it is more desirable for travelers to be intercepted as early as possible in their trips. In addition, we consider flows being intercepted probabilistically instead of the deterministic view of coverage assumed in the FIP literature. We call the proposed model the probabilistic minisum FIP (PMFIP); it involves minimizing the sum of the expected distance that each flow travels until intercepted at a facility among placed facilities. This extension allows us to evaluate the effect of facility location under any given value of the interception probability and to apply the model to a variety of situations. We apply the proposed model to an example network by assuming a hypothetical situation in which people gather at a stadium from various nodes on the network, and receive some goods or services on the way to the stadium. We analyze optimal solutions obtained by varying the number of facilities and interception probability. It is shown that the expected travel distance until intercept is greatly reduced by means of a few optimally located facilities under a moderate interception probability.     

Sustained Organizational Influence: American Legislative Exchange Council and the Diffusion of Anti‐Sanctuary Policy

Building upon existing literature, we offer a particular model of network policy diffusion—which we call sustained organizational influence. Sustained organizational influence necessitates an institutional focus across a broad range of issues and across a long period of time. Sustaining organizations are well‐financed, and exert their influence on legislators through benefits, shared ideological interests, and time‐saving opportunities. Sustaining organizations' centralized nature makes legislators' jobs easier by providing legislators with ready‐made model legislation. We argue that sustaining organizations uniquely contribute to policy diffusion in the U.S. states. We evaluate this model with a case study of state‐level immigration sanctuary policy making and the role that the American Legislative Exchange Council (ALEC) played in disseminating model legislation. Through quantitative text analysis and several negative binomial state‐level regression models, we demonstrate that ALEC has exerted an overwhelming influence on the introduction of anti‐sanctuary legislative proposals in the U.S. states over the past 7 years consistent with our particular model of network policy diffusion. Implications are discussed.     

无线网络深度覆盖技术在石窟寺保护利用中的运用——以敦煌莫高窟为例

针对莫高窟在保护利用数据传输过程中出现的问题与发展趋势,提出了利用无线网络深度覆盖技术构建数据传输平台,解决莫高窟大型洞窟内保护利用数据无法传输的问题。为构建实用性强的传输平台,采取了如下措施。首先,针对莫高窟保护利用各项业务数据采集、传输模式、传输机制等各阶段特点,提出了基于无线网络深度覆盖技术构建数据传输试验平台的需求;其次,设计了试验平台构建方案,依据莫高窟洞窟分布与建筑形制确定了试验平台构建位置。结合莫高窟目前无线网络覆盖现状,通过选型分析确定了无线网络深度覆盖关键技术,并应用该技术构建试验平台;最后,对试验平台无线信号覆盖范围、信号强度、传输性能、安全性等进行验证,确保数据传输的完整性与连续性。此试验平台已运行一年有余,应用效果良好。     

Hub-and-Spoke Networks in Air Transportation: An Analytical Review

In this review we survey advances in analysis of the hub location problem and its variants. In the course of the review opportunities for enhanced analysis become apparent. We emphasize the most pressing areas for further work. We found that first, research needs to be devoted to developing more reliable heuristics for the multiple assignment model and its extensions and second, that additional research is needed to understand the conditions under which the model will tend to have integer solutions. Research in this area will contribute to the solution of a longstanding puzzle in economics about the allocation of indivisible resources.     

A LONG-RUN INTERPRETATION OF REGIONAL INPUT-OUTPUT ANALYSIS*

ABSTRACT. Regional input-output (I-O) analysis is traditionally motivated by a short-run, extreme Keynesian vision of markets. In this paper we argue that an appropriately formulated, investment-endogenous, I-O system replicates the long-run equilibria of a wide range of regional models, many of which do not operate as I-O systems in the short run. In particular, we use a computable general equilibrium (CGE) framework to illustrate the impact of an aggregate demand disturbance on an I-O and standard neoclassical model. When run forward over a number of periods, the results from the capacity-constrained neoclassical model asymptotically approach the I-O outcome. We use sensitivity analysis to examine the speed of adjustment of the neo-classical system and investigate barriers to the attainment of the I-O result.     

ART‐P‐MAP Neural Networks Modeling of Land‐Use Change: Accounting for Spatial Heterogeneity and Uncertainty

Spatial land‐use models over large geographic areas and at fine spatial resolutions face the challenges of spatial heterogeneity, model predictability, data quality, and of the ensuing uncertainty. We propose an improved neural network model, ART‐Probability‐Map (ART‐P‐MAP), tailored to address these issues in the context of spatial modeling of land‐use change. First, it adaptively forms its own network structure to account for spatial heterogeneity. Second, it explicitly infers posterior probabilities of land conversion that facilitates the quantification of prediction uncertainty. Extensive calibration under various test settings is conducted on the proposed model to optimize its utility in seeking useful information within a spatially heterogeneous environment. The calibration strategy involves building a bagging ensemble for training and stratified sampling with varying category proportions for experimentation. Through a temporal validation approach, we examine models’ performance within a systematic assessment framework consisting of global metrics and cell‐level uncertainty measurement. Compared with two baselines, ART‐P‐MAP achieves consistently good and stable performance across experiments and exhibits superior capability to handle the spatial heterogeneity and uncertainty involved in the land‐use change problem. Finally, we conclude that, as a general probabilistic regression model, ART‐P‐MAP is applicable to a broad range of land‐use change modeling approaches, which deserves future research.     

A Network Approach to Commuting

In this paper we present a model for commuting in a network of towns. A basic assumption is that all individuals have a given residential location and that every node in the network has a fixed number of jobs. We then propose a general model for the commuting of labor between the nodes in the network.     

A Geographic Network Automata Approach for Modeling Dynamic Ecological Systems

Landscape connectivity networks are composed of nodes representing georeferenced habitat patches that link together based on a species’ maximum dispersal distance. These static representations cannot capture the complexity in species dispersal where the network of habitat patch nodes changes structure over time as a function of local dispersal dynamics. Therefore, the objective of this study is to integrate geographic information, complexity, and network science to propose a novel Geographic Network Automata (GNA) modeling approach for the simulation of dynamic spatial ecological networks. The proposed GNA modeling approach is applied to the emerald ash borer (EAB) forest insect infestation using geospatial data sets from Michigan, U.S.A. and simulates the evolution of the EAB spatiotemporal dispersal network structures across a large regional scale. The GNA model calibration and sensitivity analysis are performed. The simulated spatial network structures are quantified using graph theory measures. Results indicate that the spatial distribution of habitat patch nodes across the landscape in combination with EAB dispersal processes generate a highly connected small-world dispersal network that is robust to node removal. The presented GNA model framework is general and flexible so that different types of geospatial phenomena can be modeled, providing valuable insights for management and decision-making.     

A Combined Cluster and Interaction Model: The Hierarchical Assignment Problem

This article presents a new spatial modeling approach that deals with interactions between individual geographic entities. The developed model represents a generalization of the transportation problem and the classical assignment problem and is termed the hierarchical assignment problem (HAP). The HAP optimizes the spatial flow pattern between individual origin and destination locations, given that some grouping, or aggregation of individual origins and destinations is permitted to occur. The level of aggregation is user specified, and the aggregation step is endogenous to the model itself. This allows for the direct accounting of aggregation costs in pursuit of optimal problem solutions. The HAP is formulated and solved with several sample data sets using commercial optimization software. Trials illustrate how HAP solutions respond to changes in levels of aggregation, as well as reveal the diverse network designs and allocation schemes obtainable with the HAP. Connections between the HAP and the literature on the p-median problem, cluster analysis, and hub-and-spoke networks are discussed and suggestions for future research are made.     

Generalizing Impact Computations for the Autoregressive Spatial Interaction Model

We extend the impact decomposition proposed by LeSage and Thomas-Agnan (2015) in the spatial interaction model to a more general framework, where the sets of origins and destinations can be different, and where the relevant attributes characterizing the origins do not coincide with those of the destinations. These extensions result in three flow data configurations which we study extensively: the square, the rectangular, and the noncartesian cases. We propose numerical simplifications to compute the impacts, avoiding the inversion of a large filter matrix. These simplifications considerably reduce computation time; they can also be useful for prediction. Furthermore, we define local measures for the intra, origin, destination and network effects. Interestingly, these local measures can be aggregated at different levels of analysis. Finally, we illustrate our methodology in a case study using remittance flows all over the world.     

URBAN GROWTH EXTERNALITIES AND NEIGHBORHOOD INCENTIVES: ANOTHER CAUSE OF URBAN SPRAWL?*

ABSTRACT This paper suggests a cause of low density urban development or urban sprawl that has not been given much attention in the literature. There have been a number of arguments put forward for market failures that may account for urban sprawl, including incomplete pricing of infrastructure, environmental externalities, and unpriced congestion. The problem analyzed here is that urban growth creates benefits for an entire urban area, but the costs of growth are borne by individual neighborhoods. An externality problem arises because existing residents perceive the costs associated with the new residents locating in their neighborhoods, but not the full benefits of new entrants which accrue to the city as a whole. The result is that existing residents have an incentive to block new residents to their neighborhoods, resulting in cities that are less dense than is optimal, or too spread out. The paper models several different types of urban growth, and examines the optimal and local choice outcomes under each type. In the first model, population growth is endogenous and the physical limits of the city are fixed. The second model examines the case in which population growth in the region is given, but the city boundary is allowed to vary. We show that in both cases the city will tend to be larger and less dense than is optimal. In each, we examine the sensitivity of the model to the number of neighborhoods and to the size of infrastructure and transportation costs. Finally, we examine optimal subsidies and see how they compare to current policies such as impact fees on new development.     

A Dynamic Location-Allocation Model for Evaluating the Spatial Impacts for Just-in-Time Planning

This paper presents an interperiod network storage location-allocation (INSLA) model to solve the just-in-time production planning problem. The model is extended to a multiobjective problem in which trade-offs between delivery time and transportation costs are analyzed. The results for a hypothetical problem show that in an attempt to reduce inventories on the part of the primary purchaser of raw materials, the possibility exists for less than optimal behavior in the system.     

Statistical Network Analysis for Analyzing Policy Networks

To analyze social network data using standard statistical approaches is to risk incorrect inference. The dependencies among observations implied in a network conceptualization undermine standard assumptions of the usual general linear models. One of the most quickly expanding areas of social and policy network methodology is the development of statistical modeling approaches that can accommodate such dependent data. In this article, we review three network statistical methods commonly used in the current literature: quadratic assignment procedures, exponential random graph models (ERGMs), and stochastic actor‐oriented models. We focus most attention on ERGMs by providing an illustrative example of a model for a strategic information network within a local government. We draw inferences about the structural role played by individuals recognized as key innovators and conclude that such an approach has much to offer in analyzing the policy process.     

A Methodology for Neural Spatial Interaction Modeling

This paper attempts to develop a mathematically rigid and unified framework for neural spatial interaction modeling. Families of classical neural network models, but also less classical ones such as product unit neural network ones are considered for the cases of unconstrained and singly constrained spatial interaction flows. Current practice appears to suffer from least squares and normality assumptions that ignore the true integer nature of the flows and approximate a discrete‐valued process by an almost certainly misrepresentative continuous distribution. To overcome this deficiency we suggest a more suitable estimation approach, maximum likelihood estimation under more realistic distributional assumptions of Poisson processes, and utilize a global search procedure, called Alopex, to solve the maximum likelihood estimation problem. To identify the transition from underfitting to overfitting we split the data into training, internal validation, and test sets. The bootstrapping pairs approach with replacement is adopted to combine the purity of data splitting with the power of a resampling procedure to overcome the generally neglected issue of fixed data splitting and the problem of scarce data. In addition, the approach has power to provide a better statistical picture of the prediction variability. Finally, a benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained neural network model versions in terms of generalization performance measured by Kullback and Leibler's information criterion.