Showing papers on "Weighted network published in 2014"

Synchronization analysis of complex networks with multi-weights and its application in public traffic network

Abstract: On the basis of traditional weighted network, we study a new complex network model with multi-weights, which has one or several different types of weights between any two nodes. According to the method of network split, we split the complex network with multi-weights into several different complex networks with single weight, and study its global synchronization. Taking bus lines as the network nodes, a new public traffic roads network model with multi-weights is established by the proposed network model and space R modeling approach. Then based on the Lyapunov stability theory, the criteria is designed for the global synchronization of the public traffic roads networks with multi-weights. By changing the different weights and taking the Lorenz chaotic system for example, some numerical examples are given to discuss the balance of the whole public traffic roads network.

Community-Enhanced De-anonymization of Online Social Networks

Abstract: Online social network providers have become treasure troves of information for marketers and researchers. To profit from their data while honoring the privacy of their customers, social networking services share `anonymized' social network datasets, where, for example, identities of users are removed from the social network graph. However, by using external information such as a reference social graph (from the same network or another network with similar users), researchers have shown how such datasets can be de-anonymized. These approaches use `network alignment' techniques to map nodes from the reference graph into the anonymized graph and are often sensitive to larger network sizes, the number of seeds, and noise --- which may be added to preserve privacy. We propose a divide-and-conquer approach to strengthen the power of such algorithms. Our approach partitions the networks into `communities' and performs a two-stage mapping: first at the community level, and then for the entire network. Through extensive simulation on real-world social network datasets, we show how such community-aware network alignment improves de-anonymization performance under high levels of noise, large network sizes, and a low number of seeds. Even when nodes cannot be explicitly mapped, the community structure can be mapped between both networks, thus reducing the anonymity of users. For example, for our (real-world) Twitter dataset with 90,000 nodes, 20% noise, and 16 seeds, the state-of-the-art technique reduces anonymity by 0 bits, whereas our approach reduces anonymity by 9.71 bits (with 40% of nodes mapped).

Detours around basin stability in power networks

Abstract: To analyse the relationship between stability against large perturbations and topological properties of a power transmission grid, we employ a statistical analysis of a large ensemble of synthetic power grids, looking for significant statistical relationships between the single-node basin stability measure and classical as well as tailormade weighted network characteristics. This method enables us to predict poor values of single-node basin stability for a large extent of the nodes, offering a node-wise stability estimation at low computational cost. Further, we analyse the particular function of certain network motifs to promote or degrade the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design.

Resolving anatomical and functional structure in human brain organization: identifying mesoscale organization in weighted network representations.

Abstract: Human brain anatomy and function display a combination of modular and hierarchical organization, suggesting the importance of both cohesive structures and variable resolutions in the facilitation of healthy cognitive processes. However, tools to simultaneously probe these features of brain architecture require further development. We propose and apply a set of methods to extract cohesive structures in network representations of brain connectivity using multi-resolution techniques. We employ a combination of soft thresholding, windowed thresholding, and resolution in community detection, that enable us to identify and isolate structures associated with different weights. One such mesoscale structure is bipartivity, which quantifies the extent to which the brain is divided into two partitions with high connectivity between partitions and low connectivity within partitions. A second, complementary mesoscale structure is modularity, which quantifies the extent to which the brain is divided into multiple communities with strong connectivity within each community and weak connectivity between communities. Our methods lead to multi-resolution curves of these network diagnostics over a range of spatial, geometric, and structural scales. For statistical comparison, we contrast our results with those obtained for several benchmark null models. Our work demonstrates that multi-resolution diagnostic curves capture complex organizational profiles in weighted graphs. We apply these methods to the identification of resolution-specific characteristics of healthy weighted graph architecture and altered connectivity profiles in psychiatric disease.

Resource allocation for D2D communications under proportional fairness

Abstract: This paper deals with the dynamic spectrum sharing between underlaying device-to-device (D2D) and cellular links in a multi-carrier cellular network to maximize the weighted network sum-rate while guaranteeing the minimum individual cellular link data rates and proportional fairness among D2D links. In particular, we formulate an NP-hard non-orthogonal resource allocation problem, and develop an iterative algorithm that alternates between the sub-carrier assignment and power allocation in each iteration until convergence. It is shown that the sub-carrier assignment problem corresponds to an integer linear program while the power allocation is reformulated into a difference-between-two-concave-functions (DC) problem. We establish the important properties of the developed algorithms and prove their convergence behavior. Illustrative results indicate that the proposed non-orthogonal resource allocation algorithm significantly outperforms the orthogonal spectrum sharing counterpart.

A network-based approach to coauthorship credit allocation

Abstract: We introduce and evaluate a novel network-based approach for determining individual credit of coauthors in multi-authored papers. In the proposed model, coauthorship is conceptualized as a directed, weighted network, where authors transfer coauthorship credits among one another. We validate the model by fitting it to empirical data about authorship credits from economics, marketing, psychology, chemistry, and biomedicine. Also, we show that our model outperforms prior alternatives such as fractional, geometric, arithmetic, and harmonic counting in generating coauthorship credit allocations that approximate the empirical data. The results from the empirical evaluation as well as the model's capability to be adapted to domains with different norms for how to order authors per paper make the proposed model a robust and flexible framework for studying substantive questions about coauthorship across domains.

Statistical network analysis for functional MRI: summary networks and group comparisons

Abstract: Comparing networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges in that network. This problem arises in the analysis of both weighted and unweighted networks. The term density is often used in this context, in order to refer to the mean edge weight of a weighted network, or to the number of edges in an unweighted one. Comparing families of networks is therefore statistically difficult because differences in topology are necessarily associated with differences in density. In this review paper, we consider this problem from two different perspectives, which include (i) the construction of summary networks, such as how to compute and visualize the summary network from a sample of network-valued data points; and (ii) how to test for topological differences, when two families of networks also exhibit significant differences in density. In the first instance, we show that the issue of summarizing a family of networks can be conducted by either adopting a mass-univariate approach, which produces a statistical parametric network (SPN). In the second part of this review, we then highlight the inherent problems associated with the comparison of topological functions of families of networks that differ in density. In particular, we show that a wide range of topological summaries, such as global efficiency and network modularity are highly sensitive to differences in density. Moreover, these problems are not restricted to unweighted metrics, as we demonstrate that the same issues remain present when considering the weighted versions of these metrics. We conclude by encouraging caution, when reporting such statistical comparisons, and by emphasizing the importance of constructing summary networks.

Augmenting microarray data with literature-based knowledge to enhance gene regulatory network inference.

Abstract: Gene regulatory networks are a crucial aspect of systems biology in describing molecular mechanisms of the cell. Various computational models rely on random gene selection to infer such networks from microarray data. While incorporation of prior knowledge into data analysis has been deemed important, in practice, it has generally been limited to referencing genes in probe sets and using curated knowledge bases. We investigate the impact of augmenting microarray data with semantic relations automatically extracted from the literature, with the view that relations encoding gene/protein interactions eliminate the need for random selection of components in non-exhaustive approaches, producing a more accurate model of cellular behavior. A genetic algorithm is then used to optimize the strength of interactions using microarray data and an artificial neural network fitness function. The result is a directed and weighted network providing the individual contribution of each gene to its target. For testing, we used invasive ductile carcinoma of the breast to query the literature and a microarray set containing gene expression changes in these cells over several time points. Our model demonstrates significantly better fitness than the state-of-the-art model, which relies on an initial random selection of genes. Comparison to the component pathways of the KEGG Pathways in Cancer map reveals that the resulting networks contain both known and novel relationships. The p53 pathway results were manually validated in the literature. 60% of non-KEGG relationships were supported (74% for highly weighted interactions). The method was then applied to yeast data and our model again outperformed the comparison model. Our results demonstrate the advantage of combining gene interactions extracted from the literature in the form of semantic relations with microarray analysis in generating contribution-weighted gene regulatory networks. This methodology can make a significant contribution to understanding the complex interactions involved in cellular behavior and molecular physiology.

Epidemic spreading on weighted adaptive networks

Abstract: Considering the fact that the contact strengths among people are diverse both in the duration time and the distance, in this paper, we study the epidemic dynamics with susceptible–infective–susceptible (SIS) model on a weighted adaptive network to emphasize this contact feature. In this model, the weight of a link denotes the contact strength between two individuals connected by this link, and each susceptible individual may adaptively transfer the weight from a link to another. We find that this weight adaption process could significantly aggravate the prevalence of an epidemic. Moreover, we examine the effectiveness of the link-removal strategy with our model, and the results show that the weight adaption process may weaken the efficiency of the strategy. The theoretical analysis is supported by the simulation results.

Reconstructing functional brain networks: have we got the basics right?

Abstract: Both at rest and during the executions of cognitive tasks, the brain continuously creates and reshapes complex patterns of correlated dynamics. Thus, brain functional activity is naturally described in terms of networks, i.e., sets of nodes, representing distinct subsystems, and links connecting node pairs, representing relationships between them. Recently, brain function has started being investigated using a statistical physics understanding of graph theory, an old branch of pure mathematics (Newman, 2010). Within this framework, network properties are independent of the identity of their nodes, as they emerge in a non-trivial way from their interactions. Observed topologies are instances of a network ensemble, falling into one of few universality classes and are therefore inherently statistical in nature. Functional network reconstruction comprises various steps: first, nodes are identified; then, links are established according to a certain metric. This gives rise to a clique with an all-to-all connectivity. Deciding which links are significant is done by choosing which values of these metrics should be taken into account. Finally, network properties are computed and used to characterize the network. Each of these steps contains an element of arbitrariness, as graph theory allows characterizing systems once a network is reconstructed, but is neutral as to what should be treated as a system and to how to isolate its constituent parts. Here we discuss some aspects related to the way nodes, links and networks in general are defined in system-level studies using noninvasive techniques, which may be critical when interpreting the results of functional brain network analyses.

Neighborhood-based uncertainty generation in social networks

Abstract: Imprecision, incompleteness and dynamic exist in a wide range of network applications. It is difficult to decide the uncertainty relationship among nodes since traditional models are not meaningful in uncertain networks, and the inherent computational complexity of the problems with uncertainty is always intractable. In this paper, we study how to capture uncertainty in networks by transforming a series of snapshots of a network to an uncertain graph. A novel sampling scheme is also proposed which enables the development of efficient algorithms to measure uncertainty in networks. Considering the practical aspects of neighborhood relationship in real networks, a framework is introduced to transform an uncertain network into a deterministic weighted network where the weights on edges can be measured by Jaccard-like index. The comprehensive experimental evaluation results on real data demonstrate the effectiveness and efficiency of our algorithms.

Node-weighted measures for complex networks with directed and weighted edges for studying continental moisture recycling

Abstract: In many real-world networks nodes represent agents or objects of different sizes or importance. However, the size of the nodes is rarely taken into account in network analysis, possibly inducing bias in network measures and confusion in their interpretation. Recently, a new axiomatic scheme of node-weighted network measures has been suggested for networks with undirected and unweighted edges. However, many real-world systems are best represented by complex networks which have directed and/or weighted edges. Here, we extend this approach and suggest new versions of the degree and the clustering coefficient associated to network motifs for networks with directed and/or weighted edges and weighted nodes. We apply these measures to a spatially embedded network model and a real-world moisture recycling network. We show that these measures improve the representation of the underlying systems' structure and are of general use for studying any type of complex network.

Evaluating the evolution of subway networks: Evidence from Beijing Subway Network

Abstract: As one of the largest subway networks, the Beijing Subway Network has developed with an unprecedented velocity during the last seven years. This paper analyzes the evolution of the Beijing Subway Network during this high-speed period and proposes a new growth model, composed by an expanding mode and an intensifying mode. The two modes appear alternatively so that the network can become larger and denser. However, the expanding mode is more influential from a long-term perspective while the effects of an intensifying mode are more observable in the short-term. Moreover, in order to better understand the characteristics of subway networks, this paper uses a weighted network of lines to define and evaluate networks. Besides the weighted clustering coefficient, the number of possible paths shows better performance in measuring the development of these networks and reveals clearly the evolution of the Beijing Subway Transfer Network.

Information dissemination in a multi-technology communication network

Abstract: A method for information dissemination in a multi-technology communication network wherein network nodes are equipped with first communication means for operating via a long range communication network and with second communication means for performing short-range communication includes performing, by a central entity, the steps of determining coverage areas of the network nodes; establishing dissimilarity relations between network nodes with respect to the coverage areas of the network nodes such that a dissimilarity relation index value is larger for two network nodes covering less similar areas; and selecting, subject to configurable constraints, network nodes with a highest dissimilarity relation index value as mobile infrastructure nodes that are intended to act as relay and/or forwarder nodes for supporting optimal information penetration in a given destination dissemination area.

Predicting protein complex in protein interaction network - a supervised learning based method.

Abstract: Protein complexes are important for understanding principles of cellular organization and function. High-throughput experimental techniques have produced a large amount of protein interactions, making it possible to predict protein complexes from protein -protein interaction networks. However, most of current methods are unsupervised learning based methods which can't utilize the information of the large amount of available known complexes. We present a supervised learning-based method for predicting protein complexes in protein - protein interaction networks. The method extracts rich features from both the unweighted and weighted networks to train a Regression model, which is then used for the cliques filtering, growth, and candidate complex filtering. The model utilizes additional "uncertainty" samples and, therefore, is more discriminative when used in the complex detection algorithm. In addition, our method uses the maximal cliques found by the Cliques algorithm as the initial cliques, which has been proven to be more effective than the method of expanding from the seeding proteins used in other methods. The experimental results on several PIN datasets show that in most cases the performance of our method are superior to comparable state-of-the-art protein complex detection techniques. The results demonstrate the several advantages of our method over other state-of-the-art techniques. Firstly, our method is a supervised learning-based method that can make full use of the information of the available known complexes instead of being only based on the topological structure of the PIN. That also means, if more training samples are provided, our method can achieve better performance than those unsupervised methods. Secondly, we design the rich feature set to describe the properties of the known complexes, which includes not only the features from the unweighted network, but also those from the weighted network built based on the Gene Ontology information. Thirdly, our Regression model utilizes additional "uncertainty" samples and, therefore, becomes more discriminative, whose effectiveness for the complex detection is indicated by our experimental results.

Chaotic synchronization on complex hypergraphs

Abstract: Chaotic synchronization on hypegraphs is studied with chaotic oscillators located in the nodes and with hyperedges corresponding to nonlinear coupling among groups of p oscillators ( p ⩾ 2 ). Using the Master Stability Function approach it can be shown that the problem of stability of the state of identical synchronization for such hypergraphs (called p-hypergraphs) is equivalent to that for a weighted network in which the weights of edges linking pairs of nodes are given by the number of different hyperedges simultaneously connecting these pairs of nodes. As an example, synchronization of identical Lorenz oscillators is investigated on complex scale-free p-hypergraphs. For p even and for a proper choice of the coupling function identical synchronization can be obtained, and the propensity to synchronization depends sensitively on the coupling topology. Besides, such phenomena as partial anti-synchronization, coexistence of the synchronized and oscillation death states with intermingled basins of attraction and quasiperiodic oscillations are observed in numerical simulations.

Query-Driven Mining of Citation Networks for Patent Citation Retrieval and Recommendation

Abstract: Prior art search or recommending citations for a patent application is a challenging task. Many approaches have been proposed and shown to be useful for prior art search. However, most of these methods do not consider the network structure for integrating and diffusion of different kinds of information present among tied patents in the citation network. In this paper, we propose a method based on a time-aware random walk on a weighted network of patent citations, the weights of which are characterized by contextual similarity relations between two nodes on the network. The goal of the random walker is to find influential documents in the citation network of a query patent, which can serve as candidates for drawing query terms and bigrams for query refinement. The experimental results on CLEF-IP datasets (CLEF-IP 2010 and CLEF-IP 2011) show the effectiveness of encoding contextual similarities (common classification codes, common inventor, and common applicant) between nodes in the citation network. Our proposed approach can achieve significantly better results in terms of recall and Mean Average Precision rates compared to strong baselines of prior art search.

A GDP-driven model for the binary and weighted structure of the International Trade Network

Abstract: Recent events such as the global financial crisis have renewed the interest in the topic of economic networks. One of the main channels of shock propagation among countries is the International Trade Network (ITN). Two important models for the ITN structure, the classical gravity model of trade (more popular among economists) and the fitness model (more popular among networks scientists), are both limited to the characterization of only one representation of the ITN. The gravity model satisfactorily predicts the volume of trade between connected countries, but cannot reproduce the observed missing links (i.e. the topology). On the other hand, the fitness model can successfully replicate the topology of the ITN, but cannot predict the volumes. This paper tries to make an important step forward in the unification of those two frameworks, by proposing a new GDP-driven model which can simultaneously reproduce the binary and the weighted properties of the ITN. Specifically, we adopt a maximum-entropy approach where both the degree and the strength of each node is preserved. We then identify strong nonlinear relationships between the GDP and the parameters of the model. This ultimately results in a weighted generalization of the fitness model of trade, where the GDP plays the role of a `macroeconomic fitness' shaping the binary and the weighted structure of the ITN simultaneously. Our model mathematically highlights an important asymmetry in the role of binary and weighted network properties, namely the fact that binary properties can be inferred without the knowledge of weighted ones, while the opposite is not true.

Pairwise and edge-based models of epidemic dynamics on correlated weighted networks.

Abstract: In this paper we explore the potential of the pairwise-type modelling approach to be extended to weighted networks where nodal degree and weights are not independent. As a baseline or null model for weighted networks, we consider undirected, heterogenous networks where edge weights are randomly distributed. We show that the pairwise model successfully captures the extra complexity of the network, but does this at the cost of limited analytical tractability due the high number of equations. To circumvent this problem, we employ the edge-based modelling approach to derive models corresponding to two different cases, namely for degree-dependent and randomly distributed weights. These models are more amenable to compute important epidemic descriptors, such as early growth rate and final epidemic size, and produce similarly excellent agreement with simulation. Using a branching process approach we compute the basic reproductive ratio for both models and discuss the implication of random and correlated weight distributions on this as well as on the time evolution and final outcome of epidemics. Finally, we illustrate that the two seemingly different modelling approaches, pairwise and edge-based, operate on similar assumptions and it is possible to formally link the two.

Multimode public transportation transferring method in urban congestion period

Abstract: The invention discloses a multimode public transportation transferring method in an urban congestion period, which comprises the following steps of: step 1, constructing an urban ground-level road network based on real-time traffic information, and dividing different road sections of the urban road into a congestion road section and un-congestion road section; step 2, setting functional weight parameters for calculating costs of a ground bus, a subway and a public bicycle; step 3, establishing an urban public transportation weighted directed transferring network T; step 4, establishing an urban subway directed weighted network S; step 5, establishing a weighted directed public bicycle network B with the urban bus connected with the subway; step 6, by combining with the T network, the S network and the B network, calculating a cost function value, and adopting a breadth-first algorithm to obtain an optimal transferring solution The multimode public transportation transferring method in the urban congestion period gives consideration to the characteristic that the short-distance tripping way by using the public bicycle and subway is not affected by the congestion of the ground road, accordingly provides the multimode transferring method to adjust the transferring solution automatically based on the congestion condition of the road surface, and enables the influence from the congestion to be minimum

Network Structures in Biological Systems

Abstract: The currently popular interdisciplinary concept of network structures (networks) has been defined in two different ways in the literature: (i) as “sets of items, which we will call vertices or sometimes nodes, with connections between them, called edges” or links (Newman, 2003, p. 2) and (ii) in a more specific meaning used in this work: as systems of objects that lack a central pace-maker (leader, boss, etc.) and are characterized by predominantly cooperative interactions among their elements (nodes). Such sensu stricto networks are contrasted with structures that contain a single center (hierarchies) andas well as with those characterized bycompetitive interactions between their elements (market-type structures). Many networks have a multilevel structure that accounts for their fractal properties (a part of a sensu stricto network is a network per se). Network structures in biological systems can be subdivided into two main subgroups: (i) flat (leaderless) network structures that are composed of uniform elements and represent modular organisms or at least possess manifest integral properties and (ii) three-dimensional, partly hierarchical, structures characterized by significant individual and/or intergroup (intercaste) differences between their elements. Many network structures include an element that performs structural, protective, and communication-promoting functions. In an analogy to cell structures, this element is denoted herein as the matrix of a network structure. The matrix includes a material and an immaterial component. The material component comprises various structures that belong to the whole structure and not to any of its elements per se. The immaterial (ideal) component of the matrix includes social norms and rules regulating network elements’ behavior. These behavioral rules can be described in terms of algorithms that enable modeling the behavior of various network structures, particularly of neural networks and their artificial analogs. The diversity of network structure types in biological systems gives food for thought not only to biologists but also to scholars in the social sciences and the humanities. The implication is that “network structures,” a popular cliche in present-day society, can be subdivided into a number of substantially different organizational variants. Before promoting network structures in various areas ranging from the World Wide Web to networked businesses, we should decide what kind of networls should be more useful in terms of our specific goals.

A Novel Algorithm for Detecting Protein Complexes with the Breadth First Search

Abstract: Most biological processes are carried out by protein complexes. A substantial number of false positives of the protein-protein interaction (PPI) data can compromise the utility of the datasets for complexes reconstruction. In order to reduce the impact of such discrepancies, a number of data integration and affinity scoring schemes have been devised. The methods encode the reliabilities (confidence) of physical interactions between pairs of proteins. The challenge now is to identify novel and meaningful protein complexes from the weighted PPI network. To address this problem, a novel protein complex mining algorithm ClusterBFS (Cluster with Breadth-First Search) is proposed. Based on the weighted density, ClusterBFS detects protein complexes of the weighted network by the breadth first search algorithm, which originates from a given seed protein used as starting-point. The experimental results show that ClusterBFS performs significantly better than the other computational approaches in terms of the identification of protein complexes.

Local representatives in weighted networks

Abstract: The main features of current real-world networks are their large sizes and structures, which show varying degrees of importance of the nodes in their surroundings. The topic of evaluating the importance of the nodes offers many different approaches that usually work with unweighted networks. We present a novel, simple and straightforward approach for the evaluation of the network's nodes with a focus on local properties in their surroundings. The presented approach is intended for weighted networks where the weight can be interpreted as the proximity between the nodes. Our suggested x-representativeness then takes into account the degree of the node, its nearest neighbors and one other parameter which we call the x-representativeness base. Following that, we also present experiments with three different real-world networks. The aim of these experiments is to show that the x-representativeness can be used to deterministically reduce the network to differently sized samples of representatives, while maintaining the topological properties of the original network.

Extracting Hidden Hierarchies in 3D Distribution Networks

Abstract: Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function. Yet, the set of tools that can characterize such a weighted cycle-rich architecture in a physically relevant, mathematically compact way is sparse. In order to fill this void, we have developed a new algorithm that rests on an abstraction of the physical `tiling' in the case of a two dimensional network to an effective tiling of an abstract surface in space that the network may be thought to sit in. Generically these abstract surfaces are richer than the flat plane and as a result there are now two families of fundamental units that may aggregate upon cutting weakest links -- the plaquettes of the tiling and the longer `topological' cycles associated with the abstract surface itself. Upon sequential removal of the weakest links, as determined by the edge weight, neighboring plaquettes merge and a tree characterizing this merging process results. The properties of this characteristic tree can provide the physical and topological data required to describe the architecture of the network and to build physical models. The new algorithm can be used for automated phenotypic characterization of any weighted network whose structure is dominated by cycles, such as mammalian vasculature in the organs, the root networks of clonal colonies like quaking aspen, or the force networks in jammed granular matter.

Analysis of two crime-related networks derived from bipartite social networks

Abstract: In this paper we investigate two real crime-related networks, which are both bipartite. The bipartite networks are: a spatial network where crimes of various types are committed in different local government areas; and a dark terrorist network where individuals attend events or have common affiliations. In each case we analyse the communities found by a random-walk based algorithm in the primary weighted projection network. We demonstrate that the identified communities represent meaningful information, and in particular, that the small communities found in the terrorist network represent meaningful cliques.

Visualizing Random Forest’s Prediction Results

Abstract: The current paper proposes a new visualization tool to help check the quality of the random forest predictions by plotting the proximity matrix as weighted networks. This new visualization technique will be compared with the traditional multidimensional scale plot. The present paper also introduces a new accuracy index (proportion of misplaced cases), and compares it to total accuracy, sensitivity and specificity. It also applies cluster coefficients to weighted graphs, in order to understand how well the random forest algorithm is separating two classes. Two datasets were analyzed, one from a medical research (breast cancer) and the other from a psychology research (medical student’s academic achievement), varying the sample sizes and the predictive accuracy. With different number of observations and different possible prediction accuracies, it was possible to compare how each visualization technique behaves in each situation. The results pointed that the visualization of random forest’s predictive performance was easier and more intuitive to interpret using the weighted network of the proximity matrix than using the multidimensional scale plot. The proportion of misplaced cases was highly related to total accuracy, sensitivity and specificity. This strategy, together with the computation of Zhang and Horvath’s (2005) clustering coefficient for weighted graphs, can be very helpful in understanding how well a random forest prediction is doing in terms of classification.

Development of Gis Tool for the Solution of Minimum Spanning Tree Problem using Prim's Algorithm

Abstract: . minimum spanning tree (MST) of a connected, undirected and weighted network is a tree of that network consisting of all its nodes and the sum of weights of all its edges is minimum among all such possible spanning trees of the same network. In this study, we have developed a new GIS tool using most commonly known rudimentary algorithm called Prim’s algorithm to construct the minimum spanning tree of a connected, undirected and weighted road network. This algorithm is based on the weight (adjacency) matrix of a weighted network and helps to solve complex network MST problem easily, efficiently and effectively. The selection of the appropriate algorithm is very essential otherwise it will be very hard to get an optimal result. In case of Road Transportation Network, it is very essential to find the optimal results by considering all the necessary points based on cost factor (time or distance). This paper is based on solving the Minimum Spanning Tree (MST) problem of a road network by finding it’s minimum span by considering all the important network junction point. GIS technology is usually used to solve the network related problems like the optimal path problem, travelling salesman problem, vehicle routing problems, location-allocation problems etc. Therefore, in this study we have developed a customized GIS tool using Python script in ArcGIS software for the solution of MST problem for a Road Transportation Network of Dehradun city by considering distance and time as the impedance (cost) factors. It has a number of advantages like the users do not need a greater knowledge of the subject as the tool is user-friendly and that allows to access information varied and adapted the needs of the users. This GIS tool for MST can be applied for a nationwide plan called Prime Minister Gram Sadak Yojana in India to provide optimal all weather road connectivity to unconnected villages (points). This tool is also useful for constructing highways or railways spanning several cities optimally or connecting all cities with minimum total road length.