The investigation of the terrorist attack is a time-critical task. The investigators have a limited time window to diagnose the organizational background of the terrorists, to run down and arrest the wire-pullers, and to take an action to prevent or eradicate the terrorist attack. The intuitive interface to visualize the intelligence data set stimulates the investigators’ experience and knowledge, and aids them in decision-making for an immediately effective action. This paper presents a computational method to analyze the intelligence data set on the collective actions of the perpetrators of the attack, and to visualize it into the form of a social network diagram which predicts the positions where the wire-pullers conceals themselves.
On the other hand, the node discovery predicts the existence of an unknown node around the known nodes from the information on the collective behavior of the network. Related works in the node discovery is, however, limited. Heuristic method for node discovery is proposed in @cite_5 , @cite_10 . The method is applied to analyze the covert social network foundation behind the terrorism disasters @cite_9 . Learning techniques of latent variables can be employed, once the presence of a node is known. @cite_18 studied learning of a structure of a linear latent variable graph. @cite_7 studied learning of a structure of a dynamic probabilistic network. But, while the accuracy of the heuristic method is limited, these principled analytic approaches in learning are not practical to handle real human relationship and communication observed in a social network, where much complexity appears. The complexity includes bi-directional and cyclic influence among many observed and latent nodes. We need an efficient and accurate method to solve the node discovery problem.
@cite_18 @cite_7 @cite_9 @cite_5 @cite_10
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This paper addresses a method to analyse the covert social network foundation hidden behind the terrorism disaster. It is to solve a node discovery problem, which means to discover a node, which functions relevantly in a social network, but escaped from monitoring on the presence and mutual relationship of nodes. The method aims at integrating the expert investigator's prior understanding, insight on the terrorists' social network nature derived from the complex graph theory and computational data processing. The social network responsible for the 9 11 attack in 2001 is used to execute simulation experiment to evaluate the performance of the method. We consider the problem of neighbor discovery in static wireless ad hoc networks with directional antennas. We propose several probabilistic algorithms in which nodes perform random, independent transmissions to discover their one-hop neighbors. Our neighbor discovery algorithms are classified into two groups, viz. Direct-Discovery Algorithms in which nodes discover their neighbors only upon receiving a transmission from their neighbors and Gossip-based algorithms in which nodes gossip about their neighbors' location information to enable faster discovery. We first consider the operation of these algorithms in a slotted, synchronous system and mathematically derive their optimal parameter settings. We show how to extend these algorithms for an asynchronous system and describe their optimal design. Analysis and simulation of the algorithms show that nodes discover their neighbors much faster using gossip-based algorithms than using direct-discovery algorithms. Furthermore, the performance of gossip-based algorithms is insensitive to an increase in node density. The efficiency of a neighbor discovery algorithm also depends on the choice of antenna beamwidth. We discuss in detail how the choice of beamwidth impacts the performance of the discovery process and provide insights into how nodes can configure their beamwidths. The discovery of networks is a fundamental problem arising in numerous fields of science and technology, including communication systems, biology, sociology, and neuroscience. Unfortunately, it is often difficult, or impossible, to obtain data that directly reveal network structure, and so one must infer a network from incomplete data. This paper considers inferring network structure from "co-occurrence" data: observations that identify which network components (e.g., switches, routers, genes) carry each transmission but do not indicate the order in which they handle the transmission. Without order information, the number of networks that are consistent with the data grows exponentially with the size of the network (i.e., the number of nodes). Yet, the basic engineering evolutionary principles underlying most networks strongly suggest that not all data-consistent networks are equally likely. In particular, nodes that co-occur in many observations are probably closely connected. With this in mind, we model the co-occurrence observations as independent realizations of a random walk on the network, subjected to a random permutation to account for the lack of order information. Treating permutations as missing data, we derive an expectation-maximization (EM) algorithm for estimating the random walk parameters. The model and EM algorithm significantly simplify the problem, but the computational complexity of the reconstruction process does grow exponentially in the length of each transmission path. For networks with long paths, the exact e-step may be computationally intractable. We propose a polynomial-time Monte Carlo EM algorithm based on importance sampling and derive conditions that ensure convergence of the algorithm with high probability. Simulations and experiments with Internet measurements demonstrate the promise of this approach. We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013 The dynamic behavior of a network in which information is changing continuously over time requires robust and efficient mechanisms for keeping nodes updated about new information. Gossip protocols are mechanisms for this task in which nodes communicate with one another according to some underlying deterministic or randomized algorithm, exchanging information in each communication step. In a variety of contexts, the use of randomization to propagate information has been found to provide better reliability and scalability than more regimented deterministic approaches.In many settings, such as a cluster of distributed computing hosts, new information is generated at individual nodes, and is most "interesting" to nodes that are nearby. Thus, we propose distance-based propagation bounds as a performance measure for gossip mechanisms: a node at distance d from the origin of a new piece of information should be able to learn about this information with a delay that grows slowly with d, and is independent of the size of the network.For nodes arranged with uniform density in Euclidean space, we present natural gossip mechanisms, called spatial gossip, that satisfy such a guarantee: new information is spread to nodes at distance d, with high probability, in O(log1 + e d) time steps. Such a bound combines the desirable qualitative features of uniform gossip, in which information is spread with a delay that is logarithmic in the full network size, and deterministic flooding, in which information is spread with a delay that is linear in the distance and independent of the network size. Our mechanisms and their analysis resolve a conjecture of [1987].We further show an application of our gossip mechanisms to a basic resource location problem, in which nodes seek to rapidly learn the location of the nearest copy of a resource in a network. This problem, which is of considerable practical importance, can be solved by a very simple protocol using Spatial Gossip, whereas we can show that no protocol built on top of uniform gossip can inform nodes of their approximately nearest resource within poly-logarithmic time. The analysis relies on an additional useful property of spatial gossip, namely that information travels from its source to sinks along short paths not visiting points of the network far from the two nodes. The temporal dynamics of a complex system such as a social network or a communication network can be studied by understanding the patterns of link appearance and disappearance over time. A critical task along this understanding is to predict the link state of the network at a future time given a collection of link states at earlier time points. In existing literature, this task is known as link prediction in dynamic networks. Solving this task is more difficult than its counterpart in static networks because an effective feature representation of node-pair instances for the case of dynamic network is hard to obtain. To overcome this problem, we propose a novel method for metric embedding of node-pair instances of a dynamic network. The proposed method models the metric embedding task as an optimal coding problem where the objective is to minimize the reconstruction error, and it solves this optimization task using a gradient descent method. We validate the effectiveness of the learned feature representation by utilizing it for link prediction in various real-life dynamic networks. Specifically, we show that our proposed link prediction model, which uses the extracted feature representation for the training instances, outperforms several existing methods that use well-known link prediction features. We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our algorithms can be applied to both discrete and Gaussian random variables and our learned models are such that all the observed and latent variables have the same domain (state space). Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures such as neighbor-joining) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs. In addition, we demonstrate the applicability of our methods on real-world data sets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups data set. Given a network represented by a graph @math G=V,E, we consider a dynamical process of influence diffusion in G that evolves as follows: Initially only the nodes of a given @math S⊆V are influenced; subsequently, at each round, the set of influenced nodes is augmented by all the nodes in the network that have a sufficiently large number of already influenced neighbors. The question is to determine a small subset of nodes Sa target set that can influence the whole network. This is a widely studied problem that abstracts many phenomena in the social, economic, biological, and physical sciences. It is known [6] that the above optimization problem is hard to approximate within a factor of @math 2log1-∈|V|, for any @math ∈>0. In this paper, we present a fast and surprisingly simple algorithm that exhibits the following features: 1 when applied to trees, cycles, or complete graphs, it always produces an optimal solution i.e., a minimum size target set; 2 when applied to arbitrary networks, it always produces a solution of cardinality matching the upper bound given in [1], and proved therein by means of the probabilistic method; 3 when applied to real-life networks, it always produces solutions that substantially outperform the ones obtained by previously published algorithms for which no proof of optimality or performance guarantee is known in any class of graphs. In this work, we study the notion of competing campaigns in a social network and address the problem of influence limitation where a "bad" campaign starts propagating from a certain node in the network and use the notion of limiting campaigns to counteract the effect of misinformation. The problem can be summarized as identifying a subset of individuals that need to be convinced to adopt the competing (or "good") campaign so as to minimize the number of people that adopt the "bad" campaign at the end of both propagation processes. We show that this optimization problem is NP-hard and provide approximation guarantees for a greedy solution for various definitions of this problem by proving that they are submodular. We experimentally compare the performance of the greedy method to various heuristics. The experiments reveal that in most cases inexpensive heuristics such as degree centrality compare well with the greedy approach. We also study the influence limitation problem in the presence of missing data where the current states of nodes in the network are only known with a certain probability and show that prediction in this setting is a supermodular problem. We propose a prediction algorithm that is based on generating random spanning trees and evaluate the performance of this approach. The experiments reveal that using the prediction algorithm, we are able to tolerate about 90 missing data before the performance of the algorithm starts degrading and even with large amounts of missing data the performance degrades only to 75 of the performance that would be achieved with complete data. Many interesting domains in machine learning can be viewed as networks, with relationships (e.g., friendships) connecting items (e.g., individuals). The Active Exploration (AE) task is to identify all items in a network with a desired trait (i.e., positive labels) given only partial information about the network. The AE process iteratively queries for labels or network structure within a limited budget; thus, accurate predictions prior to making each query is critical to maximizing the number of positives gathered. However, the targeted AE query process produces partially observed networks that can create difficulties for predictive modeling. In particular, we demonstrate that these partial networks can exhibit extreme label correlation bias, which makes it difficult for conventional relational learning methods to accurately estimate relational parameters. To overcome this issue, we model the joint distribution of possible edges and labels to improve learning and inference. Our proposed method, Probabilistic Relational Expectation Maximization (PR-EM), is the first AE approach to accurately learn the complex dependencies between attributes, labels, and structure to improve predictions. PR-EM utilizes collective inference over the missing relationships in the partial network to jointly infer unknown item traits. Further, we develop a linear inference algorithm to facilitate efficient use of PR-EM in large networks. We test our approach on four real world networks, showing that AE with PR-EM gathers significantly more positive items compared to state-of-the-art methods. Experts of chance discovery have recognized a new class of problems where the previous methods fail to visualize a latent structure behind observation. There are invisible events that play an important role in the dynamics of visible events. An invisible leader in a communication network is a typical example. Such an event is named a dark event. A novel technique has been proposed to understand a dark event and to extend the process of chance discovery. This paper presents a new method named "human-computer interactive annealing" for revealing latent structures along with the algorithm for discovering dark events. Demonstration using test data generated from a scale-free network shows that the precision regarding the algorithm ranges from 80 to 90 . An experiment on discovering an invisible leader under an online collective decision-making circumstance is successful Predicting the existence of links between pairwise objects in networks is a key problem in the study of social networks. However, relationships among objects are often more complex than simple pairwise relations. By restricting attention to dyads, it is possible that information valuable for many learning tasks can be lost. The hypernetwork relaxes the assumption that only two nodes can participate in a link, permitting instead an arbitrary number of nodes to participate in so-called hyperlinks or hyperedges, which is a more natural representation for complex, multi-party relations. However, the hyperlink prediction problem has yet to be studied. In this paper, we propose HPLSF (Hyperlink Prediction using Latent Social Features), a hyperlink prediction algorithm for hypernetworks. By exploiting the homophily property of social networks, HPLSF explores social features for hyperlink prediction. To handle the problem that social features are not always observable, a latent social feature learning scheme is developed. To cope with the arbitrary cardinality hyperlink issue in hypernetworks, we design a feature-embedding scheme to map the a priori arbitrarily-sized feature set associated with each hyperlink into a uniformly-sized auxiliary space. To address the fact that observed features and latent features may be not independent, we generalize a structural SVM to learn using both observed features and latent features. In experiments, we evaluate the proposed HPLSF framework on three large-scale hypernetwork datasets. Our results on the three diverse datasets demonstrate the effectiveness of the HPLSF algorithm. Although developed in the context of social networks, HPLSF is a general methodology and applies to arbitrary hypernetworks. Learning about the structure of hidden or covert networks is a major challenge in epidemiology, sociology, and intelligence analysis. Vertices in hidden networks usually cannot be enumerated or sampled in a systematic way; they can only be revealed by tracing links emanating from already-observed vertices. Observers sometimes cannot follow links directly, and instead must rely on passive observation of a dynamic process to reveal vertices and edges. This paper outlines a framework for estimating network structures from partial observation of information diffusion through the network. Diffusion is modeled by a continuous-time Markov epidemic model. Edges are revealed by transmission events and new vertices are uncovered when information is transmitted to them. The approach is a generalization of tools developed to reconstruct drug-user networks from respondent-driven sampling studies in epidemiology. The likelihood of the diffusion process can be interpreted as an exponential random graph model. A Bayesian method for probabilistic reconstruction of the transmission-induced subgraph is described. Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near future or which existing interactions are we missing. Although this problem has been extensively studied, the challenge of how to effectively combine the information from the network structure with rich node and edge attribute data remains largely open. We develop an algorithm based on Supervised Random Walks that naturally combines the information from the network structure with node and edge level attributes. We achieve this by using these attributes to guide a random walk on the graph. We formulate a supervised learning task where the goal is to learn a function that assigns strengths to edges in the network such that a random walker is more likely to visit the nodes to which new links will be created in the future. We develop an efficient training algorithm to directly learn the edge strength estimation function. Our experiments on the Facebook social graph and large collaboration networks show that our approach outperforms state-of-the-art unsupervised approaches as well as approaches that are based on feature extraction. Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near future or which existing interactions are we missing. Although this problem has been extensively studied, the challenge of how to effectively combine the information from the network structure with rich node and edge attribute data remains largely open. We develop an algorithm based on Supervised Random Walks that naturally combines the information from the network structure with node and edge level attributes. We achieve this by using these attributes to guide a random walk on the graph. We formulate a supervised learning task where the goal is to learn a function that assigns strengths to edges in the network such that a random walker is more likely to visit the nodes to which new links will be created in the future. We develop an efficient training algorithm to directly learn the edge strength estimation function. Our experiments on the Facebook social graph and large collaboration networks show that our approach outperforms state-of-the-art unsupervised approaches as well as approaches that are based on feature extraction. The Internet and social media have fuelled enormous interest in social network analysis. New tools continue to be developed and used to analyse our personal connections, with particular emphasis on detecting communities or identifying key individuals in a social network. This raises privacy concerns that are likely to exacerbate in the future. With this in mind, we ask the question ‘Can individuals or groups actively manage their connections to evade social network analysis tools?’ By addressing this question, the general public may better protect their privacy, oppressed activist groups may better conceal their existence and security agencies may better understand how terrorists escape detection. We first study how an individual can evade ‘node centrality’ analysis while minimizing the negative impact that this may have on his or her influence. We prove that an optimal solution to this problem is difficult to compute. Despite this hardness, we demonstrate how even a simple heuristic, whereby attention is restricted to the individual’s immediate neighbourhood, can be surprisingly effective in practice; for example, it could easily disguise Mohamed Atta’s leading position within the World Trade Center terrorist network. We also study how a community can increase the likelihood of being overlooked by community-detection algorithms. We propose a measure of concealment—expressing how well a community is hidden—and use it to demonstrate the effectiveness of a simple heuristic, whereby members of the community either ‘unfriend’ certain other members or ‘befriend’ some non-members in a coordinated effort to camouflage their community. Some misbehavior detection and reputation systems in mobile ad-hoc networks rely on the dissemination of information of observed behavior, which makes them vulnerable to false accusations. This vulnerability could be removed by forbidding the dissemination of information on observed behavior in the first place, but, as we show here, this has more drawbacks than a solution that allows dissemination and copes with false accusations. We propose a method for reducing the impact of false accusations. In our approach, nodes collect first-hand information about the behavior of other nodes by direct observation. In addition, nodes maintain a rating about every other node that they care about, in the form of a continuous variable per node. From time to time nodes exchange their first-hand information with others, but, using the Bayesian approach we designed and present in this paper, only second-hand information that is not incompatible with the current rating is accepted. Ratings are slightly modified by accepted information. The reputation of a given node is the collection of ratings maintained by others about this node. By means of simulation we evaluated the robustness of our approach against several types of adversaries that spread false information, and its efficiency at detecting malicious nodes. The simulation results indicate that our system largely reduces the impact of false accusations, while still benefiting from the accelerated detection of malicious nodes provided by second-hand information. We also found that when information dissemination is not used, the time until malicious nodes are detected can be unacceptable. Time varying problems usually have complex underlying structures represented as dynamic networks where entities and relationships appear and disappear over time. The problem of efficiently performing dynamic link inference is extremely challenging due to the dynamic nature in massive evolving networks especially when there exist sparse connectivities and nonlinear transitional patterns. In this paper, we propose a novel deep learning framework, i.e., Conditional Temporal Restricted Boltzmann Machine (ctRBM), which predicts links based on individual transition variance as well as influence introduced by local neighbors. The proposed model is robust to noise and have the exponential capability to capture nonlinear variance. We tackle the computational challenges by developing an efficient algorithm for learning and inference of the proposed model. To improve the efficiency of the approach, we give a faster approximated implementation based on a proposed Neighbor Influence Clustering algorithm. Extensive experiments on simulated as well as real-world dynamic networks show that the proposed method outperforms existing algorithms in link inference on dynamic networks. We present a latent hierarchical structural learning method for object detection. An object is represented by a mixture of hierarchical tree models where the nodes represent object parts. The nodes can move spatially to allow both local and global shape deformations. The models can be trained discriminatively using latent structural SVM learning, where the latent variables are the node positions and the mixture component. But current learning methods are slow, due to the large number of parameters and latent variables, and have been restricted to hierarchies with two layers. In this paper we describe an incremental concave-convex procedure (iCCCP) which allows us to learn both two and three layer models efficiently. We show that iCCCP leads to a simple training algorithm which avoids complex multi-stage layer-wise training, careful part selection, and achieves good performance without requiring elaborate initialization. We perform object detection using our learnt models and obtain performance comparable with state-of-the-art methods when evaluated on challenging public PASCAL datasets. We demonstrate the advantages of three layer hierarchies – outperforming 's two layer models on all 20 classes. Learning low-dimensional representations of networks has proved effective in a variety of tasks such as node classification, link prediction and network visualization. Existing methods can effectively encode different structural properties into the representations, such as neighborhood connectivity patterns, global structural role similarities and other high-order proximities. However, except for objectives to capture network structural properties, most of them suffer from lack of additional constraints for enhancing the robustness of representations. In this paper, we aim to exploit the strengths of generative adversarial networks in capturing latent features, and investigate its contribution in learning stable and robust graph representations. Specifically, we propose an Adversarial Network Embedding (ANE) framework, which leverages the adversarial learning principle to regularize the representation learning. It consists of two components, i.e., a structure preserving component and an adversarial learning component. The former component aims to capture network structural properties, while the latter contributes to learning robust representations by matching the posterior distribution of the latent representations to given priors. As shown by the empirical results, our method is competitive with or superior to state-of-the-art approaches on benchmark network embedding tasks.