Information cascades are ubiquitous in both physical society and online social media, taking on large variations in structures, dynamics and semantics. Although the dynamics and semantics of information cascades have been studied, the structural patterns and their correlations with dynamics and semantics are largely unknown. Here we explore a large-scale dataset including @math million information cascades with explicit records of spreading traces, spreading behaviors, information content as well as user profiles. We find that the structural complexity of information cascades is far beyond the previous conjectures. We first propose a ten-dimensional metric to quantify the structural characteristics of information cascades, reflecting cascade size, silhouette, direction and activity aspects. We find that bimodal law governs majority of the metrics, information flows in cascades have four directions, and the self-loop number and average activity of cascades follows power law. We then analyze the high-order structural patterns of information cascades. Finally, we evaluate to what extent the structural features of information cascades can explain its dynamic patterns and semantics, and finally uncover some notable implications of structural patterns in information cascades. Our discoveries also provide a foundation for the microscopic mechanisms for information spreading, potentially leading to implications for cascade prediction and outlier detection.
We presented related work in three dimensions: cascade structures, dynamics and topics. The cascade structures have been studied in different scenarios, including blogs @cite_1 @cite_24 @cite_27 , communication network @cite_6 , Facebook @cite_12 , Twitter @cite_32 , LinkedIn @cite_31 . , or to infer structures @cite_4 . Deep-tree structures are found and modeled in Ref. @cite_19 . Goel @cite_22 studied the virality of cascades by using Wiener index. However, we find information flows in cascades have four directions, indicating complex structures than tree patterns. Furthermore, ignoring the high-order correlations between structure metrics in previous studies prevent our understandings of cascade structures.
@cite_4 @cite_22 @cite_1 @cite_32 @cite_6 @cite_24 @cite_19 @cite_27 @cite_31 @cite_12
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Cascades are a popular construct to observe and study information propagation (or diffusion) in social media such as Twitter. and are defined using notions of influence, activity, or discourse commonality (e.g., hashtags). While these notions of cascades lead to different perspectives, primarily cascades are modeled as trees. We argue in this paper an alternative viewpoint of cascades as forests (of trees) which yields a richer vocabulary of features to understand information propagation. We develop a framework to extract forests and analyze their growth by studying their evolution at the tree-level and at the node-level. Moreover, we demonstrate how the structural features of forests, properties of the underlying network, and temporal features of the cascades provide significant predictive value in forecasting the future trajectory of both size and shape of forests. We observe that the forecasting performance increases with observations, that the temporal features are highly indicative of cascade size, and that the features extracted from the underlying connected graph best forecast the shape of the cascade. Information cascades on social networks, such as retweet cascades on Twitter, have been often viewed as an epidemiological process, with the associated notion of virality to capture popular cascades that spread across the network. The notion of structural virality or average path length has been posited as a measure of global spread. In this paper, we argue that this simple epidemiological view, though analytically compelling, is not the entire story. We first show empirically that the classical SIR diffusion process on the Twitter graph, even with the best possible distribution of infectiousness parameter, cannot explain the nature of observed retweet cascades on Twitter. More specifically, rather than spreading further from the source as the SIR model would predict, many cascades that have several retweets from direct followers, die out quickly beyond that. We show that our empirical observations can be reconciled if we take interests of users and tweets into account. In particular, we consider a model where users have multi-dimensional interests, and connect to other users based on similarity in interests. Tweets are correspondingly labeled with interests, and propagate only in the subgraph of interested users via the SIR process. In this model, interests can be either narrow or broad, with the narrowest interest corresponding to a star graph on the interested users, with the root being the source of the tweet, and the broadest interest spanning the whole graph. We show that if tweets are generated using such a mix of interests, coupled with a varying infectiousness parameter, then we can qualitatively explain our observation that cascades die out much more quickly than is predicted by the SIR model. In the same breath, this model also explains how cascades can have large size, but low "structural virality" or average path length. Cascades appear in many applications, including biological graphs and social media analysis. In a cascade, a dynamic attribute propagates through a graph, following its edges. We present the results of a formal user study that tests the effectiveness of different types of cascade visualisations on node-link diagrams for the task of judging cascade spread. Overall, we found that a small multiples presentation was significantly faster than animation with no significant difference in terms of error rate. Participants generally preferred animation over small multiples and a hierarchical layout to a force-directed layout. Considering each presentation method separately, when comparing force-directed layouts to hierarchical layouts, hierarchical layouts were found to be significantly faster for both presentation methods and significantly more accurate for animation. Representing the history of the cascade had no significant effect. Thus, for our task, this experiment supports the use of a small multiples interf... Information spreads across social and technological networks, but often the network structures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures from these observed cascades? What kind of cascades and how many cascades do we need? Are there some network structures which are more difficult than others to recover? Can we design efficient inference algorithms with provable guarantees? Despite the increasing availability of cascade data and methods for inferring networks from these data, a thorough theoretical understanding of the above questions remains largely unexplored in the literature. In this paper, we investigate the network structure inference problem for a general family of continuous-time diffusion models using an @math -regularized likelihood maximization framework. We show that, as long as the cascade sampling process satisfies a natural incoherence condition, our framework can recover the correct network structure with high probability if we observe @math cascades, where @math is the maximum number of parents of a node and @math is the total number of nodes. Moreover, we develop a simple and efficient soft-thresholding inference algorithm, which we use to illustrate the consequences of our theoretical results, and show that our framework outperforms other alternatives in practice. Cascades are ubiquitous in various network environments. How to predict these cascades is highly nontrivial in several vital applications, such as viral marketing, epidemic prevention and traffic management. Most previous works mainly focus on predicting the final cascade sizes. As cascades are typical dynamic processes, it is always interesting and important to predict the cascade size at any time, or predict the time when a cascade will reach a certain size (e.g. an threshold for outbreak). In this paper, we unify all these tasks into a fundamental problem: cascading process prediction. That is, given the early stage of a cascade, how to predict its cumulative cascade size of any later time? For such a challenging problem, how to understand the micro mechanism that drives and generates the macro phenomena (i.e. cascading process) is essential. Here we introduce behavioral dynamics as the micro mechanism to describe the dynamic process of a node's neighbors getting infected by a cascade after this node getting infected (i.e. one-hop subcascades). Through data-driven analysis, we find out the common principles and patterns lying in behavioral dynamics and propose a novel Networked Weibull Regression model for behavioral dynamics modeling. After that we propose a novel method for predicting cascading processes by effectively aggregating behavioral dynamics, and present a scalable solution to approximate the cascading process with a theoretical guarantee. We extensively evaluate the proposed method on a large scale social network dataset. The results demonstrate that the proposed method can significantly outperform other state-of-the-art baselines in multiple tasks including cascade size prediction, outbreak time prediction and cascading process prediction. On many social networking web sites such as Facebook and Twitter, resharing or reposting functionality allows users to share others' content with their own friends or followers. As content is reshared from user to user, large cascades of reshares can form. While a growing body of research has focused on analyzing and characterizing such cascades, a recent, parallel line of work has argued that the future trajectory of a cascade may be inherently unpredictable. In this work, we develop a framework for addressing cascade prediction problems. On a large sample of photo reshare cascades on Facebook, we find strong performance in predicting whether a cascade will continue to grow in the future. We find that the relative growth of a cascade becomes more predictable as we observe more of its reshares, that temporal and structural features are key predictors of cascade size, and that initially, breadth, rather than depth in a cascade is a better indicator of larger cascades. This prediction performance is robust in the sense that multiple distinct classes of features all achieve similar performance. We also discover that temporal features are predictive of a cascade's eventual shape. Observing independent cascades of the same content, we find that while these cascades differ greatly in size, we are still able to predict which ends up the largest. The origin of large but rare cascades that are triggered by small initial shocks is a phenomenon that manifests itself as diversely as cultural fads, collective action, the diffusion of norms and innovations, and cascading failures in infrastructure and organizational networks. This paper presents a possible explanation of this phenomenon in terms of a sparse, random network of interacting agents whose decisions are determined by the actions of their neighbors according to a simple threshold rule. Two regimes are identified in which the network is susceptible to very large cascades—herein called global cascades—that occur very rarely. When cascade propagation is limited by the connectivity of the network, a power law distribution of cascade sizes is observed, analogous to the cluster size distribution in standard percolation theory and avalanches in self-organized criticality. But when the network is highly connected, cascade propagation is limited instead by the local stability of the nodes themselves, and the size distribution of cascades is bimodal, implying a more extreme kind of instability that is correspondingly harder to anticipate. In the first regime, where the distribution of network neighbors is highly skewed, it is found that the most connected nodes are far more likely than average nodes to trigger cascades, but not in the second regime. Finally, it is shown that heterogeneity plays an ambiguous role in determining a system's stability: increasingly heterogeneous thresholds make the system more vulnerable to global cascades; but an increasingly heterogeneous degree distribution makes it less vulnerable. To comprehend the multipartite organization of large-scale biological and social systems, we introduce an information theoretic approach that reveals community structure in weighted and directed networks. We use the probability flow of random walks on a network as a proxy for information flows in the real system and decompose the network into modules by compressing a description of the probability flow. The result is a map that both simplifies and highlights the regularities in the structure and their relationships. We illustrate the method by making a map of scientific communication as captured in the citation patterns of >6,000 journals. We discover a multicentric organization with fields that vary dramatically in size and degree of integration into the network of science. Along the backbone of the network—including physics, chemistry, molecular biology, and medicine—information flows bidirectionally, but the map reveals a directional pattern of citation from the applied fields to the basic sciences. In this paper, we propose a novel approach for efficient training of deep neural networks in a bottom-up fashion using a layered structure. Our algorithm, which we refer to as deep cascade learning, is motivated by the cascade correlation approach of Fahlman and Lebiere, who introduced it in the context of perceptrons. We demonstrate our algorithm on networks of convolutional layers, though its applicability is more general. Such training of deep networks in a cascade directly circumvents the well-known vanishing gradient problem by ensuring that the output is always adjacent to the layer being trained. We present empirical evaluations comparing our deep cascade training with standard end–end training using back propagation of two convolutional neural network architectures on benchmark image classification tasks (CIFAR-10 and CIFAR-100). We then investigate the features learned by the approach and find that better, domain-specific, representations are learned in early layers when compared to what is learned in end–end training. This is partially attributable to the vanishing gradient problem that inhibits early layer filters to change significantly from their initial settings. While both networks perform similarly overall, recognition accuracy increases progressively with each added layer, with discriminative features learned in every stage of the network, whereas in end–end training, no such systematic feature representation was observed. We also show that such cascade training has significant computational and memory advantages over end–end training, and can be used as a pretraining algorithm to obtain a better performance. The problem of learning classifier cascades is considered. A new cascade boosting algorithm, fast cascade boosting (FCBoost), is proposed. FCBoost is shown to have a number of interesting properties, namely that it 1) minimizes a Lagrangian risk that jointly accounts for classification accuracy and speed, 2) generalizes adaboost, 3) can be made cost-sensitive to support the design of high detection rate cascades, and 4) is compatible with many predictor structures suitable for sequential decision making. It is shown that a rich family of such structures can be derived recursively from cascade predictors of two stages, denoted cascade generators. Generators are then proposed for two new cascade families, last-stage and multiplicative cascades, that generalize the two most popular cascade architectures in the literature. The concept of neutral predictors is finally introduced, enabling FCBoost to automatically determine the cascade configuration, i.e., number of stages and number of weak learners per stage, for the learned cascades. Experiments on face and pedestrian detection show that the resulting cascades outperform current state-of-the-art methods in both detection accuracy and speed. Many of the world's most popular websites catalyze their growth through invitations from existing members. New members can then in turn issue invitations, and so on, creating cascades of member signups that can spread on a global scale. Although these diffusive invitation processes are critical to the popularity and growth of many websites, they have rarely been studied, and their properties remain elusive. For instance, it is not known how viral these cascades structures are, how cascades grow over time, or how diffusive growth affects the resulting distribution of member characteristics present on the site. In this paper, we study the diffusion of LinkedIn, an online professional network comprising over 332 million members, a large fraction of whom joined the site as part of a signup cascade. First we analyze the structural patterns of these signup cascades, and find them to be qualitatively different from previously studied information diffusion cascades. We also examine how signup cascades grow over time, and observe that diffusion via invitations on LinkedIn occurs over much longer timescales than are typically associated with other types of online diffusion. Finally, we connect the cascade structures with rich individual-level attribute data to investigate the interplay between the two. Using novel techniques to study the role of homophily in diffusion, we find striking differences between the local, edge-wise homophily and the global, cascade-level homophily we observe in our data, suggesting that signup cascades form surprisingly coherent groups of members. Consider the random graph models G(n, #edges = M) and G(n, Prob(edge) = p) with M = M(n) = (1 + )n-1 3)n 2 and p = p(n) = (1 +An-1 3) n . For 1 > -1 define an i-component of a random graph as a component which has exactly I more edges than vertices. Call an i-component with I > 1 a complex component. For both models, we show that when A is constant, the expected number of complex components is bounded, almost surely (a.s.) each of these components (if any exist) has size of order n2 3, and the maximum value of I is bounded in probability. We prove that a.s. the largest suspended tree in each complex component has size of order n2 3, and deletion of all suspended trees results in a "smoothed" graph of size of order n 3, with the maximum vertex degree 3. The total number of branching vertices, i.e., of degree 3, is bounded in probability. Thus, each complex component is almost surely topologically equivalent to a 3-regular multigraph of a uniformly bounded size. Lengths of the shortest cycle and of the shortest path between two branching vertices of a smoothed graph are each of order n 3. We find a relatively simple integral formula for the limit distribution of the numbers of complex components, which implies, in particular, that all values of the "complexity spectrum" have positive limiting probabilities. We also answer questions raised by Erdos and Renyi back in 1960. It is proven that there exists p(A), the limiting planarity probability, with 0 < p(A) < 1, p(-oo) = 1, p(oo) = 0. In particular, G(n, M) (G(n, p), resp.) is almost surely nonplanar iff (M n 2)n-213 -* 00 ((np I)n-1 3) -+ oo, resp.). We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We investigate phase transitions in graph structure as the relative weighting of these two components of the attachment rule is varied. Previous work of one of the authors showed that when the geometric component is weak, the limiting degree sequence of the resulting graph coincides with that of the standard Barab 'asi--Albert preferential attachment model. We show that at the other extreme, in the case of a sufficiently strong geometric component, the limiting degree sequence coincides with that of a purely geometric model, the on-line nearest-neighbour graph, which is of interest in its own right and for which we prove some extensions of known results. We also show the presence of an intermediate regime, in which the behaviour differs significantly from both the on-line nearest-neighbour graph and the Barab 'asi--Albert model; in this regime, we obtain a stretched exponential upper bound on the degree sequence. Our results lend some mathematical support to simulation studies of Manna and Sen, while proving that the power law to stretched exponential phase transition occurs at a different point from the one conjectured by those authors. Abstract : The Cascade-Correlation learning algorithm constructs a multi-layer artificial neural network as it learns to perform a given task. The resulting network's size and topology are chosen specifically for this task. In the resulting 'cascade' networks, each new hidden unit receives incoming connections from all input and pre-existing hidden units. In effect, each new unit adds a new layer to the network. This allows Cascade-Correlation to create complex feature detectors, but it typically results in a network that is deeper, in terms of the longest path from input to output, than is necessary to solve the problem efficiently. In this paper we investigate a simple variation of Cascade-Correlation that will build deep nets if necessary, but that is biased toward minimizing network depth. We demonstrate empirically, across a range of problems, that this simple technique can reduce network depth, often dramatically. However, we show that this technique does not, in general, reduce the total number of weights or improve the generalization ability of the resulting networks. We present the H3 layout technique for drawing large directed graphs as node-link diagrams in 3D hyperbolic space. We can lay out much larger structures than can be handled using traditional techniques for drawing general graphs because we assume a hierarchical nature of the data. We impose a hierarchy on the graph by using domain-specific knowledge to find an appropriate spanning tree. Links which are not part of the spanning tree do not influence the layout but can be selectively drawn by user request. The volume of hyperbolic 3-space increases exponentially, as opposed to the familiar geometric increase of euclidean 3-space. We exploit this exponential amount of room by computing the layout according to the hyperbolic metric. We optimize the cone tree layout algorithm for 3D hyperbolic space by placing children on a hemisphere around the cone mouth instead of on its perimeter. Hyperbolic navigation affords a Focus+Context view of the structure with minimal visual clutter. We have successfully laid out hierarchies of over 20,000 nodes. Our implementation accommodates navigation through graphs too large to be rendered interactively by allowing the user to explicitly prune or expand subtrees. Models of networked diffusion that are motivated by analogy with the spread of infectious disease have been applied to a wide range of social and economic adoption processes, including those related to new products, ideas, norms and behaviors. However, it is unknown how accurately these models account for the empirical structure of diffusion over networks. Here we describe the diffusion patterns arising from seven online domains, ranging from communications platforms to networked games to microblogging services, each involving distinct types of content and modes of sharing. We find strikingly similar patterns across all domains. In particular, the vast majority of cascades are small, and are described by a handful of simple tree structures that terminate within one degree of an initial adopting "seed." In addition we find that structures other than these account for only a tiny fraction of total adoptions; that is, adoptions resulting from chains of referrals are extremely rare. Finally, even for the largest cascades that we observe, we find that the bulk of adoptions often takes place within one degree of a few dominant individuals. Together, these observations suggest new directions for modeling of online adoption processes. Cascade is a classic yet powerful architecture that has boosted performance on various tasks. However, how to introduce cascade to instance segmentation remains an open question. A simple combination of Cascade R-CNN and Mask R-CNN only brings limited gain. In exploring a more effective approach, we find that the key to a successful instance segmentation cascade is to fully leverage the reciprocal relationship between detection and segmentation. In this work, we propose a new framework, Hybrid Task Cascade (HTC), which differs in two important aspects: (1) instead of performing cascaded refinement on these two tasks separately, it interweaves them for a joint multi-stage processing; (2) it adopts a fully convolutional branch to provide spatial context, which can help distinguishing hard foreground from cluttered background. Overall, this framework can learn more discriminative features progressively while integrating complementary features together in each stage. Without bells and whistles, a single HTC obtains 38.4 and 1.5 improvement over a strong Cascade Mask R-CNN baseline on MSCOCO dataset. Moreover, our overall system achieves 48.6 mask AP on the test-challenge split, ranking 1st in the COCO 2018 Challenge Object Detection Task. Code is available at: this https URL. We describe a methodology to examine bipartite relational data structures as exemplified in networks of corporate interlocking. These structures can be represented as bipartite graphs of directors and companies, but direct comparison of empirical datasets is often problematic because graphs have different numbers of nodes and different densities. We compare empirical bipartite graphs to simulated random graph distributions conditional on constraints implicit in the observed datasets. We examine bipartite graphs directly, rather than simply converting them to two 1-mode graphs, allowing investigation of bipartite statistics important to connection redundancy and bipartite connectivity. We introduce a new bipartite clustering coefficient that measures tendencies for localized bipartite cycles. This coefficient can be interpreted as an indicator of inter-company and inter-director closenesss but high levels of bipartite clustering have a cost for long range connectivity. We also investigate degree distributions, path lengths, and counts of localized subgraphs. Using this new approach, we compare global structural properties of US and Australian interlocking company directors. By comparing observed statistics against those from the simulations, we assess how the observed graphs are structured, and make comparisons between them relative to the simulated graph distributions. We conclude that the two networks share many similarities and some differences. Notably, both structures tend to be influenced by the clustering of directors on boards, more than by the accumulation of board seats by individual directorss that shared multiple board memberships (multiple interlocks) are an important feature of both infrastructures, detracting from global connectivity (but more so in the Australian case)s and that company structural power may be relatively more diffuse in the US structure than in Australia. This paper considers the reconstruction of structured-sparse signals from noisy linear observations. In particular, the support of the signal coefficients is parameterized by hidden binary pattern, and a structured probabilistic prior (e.g., Markov random chain field tree) is assumed on the pattern. Exact inference is discussed and an approximate inference scheme, based on loopy belief propagation (BP), is proposed. The proposed scheme iterates between exploitation of the observation-structure and exploitation of the pattern-structure, and is closely related to noncoherent turbo equalization, as used in digital communication receivers. An algorithm that exploits the observation structure is then detailed based on approximate message passing ideas. The application of EXIT charts is discussed, and empirical phase transition plots are calculated for Markov-chain structured sparsity.1 Cascades of information-sharing are a primary mechanism by which content reaches its audience on social media, and an active line of research has studied how such cascades, which form as content is reshared from person to person, develop and subside. In this paper, we perform a large-scale analysis of cascades on Facebook over significantly longer time scales, and find that a more complex picture emerges, in which many large cascades recur, exhibiting multiple bursts of popularity with periods of quiescence in between. We characterize recurrence by measuring the time elapsed between bursts, their overlap and proximity in the social network, and the diversity in the demographics of individuals participating in each peak. We discover that content virality, as revealed by its initial popularity, is a main driver of recurrence, with the availability of multiple copies of that content helping to spark new bursts. Still, beyond a certain popularity of content, the rate of recurrence drops as cascades start exhausting the population of interested individuals. We reproduce these observed patterns in a simple model of content recurrence simulated on a real social network. Using only characteristics of a cascade's initial burst, we demonstrate strong performance in predicting whether it will recur in the future.