The fast growth of social networks and their privacy requirements in recent years, has lead to increasing difficulty in obtaining complete topology of these networks. However, diffusion information over these networks is available and many algorithms have been proposed to infer the underlying networks by using this information. The previously proposed algorithms only focus on inferring more links and do not pay attention to the important characteristics of the underlying social networks In this paper, we propose a novel algorithm, called DANI, to infer the underlying network structure while preserving its properties by using the diffusion information. Moreover, the running time of the proposed method is considerably lower than the previous methods. We applied the proposed method to both real and synthetic networks. The experimental results showed that DANI has higher accuracy and lower run time compared to well-known network inference methods.
: The only major work in this category proposes a stochastic generative model named CCN that uses both the complete network topology and diffusion information to extract communities @cite_8 . This model does not consider any special assumption about link formation, arrival probability of a contagion at each node, cascades models over the network, and rather tries to model them with a random process. Despite good features such as overlapping community detection, this method suffers from high running time complexity. In @cite_6 , the authors expand CCN by considering that the underlying network is not available. This method adopts a mathematical model similar to CCN, and uses an independent cascade assumption to introduce a model called C-IC, and also uses NETRATE to introduce a model called C-Rate. The output of this method is the network communities without producing the links of network.
@cite_6 @cite_8
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Given a directed social graph and a set of past informa- tion cascades observed over the graph, we study the novel problem of detecting modules of the graph (communities of nodes), that also explain the cascades. Our key observation is that both information propagation and social ties forma- tion in a social network can be explained according to the same latent factor, which ultimately guide a user behavior within the network. Based on this observation, we propose the Community-Cascade Network (CCN) model, a stochas- tic mixture membership generative model that can fit, at the same time, the social graph and the observed set of cas- cades. Our model produces overlapping communities and for each node, its level of authority and passive interest in each community it belongs. For learning the parameters of the CCN model, we devise a Generalized Expectation Maximization procedure. We then apply our model to real-world social networks and in- formation cascades: the results witness the validity of the proposed CCN model, providing useful insights on its signif- icance for analyzing social behavior. The proliferation of models for networks raises challenging problems of model selection: the data are sparse and globally dependent, and models are typically high-dimensional and have large numbers of latent variables. Together, these issues mean that the usual model-selection criteria do not work properly for networks. We illustrate these challenges, and show one way to resolve them, by considering the key network-analysis problem of dividing a graph into communities or blocks of nodes with homogeneous patterns of links to the rest of the network. The standard tool for undertaking this is the stochastic block model, under which the probability of a link between two nodes is a function solely of the blocks to which they belong. This imposes a homogeneous degree distribution within each block; this can be unrealistic, so degree-corrected block models add a parameter for each node, modulating its overall degree. The choice between ordinary and degree-corrected block models matters because they make very different inferences about communities. We present the first principled and tractable approach to model selection between standard and degree-corrected block models, based on new large-graph asymptotics for the distribution of log-likelihood ratios under the stochastic block model, finding substantial departures from classical results for sparse graphs. We also develop linear-time approximations for log-likelihoods under both the stochastic block model and the degree-corrected model, using belief propagation. Applications to simulated and real networks show excellent agreement with our approximations. Our results thus both solve the practical problem of deciding on degree correction and point to a general approach to model selection in network analysis. We propose introspective convolutional networks (ICN) that emphasize the importance of having convolutional neural networks empowered with generative capabilities. We employ a reclassification-by-synthesis algorithm to perform training using a formulation stemmed from the Bayes theory. Our ICN tries to iteratively: (1) synthesize pseudo-negative samples; and (2) enhance itself by improving the classification. The single CNN classifier learned is at the same time generative --- being able to directly synthesize new samples within its own discriminative model. We conduct experiments on benchmark datasets including MNIST, CIFAR-10, and SVHN using state-of-the-art CNN architectures, and observe improved classification results. The convolutional neural network (ConvNet or CNN) has proven to be very successful in many tasks such as those in computer vision. In this conceptual paper, we study the generative perspective of the discriminative CNN. In particular, we propose to learn the generative FRAME (Filters, Random field, And Maximum Entropy) model using the highly expressive filters pre-learned by the CNN at the convolutional layers. We show that the learning algorithm can generate realistic and rich object and texture patterns in natural scenes. We explain that each learned model corresponds to a new CNN unit at a layer above the layer of filters employed by the model. We further show that it is possible to learn a new layer of CNN units using a generative CNN model, which is a product of experts model, and the learning algorithm admits an EM interpretation with binary latent variables.