Recently, there has been tremendous interest in the phenomenon of influence propagation in social networks. The studies in this area assume they have as input to their problems a social graph with edges labeled with probabilities of influence between users. However, the question of where these probabilities come from or how they can be computed from real social network data has been largely ignored until now. Thus it is interesting to ask whether from a social graph and a log of actions by its users, one can build models of influence. This is the main problem attacked in this paper. In addition to proposing models and algorithms for learning the model parameters and for testing the learned models to make predictions, we also develop techniques for predicting the time by which a user may be expected to perform an action. We validate our ideas and techniques using the Flickr data set consisting of a social graph with 1.3M nodes, 40M edges, and an action log consisting of 35M tuples referring to 300K distinct actions. Beyond showing that there is genuine influence happening in a real social network, we show that our techniques have excellent prediction performance.

There is significant current interest in the problem of influence maximization: given a directed social network with influence weights on edges and a number k, find k seed nodes such that activating them leads to the maximum expected number of activated nodes, according to a propagation model. Kempe et al. [1] showed, among other things, that under the Linear Threshold model, the problem is NP-hard, and that a simple greedy algorithm guarantees the best possible approximation factor in PTIME. However, this algorithm suffers from various major performance drawbacks. In this paper, we propose SIMPATH, an efficient and effective algorithm for influence maximization under the linear threshold model that addresses these drawbacks by incorporating several clever optimizations. Through a comprehensive performance study on four real data sets, we show that SIMPATH consistently outperforms the state of the art w.r.t. running time, memory consumption and the quality of the seed set chosen, measured in terms of expected influence spread achieved.

Influence maximization is the problem of finding a set of users in a social network, such that by targeting this set, one maximizes the expected spread of influence in the network. Most of the literature on this topic has focused exclusively on the social graph, overlooking historical data, i.e., traces of past action propagations. In this paper, we study influence maximization from a novel data-based perspective. In particular, we introduce a new model, which we call credit distribution, that directly leverages available propagation traces to learn how influence flows in the network and uses this to estimate expected influence spread. Our approach also learns the different levels of influenceability of users, and it is time-aware in the sense that it takes the temporal nature of influence into account.We show that influence maximization under the credit distribution model is NP-hard and that the function that defines expected spread under our model is submodular. Based on these, we develop an approximation algorithm for solving the influence maximization problem that at once enjoys high accuracy compared to the standard approach, while being several orders of magnitude faster and more scalable.

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We introduce a novel frequent pattern mining approach to discover leaders and tribes in social networks. In particular, we consider social networks where users perform actions. Actions may be as simple as tagging resources (urls) as in del.icio.us, rating songs as in Yahoo! Music, or movies as in Yahoo! Movies, or users buying gadgets such as cameras, handhelds, etc. and blogging a review on the gadgets. The assumption is that actions performed by a user can be seen by their network friends. Users seeing their friends' actions are sometimes tempted to perform those actions. We are interested in the problem of studying the propagation of such "influence", and on this basis, identifying which users are leaders when it comes to setting the trend for performing various actions. We consider alternative definitions of leaders based on frequent patterns and develop algorithms for their efficient discovery. Our definitions are based on observing the way influence propagates in a time window, as the window is moved in time. Given a social graph and a table of user actions, our algorithms can discover leaders of various flavors by making one pass over the actions table. We run detailed experiments to evaluate the utility and scalability of our algorithms on real-life data. The results of our experiments confirm on the one hand, the efficiency of the proposed algorithm, and on the other hand, the effectiveness and relevance of the overall framework. To the best of our knowledge, this the first frequent pattern based approach to social network mining.

One of the key objectives of viral marketing is to identify a small set of users in a social network, who when convinced to adopt a product will influence others in the network leading to a large number of adoptions in an expected sense. The seminal work of Kempe et al. [13] approaches this as the problem of influence maximization. This and other previous papers tacitly assume that a user who is influenced (or, informed) about a product necessarily adopts the product and encourages her friends to adopt it. However, an influenced user may not adopt the product herself, and yet form an opinion based on the experiences of her friends, and share this opinion with others. Furthermore, a user who adopts the product may not like it and hence not encourage her friends to adopt it to the same extent as another user who adopted and liked the product. This is independent of the extent to which those friends are influenced by her. Previous works do not account for these phenomena.We argue that it is important to distinguish product adoption from influence. We propose a model that factors in a user's experience (or projected experience) with a product. We adapt the classical Linear Threshold (LT) propagation model by defining an objective function that explicitly captures product adoption, as opposed to influence. We show that under our model, adoption maximization is NP-hard and the objective function is monotone and submodular, thus admitting an approximation algorithm. We perform experiments on three real popular social networks and show that our model is able to distinguish between influence and adoption, and predict product adoption much more accurately than the classical LT model.

Kempe et al. [4] (KKT) showed the problem of influence maximization is NP-hard and a simple greedy algorithm guarantees the best possible approximation factor in PTIME. However, it has two major sources of inefficiency. First, finding the expected spread of a node set is #P-hard. Second, the basic greedy algorithm is quadratic in the number of nodes. The first source is tackled by estimating the spread using Monte Carlo simulation or by using heuristics [4,6,2,5,1,3]. Leskovec et al. [6] proposed the CELF algorithm for tackling the second. In this work, we propose CELF++ and empirically show that it is 35-55% faster than CELF.

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