Attribute based diversification of seeds for targeted influence maximization

Abstract

Embedding diversity into knowledge discovery is important: the patterns mined will be more novel, more meaningful, and broader. Surprisingly, in the classic problem of influence maximization in social networks, relatively little study has been devoted to diversity and its integration into the objective function of an influence maximization method.

In this work, we propose the integration of a categorical-based notion of seed diversity into the objective function of a targeted influence maximization problem. In this respect, we assume that the users of a social network are associated with a categorical dataset where each tuple expresses the profile of a user according to a predefined schema of categorical attributes. Upon this assumption, we design a class of monotone submodular functions specifically conceived for determining the diversity of the subset of categorical tuples associated with the seed users to be discovered. This allows us to develop an efficient approximate method, with a constant-factor guarantee of optimality. More precisely, we formulate the attribute-based diversity-sensitive targeted influence maximization problem under the state-of-the-art reverse influence sampling framework, and we develop a method, dubbed ADITUM, that ensures a $(1-1/e-∊)$-approximate solution under the general triggering diffusion model. Extensive experimental evaluation based on real-world networks as well as synthetically generated data has shown the meaningfulness and uniqueness of our proposed class of set diversity functions and of the ADITUM algorithm, also in comparison with methods that exploit numerical-attribute-based diversity and topology-driven diversity in influence maximization.

Introduction

Online social networks (OSNs) are a suitable environment for propagating influence between connected individuals, so that they have become the most profitable channel for a variety of purposes related to viral marketing, advertisement campaigns, news propagation, and many others. In this regard, a classic optimization problem is influence maximization (IM), which is to discover a set of seeds, i.e., initial influencers or early-adopters, that can maximize the spread of information through the network (e.g., advertising of a product) [21]. The basic principle is that, by finding the most effective users to endorse an idea/product/information and to influence other users in the network, a chain reaction of influence can be activated and driven by a “word-of-mouth” effect, in such a way that with a very small marketing cost (i.e., the number of initial influencers) a very large portion of the network will be reached. The extent of this portion can conveniently be limited to a selection of users depending on predetermined constraints, such as based on strategic location or interest in contents that are being diffused; in fact, in many practical scenarios, companies want to tailor their advertisement strategies in order to address only selected OSN-users as potential customers. This is the perspective adopted in the context of targeted IM, which is also a focus of this work.

Maximizing the spread of information is directly related to an a priori specified budget as the number of seeds. In a more complex “budgeted” scenario of profit maximization, each of these seeds could be associated with a different cost to engage it as early-adopter, which would imply to account for these costs as constraints in a (targeted) IM problem. Moreover, we have the opportunity to make the seed-selection step in IM more sensitive to user features. In particular, we believe that the “influence potential” of the seeds being selected can be well-explained in terms of diversity that may characterize the seeds.

Intuitively, influencers that are diverse to each other according to certain features (e.g., age, gender, socio-cultural aspects, preferences) might have more opinions, experiences, and perspectives to bear on the influence propagation process. As a consequence, identifying a set of seed users that have as more different characteristics as possible from each other, will be helpful to enhance the marketing or information-propagation campaign strategies to engage the target users. Indeed, before taking any decision for active involvement in a given propagation scenario, every user in the network would like to acquire enough information, possibly from different perspectives. Therefore, by identifying the most diverse seed users, the triggering stimuli will also be diversified, and since diverse individuals tend to connect to many different types of members, the likelihood of influencing the targets would be higher.

Accounting for diversity in influence propagation has important implications, also from an ethical viewpoint. In fact, favoring diversity in selecting the early-adopters as well as in targeting the users to reach is strictly related to being exposed to diverse opinions: as previously argued in [1], the latter can significantly contribute to disrupt information bubbles or echo chambers — where pre-existing opinions are maintained and reinforced — thus raising the level of democratic debate.

Despite the importance of leveraging diversity for improved solutions to IM problems, it comes to our surprise that relatively few studies have considered diversity in such a context. Some work has focused on understanding relations between diversity, or fairness, and effectiveness/efficiency in the spreading ability [3], [19], [14], [45]. Node diversity into the IM task was first introduced by Tang et al. [46], where numerical attributes reflecting user preferences on some predefined categories (e.g., movie genres) are considered to address a generic IM task. In [6], we originally defined an IM problem that is both targeted and diversity-sensitive for the seed selection, however, it only considers specific notions of diversity that are driven by the topology of the information diffusion graph. Also, [1] studied diversity of exposure, which relies on an item-aware propagation setting.

Contributions. In this work, we aim to advance research on IM by formulating a novel targeted IM problem that accounts for categorical attribute-based diversity of the seeds to be identified. Our contributions are summarized as follows.

• We propose  the Attribute-based DIversity-sensitive  Targeted InflUence Maximization problem, dubbed ADITUM.¹ A key aspect is that the set of nodes in the network is associated with a categorical dataset, which would represent the node profiles according to a schema of categorical attributes and corresponding values.

• We provide conceptually different notions of diversity that are able to reflect the variety in the categorical attributes and their values that characterize the seeds being discovered. Remarkably, we design a class of nondecreasing monotone and submodular functions for categorical diversity, each of which also has the nice property of enabling incremental computation of a node’s marginal gain when added to the current seed set. To the best of our knowledge, we are the first to propose a formal systematization of approaches and functions for determining submodular set diversity in influence propagation and related problems in information networks.

• We design our solution to the ADITUM problem under the Reverse Influence Sampling (RIS) paradigm [4], [49], which is widely recognized as the state-of-the-art approach for IM problems. One challenge that we address is revisiting the RIS framework to deal with both the targeted nature and the diversity-awareness of the ADITUM problem.

• We develop the ADITUM algorithm, which returns a size-k seed set ensuring an approximation ratio of $(1-1/e-∊)$, with high probability (at least $1-|\mathcal{V}{|}^{-1}$), in $O\left({∊}^{-2}k\right(\left|\mathcal{E}\right|+\left|\mathcal{V}\right|\left)\log \right|\mathcal{V}\left|\right)$ time (with $∊$ sampling error) on a diffusion graph with $\left|\mathcal{V}\right|$ nodes and $\left|\mathcal{E}\right|$ edges, under the Triggering model, which is a general diffusion model adopted by most existing work in monotone submodular IM.

• We thoroughly analyzed our proposed diversity functions on synthetically generated datasets, and we experimentally evaluated ADITUM on publicly available network datasets, three of which were used in a user engagement context, one in community interaction, and the other one in recommendation. We make this choice so we can compare ADITUM against the methods in [46], [6].

Plan of the paper. The remainder of this paper is organized as follows. Section 2 discusses related work, with emphasis on targeted IM and diversity-aware IM. Section 3 formalizes the information diffusion context model, the objective function, and the optimization problem under consideration. Section 4 presents our study on monotone and submodular diversity functions for categorical data modeling the profiles of nodes in a network. Section 5 describes our proposed approach and algorithm for the ADITUM problem. Sections 6 Evaluation methodology, 7 Experimental results contain our experimental evaluation methodology and results, respectively. In Section 8, we provide our conclusions and pointers for future research.