Ranking Marginal Influencers in a Target-labeled Network Pranay Lohia Kalapriya Kannan Karan Rai Srikanta Bedathur IBM Research AI, India IBM Research AI, India Microsoft, United States IIT Delhi, India ABSTRACT are reached with sufficiently strong paths. In other words, the goal Using social networks for spreading marketing information is a is not to find globally influential nodes in the network, butfind commonly used strategy to help in quick adoption of innovations, nodes that maximize the ability to reach and influence these tar- retention of customers and for improving brand awareness. In many geted nodes in the network. At the same time, the problem also settings, the set of entities in the network who must be the targets has the implicit requirement that non-target nodes should not be of such an information spread are already known, either implicitly activated in order to minimize their spam or the cost of communi- or explicitly. It would still be beneficial to route the information cation involved. We motivate this with a scenario from recruitment to them through a carefully chosen set of influencers in the net- network where we first encountered this problem. work. We term networks where we have such vertices labeled as Recruitment Network Scenario: Consider a concrete scenario targeted recipients as targeted networks. For instance, in an online of a recruiter who would like to identify certain set of nodes in a marketing channel of a fashion product, where vertices are tagged professional network. These nodes can recommend a job advertisement with ‘fashion’ as their preferred choice of online shopping, forms a to members in their network who fit the job requirements (i.e., target targeted network. In such targeted networks, how to select a small nodes). Clearly the recruiter would not like this advertisement to subset of vertices that maximizes the influence over target nodes reach candidates who do not qualify (i.e., non-target nodes). From while simultaneously minimizing the non-target nodes which get the recruiters perspective, it will increase the effectiveness as only the information (e.g., to reduce their spam, or in some cases, due to those nodes that match the job description will respond. This will costs)? We term this as the problem of maximizing the marginal also avoid “spamming” the other candidates who do not match the influence over target networks and propose an iterative algorithm requirements. Also, if many non-relevant job descriptions are sent to to solve this problem. We present the results of our experiment a candidate, there is a possibility of the recruiter being tagged as a with large information networks, derived from English Wikipedia “spammer”. This can lead to a scenario where a potentially perfectly graph, which show that the proposed algorithm effectively iden- matching job description is ignored by the candidate. We observe that tifies influential nodes that help reach pages identified through existing traditional approaches of selecting influencers do not address queries/topics. Qualitative analysis of our results shows that we these issues. Figure 1 shows an example scenario where the central can generate a semantically meaningful ranking of query-specific node ‘Query node’ represents the recruiter. M represents the level of influential nodes. matching to the recruiters query say searching for candidates with matching skill set for a job description. M having zero indicates non- ACM Reference Format: matching nodes and a real values indicate the level of matching the Pranay Lohia, Kalapriya Kannan, Karan Rai, and Srikanta Bedathur. 2020. Ranking Marginal Influencers in a Target-labeled Network. In 7th ACM the query. Thus green node have full match, while the yellow nodes IKDD CoDS and 25th COMAD (CoDS COMAD 2020), January 5–7, 2020, match according to M. The goal is to avoid reaching red nodes that Hyderabad, India. ACM, New York, NY, USA, 7 pages. https://doi.org/10. does not have any match while we aim to reach the matching nodes 1145/3371158.3371197 at any level. □ 1 INTRODUCTION Social networks are increasingly useful in several activities ranging from e-commerce [2, 10] to job recruitments [3]. Tangible benefits of using social networks are achieved only when we are able to identify the appropriate set of nodes in the social network, be it influential nodes or high-centrality nodes. In this paper, we consider a crucial variant of the problem of identifying and ranking of nodes which have the potential to influ- ence a large social network. We observe that in many settings, there are certain nodes which can be labeled upfront as target nodes and the goal of a campaign is to ensure these nodes labeled as targets Permission to make digital or hard copies of all or part of this work for personal or Figure 1: Example graph illustrating different nodes classroom use is granted without fee provided that copies are not made or distributed Our goal is identifying nodes that not only have the ability to for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM reach a large number of target nodes that should be recipients must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, of the information but also minimize the number of undesirable to post on servers or to redistribute to lists, requires prior specific permission and/or a recipients of the information at the same time. We model this as a fee. Request permissions from [email protected]. CoDS COMAD 2020, January 5–7, 2020, Hyderabad, India problem of ranking nodes based on their marginal influence score. © 2020 Association for Computing Machinery. Intuitively, a node has a high marginal influence score if it can ACM ISBN 978-1-4503-7738-6/20/01...$15.00 https://doi.org/10.1145/3371158.3371197 254 CoDS COMAD 2020, January 5–7, 2020, Hyderabad, India Pranay, et al. influence many valuable target nodes and, at the same time, reaches presented in [13]. However, in [13] the target was to obtain an minimal number of low value nodes in the network. objective function to maximize targeted influence for which they Interestingly, application of our marginal influence ranking on a have used an information diffusion based technique. Our focus Wikipedia-like setting exhibits an unique feature. In a Wikipedia is on coming up with a scalable and efficient algorithm. Finally, graph, for each search string, it helps in listing those pages that [13] shows identification of target vs non-target nodes are sub- can lead to the target pages and avoid broad categories of matches, modular and can be addressed independently. In their work they thus providing better way to navigate. We have implemented our have considered the notion of time of diffusion information to algorithm for a recruitment solution. Feedback obtained suggests derive nodes that are influenced over time. In our work we use the that our algorithm has higher effect compared to the traditional propagation quantity and aggregate the influences to consider the referral sourcing in the business setting. net benefit and do not discount the benefits due to time factor. Our contribution in the paper are as follows: (1) We introduce the notion of marginal influencers (MI) and propose an iterative 3 MODELING MARGINAL INFLUENCERS algorithm to rank nodes by benefit and loss in terms of them influ- Marginal influence score of a node measures the relative influence encing target nodes. (2) Evaluation results over a large Wikipedia of the information originating from that node on the population of corpus and enterprise recruitment application. target nodes versus the non-target nodes. We model this process using its benefit and loss functions. In this section, we develop this 2 RELATED WORK model formally. Finding top influencer(s) have been a subject of large interest to research community. References [7] and [4] talk about general in- 3.1 Problem Setting fluence maximization and how it can be made more efficient. In We operate on an edge-weighted, directed graph G = ¹V; E;wº, general influence maximization, one tries to select the best setof where V is the vertex-set, E is the edge-set and w : E ! R≥ seed nodes such that the information can be sent to as many nodes 0 is a function that associates a real-valued weight with each edge as possible. There is no notion of quality of nodes or even their prop- to represent the strength of relationship between the two nodes erties. References [14], [11] and [16] look at a different aspect of a connected by the edge. In real-world networks, we treat this as a similar problem. Their objective is to find best matching documents probability measure. It models the probability of the propagation by with respect to a query node such that tagging of those documents the source node, given information along that edge. A special vertex are relevant to the user. In a sense, here they are considering the Q 2 V is designated as the query vertex responsible for initiating influence of other network users for deciding which are thebest the information flow. The nodes which are targeted for activation documents for someone to look at. (either by Q as the target audience, or by prior preference settings Finding MI on labeled nodes is tackled in [8] where they look at of nodes) are modelled through a non-negative weight function influencing nodes with specific labels. But they do not consider how y : V ! R≥ , that corresponds to the relevance of a vertex to many non-labeled nodes have been influenced. or if they should 0 the information which is being propagated from the vertex Q.