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MEASURING INFLUENCE ON INSTAGRAM: A NETWORK-OBLIVIOUS APPROACH 2 On LinkedIn, a professional OSN, Budalakoti and Bekker- man suggested a fair-bets model for ranking via transfer of authority [32], and on Instagram Egger suggested a PageRank extension for influencer ranking [33]. On Instagram, unlike Twitter, follower data is not pub- licly available. While this information can still be collected via crawling, it is a long and expensive process. A possible solution would be to infer the underlying network structure using the user activity logs, as described by Barbieri et al. [16]. Even in the event a graph is constructed, it would not necessarily be of much use given that information decays exponentially along the graph even under optimal passive information propagation, which is not the case. 3 PROBLEM FORMULATION The influence of a user in an OSN has been described either in simple, intuitive measures or as a non-intuitive measurable graph statistic with no real-world meaning [30], [33], [34]. One such measure is the user’s expected post engagements. We extend this definition in the realization that being exposed to specific content often does not lead to active engagement. We say the influence of an Instagram user (Instagrammer) is the expected exposure their content would receives, or, their expected number of views per post. Adhering to the law of large numbers, we can estimate the users’ influence using Definition 3.1: Definition 3.1. Let U be the set of all Instagrammers, C be all content posted on Instagram, vc the number of Instagrammers thatsawpostc∈CandCu ⊂Cisthecontentpostedbyu∈U. We say that the influence of Instagrammer u is: c∈Cu vc Infu= |Cu| . 4 INSTAGRAM DATASET For the purpose of this study, a set of Instagram data was prepared in April 2017, including posts published during 2015-2016 but prior to September 2016. We focused on a sub- set of Instagram posts where view counts were accessible. Independent studies have shown that 50% of engagements of an Instagram post happen within 72 minutes of publi- cation and 95% within the following week1. As the change of feed ranking in March 2016 did not cause statistically significant changes to activity, and as all posts examined by us were over 6 months old, we say that the data is stable, meaning, all posts have reached at least 95% of their potential views and engagements. The data was prepared as follows: 1) We gathered information on videos 2 published by a set of randomly selected Instagrammers with pub- licly accessible profiles. Denote the set of users as U . Each of these Instagrammers must have published a minimum of 10 video posts before September 2016. 1. https://blog.takumi.com/the-half-life-of-instagram-posts-3db61fb1db75 2) For each video c ∈ C, we collected the following metrics: • likesc - Number of likes awarded to post c. • commentsc - Number of comments given to post c. • vc - Number of Instagrammers who watched part of the video. A total of 940,439 posts by 115,044 Instagrammers was collected3 . 4.1 Instagram Statistics The distribution for log average views per Instagrammer is presented in Figure 1a, from which we can tell that this statistic behaves in a log-normal distribution with a mean of 748 views. Furthermore, as this distribution is so close to normal, we ascertain that our selection of sampled Insta- grammers is a good semblance of real-world influence with micro-influencers populating the dense mean and casual users and celebrities appearing at the distribution extremes. Post views per followers and per engagement appear in Figures 1b and 1c, respectively; these show some underline truths of Instagram. It can be seen that normally, the number of followers a user has outnumber his views, as we expect following the described flow of information. However, we found that this is not the case for sponsored posts, massively engaged content or externally referenced content. Another unlikely situation is of posts having more engagements than views. This relates either to bought engagements, often via automation tools and fake accounts, or to an interesting phenomenon on Instagram known as ”Like You, Like Me” where content is engaged simply to reciprocate prior engagements. The issue mitigates as the number of engagements increase. To avoid these sorts of odd behaviors, we performed uni- variate outliers removal, ignoring the top and bottom posts for users with posts statistics above 2 standard deviations. 4.2 Features Collected For the purpose of this work, we collected basic features directly from Instagram. Expanding on the posts features mentioned above, we also collected user specific statistics. We then considered each user as a data point with the following statistics: • • • • • • likes - The average number of user post likes. comments - The average number of comments per user post. f ollowers - The users audience size. √ likes·followers - Geometric mean of likes and followers, taken as neither statistic is an exact rep- resentation of influence. followers - Used to suggest odd behavior as same post level influencers should have similar ratios. comments - Another odd behavior indicator as likes bought engagements tend to effect likes more than comments. 2. We used Instagram API to collect user statistics. We did not use the API to gather data for the posts themselves due to API limits. Instead, 3. This collection of anonymized public information is available at we parsed each post web-page. https://klear.com/sigir/instagram data.zipPDF Image | MEASURING INFLUENCE ON INSTAGRAM: A NETWORK-OBLIVIOUS APPROACH
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