The structure of social influence in recommender networks
Pantelis Pipergias Analytis, Daniel Barkoczi, Philipp Lorenz-Spreen, Stefan HerzogPeople’s ability to influence others’ opinion on matters of taste varies greatly. Consider renowned film critics such as Roger Ebert or wine critics such as Robert Parker: their judgments are recognized as an indicator of quality by most other critics and the general public alike, to the extent that their opinions can alter the price or financial performance of products. Still, for each influential individual there are many more whose opinions are not considered attention-worthy by others. What are the mechanisms underlying these striking differences?
Method: We start our inquiry looking at the strategies that people use to inform their decisions and learn from others. There are two central principles at play in almost all decision strategies (i) weighing of different informational sources and (ii) selecting relevant information. We use the weighted k-nearest neighbors algorithm (k-nn) as applied in recommender systems to capture these two tendencies and represent a wide array of social learning strategies. We then use taste similarity between individuals (as captured by the correlation in their opinions) to identify nearest neighbors and calculate weights. We then construct networks with nodes representing different individuals and edges representing connections created by the k-nn algorithm. We use degree and node strength as measures of an individual’s social influence, since they naturally fit the weighted social learning strategies we study.
Datasets and procedure: We analyze an array of datasets, including Jester, a widely studied collaborative filtering dataset on humor, datasets on visual art, architecture, and landscapes, and data on people’s attractiveness. The datasets represent key domains of interest for the recommender systems community (e.g., real estate, travel, dating). For all individuals in a dataset, we calculated the performance of different versions of the weighted k-nn algorithm by independently varying the number of people the algorithm looks at and its sensitivity to differences in the observed similarity with others. We assessed the out-of-sample performance of the algorithm by splitting the data into two equally sized parts: training vs. test sets. We used the training set to estimate the free parameters. We then created all possible paired comparisons between two items in the test set and predicted which items people would prefer more strongly.
Results: We show three novel results that apply both to offline advice taking and online recommender settings. First, in all the datasets that we examined influential individuals have mainstream tastes and high dispersion in their taste similarity with others. They are also the people who benefit most from social learning (or recommender systems). Second, the fewer people an individual or algorithm consults (i.e., the lower k is) or the larger the weight placed on the opinions of more similar others, the smaller the group of people with substantial influence. Third, the influence networks emerging from deploying the k-nn algorithm are hierarchically organized. That it, the local clustering coefficient is inversely related to the in-degree following a power law: the less influence individuals exert over others, the tighter the clusters they tend to form.