2021 Theses Doctoral

# Essays on Network Analysis with Applications to Seeding and Art Valuation

The rise and growth of online social networks have spurred tremendous changes in our understanding of human behavior. Social scientists and companies have devised new tools to analyze the vast amounts of data obtained from these networks. Such advances have had two major consequences. First, it has allowed firms to significantly improve their segmentation and targeting strategies. Second, it also modified how problems are conceptualized. For example, books, academic papers, or webpages are now being studied under methods developed for social network analysis.

This dissertation contributes to both applications. Essays 1 and 2 describe efficient targeting strategies in situations where access to information or computing power is costly. Although existing “seeding” methods have been quite successful in social networks, they often do not account for firms' limited computing power or assume that firms are omniscient. Essay 3 focuses on the art industry by conceptualizing paintings as items connected to each other in a network through their visual similarities. Indeed, we still do not perfectly understand what makes art financially valuable and even major auction houses are at awe when paintings are sold at prices multiple times higher than what they expected. In particular, we aim to quantify how an art piece's visual features and historical importance may impact prices and assess how auction houses and their marketing efforts may modify how art is evaluated and valued.

This dissertation has three essays. In the first essay, we analyze how the friendship paradox, which states that your friends have more friends than you, may be generalized to situations where relationships are asymmetric. Indeed, the result assumes symmetric relations: if two people are friends, then each is the other's friend. For social networks that satisfy this assumption (e.g., Facebook), the friendship paradox implies that firms can potentially achieve faster and more widespread diffusion of information by seeding it with the friends of a group of people than with people in the group itself. We generalize the result to allow one-sided (leader/follower) relations and examine the implications for seeding in social networks where messages can be sent only by a leader to his/her followers. We obtain necessary and sufficient conditions under which the highest number of followers is obtained by seeding with (1) leaders, (2) followers, and (3) individuals chosen by ignoring the distinction between leaders and followers. We examine the seeding implications of the results for a subset of Twitter users.

The second essay furthers our understanding of the friendship paradox and relates it to beta centrality and eigenvector centrality. We generalize the results to asymmetric relations, define two beta centrality measures and relate them to the singular vectors of the associated directed graph. Our first generalization shows that the expected number of k removed friends is no smaller than the expected number of k-1 removed friends when k is an even number. Such a relation does not necessarily exist when k is an odd number. As k increases to infinity, the limiting value of the expected number of k removed friends converges to the largest eigenvalue of the associated undirected graph. We interpret beta centrality to be a weighted sum of an infinite series of the numbers of k removed friends. It approaches eigenvector centrality when the weighting parameter becomes arbitrarily close to the inverse of the limiting value of the expected number of k removed friends. We further generalize these results to asymmetric relations (say, between followers and leaders) that can be represented by directed graphs. We show that the last person in a randomly selected alternating sequence of 2k+1 leaders and followers (followers and leaders) has no fewer followers (leaders) than the last person in a randomly selected alternating sequence of 2k followers and leaders (leaders and followers). As k increases to infinity, the expected number of leaders of the last person in a randomly selected sequence of 2k alternating leaders and followers converges to a value proportional to the largest singular value of the associated directed graph. Similarly, the expected number of followers of the last person in a randomly selected sequence of 2k alternating followers and leaders converges to a (different) value proportional to the largest singular value of the associated directed graph. We show that there is a reciprocal relation between the limiting expected values of leaders and followers. We generalize beta centrality to asymmetric relations and relate the limiting values of beta centrality scores for followers and leaders to the singular vectors of the associated directed graph.

The third essay focuses on the art market. Auction houses hold auctions regularly throughout the year. However, once or twice a year, art investors and wealthy consumers attend highly selective marquee events: day and evening sales. Those carefully designed and highly marketed events often generate a lot of excitement for connoisseurs as most paintings get sold for tremendous amounts of money. But what makes those paintings special? We investigate how art is evaluated across those three types of auctions. Specifically, we build a deep learning model to summarize the paintings into a low dimensional representation space where each factor encodes a specific feature of the paintings’ aesthetics and further utilize those components to create “network” variables that will determine how influential and creative a painting is. We use those predictors in hedonic regression models to study how art returns differs across the three types of sales and subsequently analyze whether the paintings are evaluated differently. In particular, we find that paintings sold in evening sales generated an annualized return of 14.33% in the period 1999-2018 - more than three times the returns of paintings sold in regular or day auctions. Finally, we adopt a propensity score matching approach to create a homogeneous population of paintings - based on their likelihood to be auctioned in an evening sale - to assess the causal impact of being featured in an evening sale and find that such highlight increases a painting's price by almost $6 million.

## Files

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## More About This Work

- Academic Units
- Business
- Thesis Advisors
- Kohli, Rajeev
- Jedidi, Kamel
- Degree
- Ph.D., Columbia University
- Published Here
- April 19, 2021