Infuencers and communities in social networks

Abstract

An integration of social media characteristics into an econometric framework requires modeling a high dimensional dynamic network with dimensions of parameter?Θ?typically much larger than the number of observations. To cope with this problem we impose two structural assumptions onto the singular value decomposition of?Θ???= UDV >. Firstly, the matrix with probabilities of connections between the nodes of a network has a rank much lower than the number of nodes. Therefore, there is limited amount of non-zero elements on the diagonal of D and the whole operator admits a lower dimensional factorisation. Secondly, in observed social networks only a small portion of users are highly-affecting, leading to a sparsity regularization imposed on singular vectors V . Using a novel dataset of 1069K messages from 30K users posted on the microblogging platform StockTwits during a 4-year period (01.2014- 12.2018) and quantifying their opinions via natural language processing, we model their dynamic opinions network and further separate the network into communities. With a sparsity regularization, we are able to identify important nodes in the network. Keywords: social media, network, community, opinion mining, natural language processing