  In this study, we explore peer-interaction effects in online networks on
speaking skill development. In particular, we present an evidence for gradual
buildup of skills in a small-group setting that has not been reported in the
literature. We introduce a novel dataset of six online communities consisting
of 158 participants focusing on improving their speaking skills. They
video-record speeches for 5 prompts in 10 days and exchange comments and
performance-ratings with their peers. We ask (i) whether the participants'
ratings are affected by their interaction patterns with peers, and (ii) whether
there is any gradual buildup of speaking skills in the communities towards
homogeneity. To analyze the data, we employ tools from the emerging field of
Graph Signal Processing (GSP). GSP enjoys a distinction from Social Network
Analysis in that the latter is concerned primarily with the connection
structures of graphs, while the former studies signals on top of graphs. We
study the performance ratings of the participants as graph signals atop
underlying interaction topologies. Total variation analysis of the graph
signals show that the participants' rating differences decrease with time
(slope=-0.04, p<0.01), while average ratings increase (slope=0.07,
p<0.05)--thereby gradually building up the ratings towards community-wide
homogeneity. We provide evidence for peer-influence through a prediction
formulation. Our consensus-based prediction model outperforms baseline
network-agnostic regression models by about 23% in predicting performance
ratings. This, in turn, shows that participants' ratings are affected by their
peers' ratings and the associated interaction patterns, corroborating previous
findings. Then, we formulate a consensus-based diffusion model that captures
these observations of peer-influence from our analyses.
