Rasoul Shafipour

Network topology inference from non-stationary graph signals

We address the problem of inferring a graph from nodal observations, which are modeled as non-stationary graph signals generated by local diffusion dynamics that depend on the structure of the sought network. Using the so-called graph-shift operator (GSO) as a matrix representation of the graph, we first identify the eigenvectors of the shift matrix from realizations of the diffused signals, and then we rely on these spectral templates to estimate the eigenvalues by imposing desirable properties on the graph to be recovered. Different from the stationary setting where the GSO and the covariance matrix of the observed signals are simultaneously diagonalizable, here they are not. Hence, estimating the eigenvectors requires first estimating the unknown diffusion (graph) filter - a polynomial in the GSO which does preserve the sought eigenbasis. To carry out this initial system identification step, we leverage different sources of information on the input signal driving the diffusion process on the graph. Numerical tests showcase the effectiveness of the proposed algorithms in recovering social and structural brain graphs.

Buildup of speaking skills in an online learning community: a network-analytic exploration

Studies in learning communities have consistently found evidence that peer-interactions contribute to students’ performance outcomes. A particularly important competence in the modern context is the ability to communicate ideas effectively. One metric of this is speaking, which is an important skill in professional and casual settings. 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. Evaluating the development of such skills requires studying objective evidence, for which purpose, 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. We anticipate that this study will open up future avenues for a broader exploration of peer-influenced skill development mechanisms, and potentially help design innovative interventions in small-groups to maximize peer-effects.