Understanding the Effect of GCN Convolutions in Regression Tasks

Graph Convolutional Networks (GCNs) have become a pivotal method in machine learning for modeling functions over graphs. Despite their widespread success across various applications, their statistical properties (e.g. consistency, convergence rates) remain ill-characterized. To begin addressing this knowledge gap, in this paper, we provide a formal analysis of the impact of convolution operators on regression tasks over homophilic networks. Focusing on estimators based solely on neighborhood aggregation, we examine how two common convolutions - the original GCN and GraphSage convolutions - affect the learning error as a function of the neighborhood topology and the number of convolutional layers. We explicitly characterize the bias-variance trade-off incurred by GCNs as a function of the neighborhood size and identify specific graph topologies where convolution operators are less effective. Our theoretical findings are corroborated by synthetic experiments, and provide a start to a deeper quantitative understanding of convolutional effects in GCNs for offering rigorous guidelines for practitioners.

SalienTime: User-driven Selection of Salient Time Steps for Large-Scale Geospatial Data Visualization

The voluminous nature of geospatial temporal data from physical monitors and simulation models poses challenges to efficient data access, often resulting in cumbersome temporal selection experiences in web-based data portals. Thus, selecting a subset of time steps for prioritized visualization and pre-loading is highly desirable. Addressing this issue, this paper establishes a multifaceted definition of salient time steps via extensive need-finding studies with domain experts to understand their workflows. Building on this, we propose a novel approach that leverages autoencoders and dynamic programming to facilitate user-driven temporal selections. Structural features, statistical variations, and distance penalties are incorporated to make more flexible selections. User-specified priorities, spatial regions, and aggregations are used to combine different perspectives. We design and implement a web-based interface to enable efficient and context-aware selection of time steps and evaluate its efficacy and usability through case studies, quantitative evaluations, and expert interviews.