Role detection in bicycle-sharing networks using multilayer stochastic block models

Abstract

In urban systems, there is an interdependency between neighborhood roles and transportation patterns between neighborhoods. In this paper, we classify docking stations in bicycle-sharing networks to gain insight into the human mobility patterns of three major cities in the United States. We propose novel time-dependent stochastic block models, with degree-heterogeneous blocks and either mixed or discrete block membership, which classify nodes based on their time-dependent activity patterns. We apply these models to (1) detect the roles of bicycle-sharing stations and (2) describe the traffic within and between blocks of stations over the course of a day. Our models successfully uncover work blocks, home blocks, and other blocks; they also reveal activity patterns that are specific to each city. Our work gives insights for the design and maintenance of bicycle-sharing systems, and it contributes new methodology for community detection in temporal and multilayer networks with heterogeneous degrees.

A tensor factorization model of multilayer network interdependence

“…In [61] a multilayer SBM is developed by fitting a new SBM to each layer, assuming that neither node-membership nor group-togroup connectivity is fixed across layers. In [11] and [16], a node's membership vectors are held fixed across layers, but a new affinity matrix is fit for each layer. A similar model is proposed in [47] but with node membership vectors constrained to take on binary values and with a Bernoulli distribution assumption instead of Poisson.…”

“…Introduction. Multilayer networks capture the many ways that a set of units can be connected: through different types of relationships in a social network [7,48,10,52]; at different time steps [11,22,58]; through different types of interactions between genes or proteins [18,39]; or by different modes of transit in a transportation network [20,24] (see reviews [36,9] for more examples). As more and more data take on a multilayer network form, tools for network analysis are being steadily adapted to multilayer contexts.…”

“…Recent work has productively cast the study of multilayer community structure in the language of multilinear algebra [67], furnishing tensor-based definitions of multilayer stochastic block models (SBMs) [16,25,11,57]. In this work we extend and generalize these efforts, connecting the tensorial nonnegative Tucker decomposition with KL-divergence to the statistical Who do you spend time with?…”

“…DeBacco et al (2017) [16] andCarlen et al (2019) [11] Y is constrained so that Y := I.Paul and Chen (2016)[47] U := V constrained to only take on binary values, Y is constrained so that Y := I, and the model assumes a Bernoulli distribution (as opposed to Poisson).Tarrés-Deulofeu et al (2019) [57] U , V , and Y have constraint C = K and a new core tensor G is estimated for each type of link in the network.…”