The complex relationships in an urban environment can be captured through multiple interrelated sources of data. These relationships form multilayer networks, that are also spatially embedded in an area, could be used to identify latent patterns. In this work, we propose a low-dimensional representation learning approach that considers multiple layers of a multiplex network simultaneously and is able to encode similarities between nodes across different layers. In particular, we introduce a novel neural network architecture to jointly learn low-dimensional representations of each network node from multiple layers of a network. This process simultaneously fuses knowledge of various data sources to better capture the characteristics of the nodes. To showcase the proposed method we focus on the problem of identifying the functionality of an urban region. Using a variety of public data sources for New York City, we design a multilayer network and evaluate our approach. Our results indicate that our proposed approach can improve the accuracy of traditional approaches in an unsupervised task.
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Latent space models for multiplex networks with shared structure
Summary Latent space models are frequently used for modelling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well developed for more complex network structures, which are becoming increasingly common in practice. In this article we propose a new latent space model for multiplex networks, i.e., multiple heterogeneous networks observed on a shared node set. Multiplex networks can represent a network sample with shared node labels, a network evolving over time, or a network with multiple types of edges. The key feature of the proposed model is that it learns from data how much of the network structure is shared between layers and pools information across layers as appropriate. We establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear-norm penalty, and prove a guarantee of recovery for the latent positions provided there is sufficient separation between the shared and the individual latent subspaces. We compare the model with competing methods in the literature on simulated networks and on a multiplex network describing the worldwide trade of agricultural products.
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- NSF-PAR ID:
- 10349744
- Date Published:
- Journal Name:
- Biometrika
- ISSN:
- 0006-3444
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/biomet/asab058
