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Multilayer networks describe the rich ways in which nodes are related by accounting for different relationships in separate layers. These multiple relationships are naturally represented by an adjacency tensor. In this work we study the use of the nonnegative Tucker decomposition (NNTuck) of such tensors under a KL loss as an expressive factor model that naturally generalizes existing stochastic block models of multilayer networks. Quantifying interdependencies between layers can identify redundancies in the structure of a network, indicate relationships between disparate layers, and potentially inform survey instruments for collecting social network data. We propose definitions of layer independence, dependence, and redundancy based on likelihood ratio tests between nested nonnegative Tucker decompositions. Using both synthetic and real-world data, we evaluate the use and interpretation of the NNTuck as a model of multilayer networks. Algorithmically, we show that using expectation maximization (EM) to maximize the log-likelihood under the NNTuck is step-by-step equivalent to tensorial multiplicative updates for the NNTuck under a KL loss, extending a previously known equivalence from nonnegative matrices to nonnegative tensors.
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Discovering functionality of urban regions by learning low-dimensional representations of a spatial multiplex network
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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- Award ID(s):
- 1739413
- PAR ID:
- 10074570
- Date Published:
- Journal Name:
- Proceedings of the Third Mining Urban Data Workshop (MUD 2018)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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