Perform inference on networks with metadata on both edges and nodes.
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Caption photos easily. On the left, a road goes through a tunnel. Middle, leaves artistically fall in a hipster photoshoot. Right, in another hipster photoshoot, a lumberjack grasps a handful of pine needles.
This image can also have a caption. It's like magic.
You can also put regular text between your rows of images, even citations (Contisciani et al., 2020)(Higham et al., 2022)(Contisciani* et al., 2024). Say you wanted to write a bit about your project before you posted the rest of the images. You describe how you toiled, sweated, bled for your project, and then… you reveal its glory in the next row of images.
You can also have artistically styled 2/3 + 1/3 images, like these.
The code is simple. Just wrap your images with <div class="col-sm"> and place them inside <div class="row"> (read more about the Bootstrap Grid system). To make images responsive, add img-fluid class to each; for rounded corners and shadows use rounded and z-depth-1 classes. Here’s the code for the last row of images above:
Community detection in networks is commonly performed using information about interactions between nodes. Recent advances have been made to incorporate multiple types of interactions, thus generalizing standard methods to multilayer networks. Often, though, one can access additional information regarding individual nodes, attributes, or covariates. A relevant question is thus how to properly incorporate this extra information in such frameworks. Here we develop a method that incorporates both the topology of interactions and node attributes to extract communities in multilayer networks. We propose a principled probabilistic method that does not assume any a priori correlation structure between attributes and communities but rather infers this from data. This leads to an efficient algorithmic implementation that exploits the sparsity of the dataset and can be used to perform several inference tasks; we provide an open-source implementation of the code online. We demonstrate our method on both synthetic and real-world data and compare performance with methods that do not use any attribute information. We find that including node information helps in predicting missing links or attributes. It also leads to more interpretable community structures and allows the quantification of the impact of the node attributes given in input.
[4]
Multilayer patent citation networks: A comprehensive analytical framework for studying explicit technological relationships
Kyle Higham, Martina Contisciani, and Caterina De Bacco
The use of patent citation networks as research tools is becoming increasingly commonplace in the field of innovation studies. However, these networks rarely consider the contexts in which these citations are generated and are generally restricted to a single jurisdiction. Here, we propose and explore the use of a multilayer network framework that can naturally incorporate citation metadata and stretch across jurisdictions, allowing for a complete view of the global technological landscape that is accessible through patent data. Taking a conservative approach that links citation network layers through triadic patent families, we first observe that these layers contain complementary, rather than redundant, information about technological relationships. To probe the nature of this complementarity, we extract network communities from both the multilayer network and analogous single-layer networks, then directly compare their technological composition with established technological similarity networks. We find that while technologies are more splintered across communities in the multilayer case, the extracted communities match much more closely the established networks. We conclude that by capturing citation context, a multilayer representation of patent citation networks is, conceptually and empirically, better able to capture the significant nuance that exists in real technological relationships when compared to traditional, single-layer approaches. We suggest future avenues of research that take advantage of novel computational tools designed for use with multilayer networks.
[P1]
Flexible inference in heterogeneous and attributed multilayer networks
Martina Contisciani*, Marius Hobbhahn*, Eleanor A Power, Philipp Hennig, and Caterina De Bacco
Networked datasets are often enriched by different types of information about individual nodes or edges. However, most existing methods for analyzing such datasets struggle to handle the complexity of heterogeneous data, often requiring substantial model-specific analysis. In this paper, we develop a probabilistic generative model to perform inference in multilayer networks with arbitrary types of information. Our approach employs a Bayesian framework combined with the Laplace matching technique to ease interpretation of inferred parameters. Furthermore, the algorithmic implementation relies on automatic differentiation, avoiding the need for explicit derivations. This makes our model scalable and flexible to adapt to any combination of input data. We demonstrate the effectiveness of our method in detecting overlapping community structures and performing various prediction tasks on heterogeneous multilayer data, where nodes and edges have different types of attributes. Additionally, we showcase its ability to unveil a variety of patterns in a social support network among villagers in rural India by effectively utilizing all input information in a meaningful way.