"Learning Low-Rank Latent Mesoscale Structures in Networks"

One of my papers came out in final form today. Here are some details.

Title: Learning Low-Rank Latent Mesoscale Structures in Networks

Authors: Hanbaek Lyu, Yacoub H. Kureh, Joshua Vendrow, and Mason A. Porter

Abstract: Researchers in many fields use networks to represent interactions between entities in complex systems. To study the large-scale behavior of complex systems, it is useful to examine mesoscale structures in networks as building blocks that influence such behavior. In this paper, we present an approach to describe low-rank mesoscale structures in networks. We find that many real-world networks possess a small set of latent motifs that effectively approximate most subgraphs at a fixed mesoscale. Such low-rank mesoscale structures allow one to reconstruct networks by approximating subgraphs of a network using combinations of latent motifs. Employing subgraph sampling and nonnegative matrix factorization enables the discovery of these latent motifs. The ability to encode and reconstruct networks using a small set of latent motifs has many applications in network analysis, including network comparison, network denoising, and edge inference.

"Mesoscale Analyses of Fungal Networks as an Approach for Quantifying Phenotypic Traits"

Another of my papers just came out in final form, and in fact it appears consecutively with another of my papers. It too has been available for quite a while in the journal, but we finally have our coordinates (page numbers, etc.).

Along with this paper, we have released a large data set of fungal networks. We hope that you enjoy playing with the data!

Here are some more details.

Title: "Mesoscale Analyses of Fungal Networks as an Approach for Quantifying Phenotypic Traits"

Authors: Sang Hoon Lee, Mark D. Fricker, and Mason A. Porter

Abstract: We investigate the application of mesoscopic response functions (MRFs) to characterize a large set of networks of fungi and slime moulds grown under a wide variety of different experimental treatments, including inter-species competition and attack by fungivores. We construct 'structural networks' by estimating cord conductances (which yield edge weights) from the experimental data, and we construct 'functional networks' by calculating edge weights based on how much nutrient traffic is predicted to occur along each edge. Both types of networks have the same topology, and we compute MRFs for both families of networks to illustrate two different ways of constructing taxonomies to group the networks into clusters of related fungi and slime moulds. Although both network taxonomies generate intuitively sensible groupings of networks across species, treatments and laboratories, we find that clustering using the functional-network measure appears to give groups with lower intra-group variation in species or treatments. We argue that MRFs provide a useful quantitative analysis of network behaviour that can (1) help summarize an expanding set of increasingly complex biological networks and (2) help extract information that captures subtle changes in intra- and inter-specific phenotypic traits that are integral to a mechanistic understanding of fungal behaviour and ecology. As an accompaniment to our paper, we also make a large data set of fungal networks available in the public domain.

Tales from the ArXiv: A "Topological Middle Class"

This new arXiv paper, by Dani Bassett and company, has a lovely turn of phrase, a "topological middle class", which twist on the classical term rich-club phenomenon. Previously, in this paper, my collaborators and I introduced the term "poor-club phenomenon" via a similar play on words.

"Detection of Core–Periphery Structure in Networks Using Spectral Methods and Geodesic Paths"

The special issue in European Journal of Applied Mathematics on "Network Analysis and Modelling" that I co-edited also includes a research paper that I coauthored. Here are some details about that paper.

Title: Detection of Core–Periphery Structure in Networks Using Spectral Methods and Geodesic Paths

Authors: Mihai Cucuringu, Puck Rombach, Sang Hoon Lee, and Mason A. Porter

Abstract: We introduce several novel and computationally efficient methods for detecting "core–periphery structure" in networks. Core–periphery structure is a type of mesoscale structure that consists of densely connected core vertices and sparsely connected peripheral vertices. Core vertices tend to be well-connected both among themselves and to peripheral vertices, which tend not to be well-connected to other vertices. Our first method, which is based on transportation in networks, aggregates information from many geodesic paths in a network and yields a score for each vertex that reflects the likelihood that that vertex is a core vertex. Our second method is based on a low-rank approximation of a network’s adjacency matrix, which we express as a perturbation of a tensor-product matrix. Our third approach uses the bottom eigenvector of the random-walk Laplacian to infer a coreness score and a classification into core and peripheral vertices. We also design an objective function to (1) help classify vertices into core or peripheral vertices and (2) provide a goodness-of-fit criterion for classifications into core versus peripheral vertices. To examine the performance of our methods, we apply our algorithms to both synthetically generated networks and a variety of networks constructed from real-world data sets.

What Happens in Lake Como Stays in Lake Como

Today I'm flying to Italy to participate in the second Lake Como School on Complex Networks. I'll be giving a tutorial on mesoscale structures in networks.