1. Community Detection and Detectability in Multilayer Networks

Collaborators: Saray Shai, Dane Taylor, Peter Mucha

Multilayer networks refer to a collection of networks, where each ‘layer’ encodes one type of interaction. For example, a temporal network can be considered a multilayer network where each layer encodes a network at a particular time. In an effort to understand how community structure can be detected and understood in multilayer networks, we have developed strata multilayer stochastic block model, which is a stochastic block model for multilayer networks. Since community structure can be difficult to detect when networks are sparse, we explored limits of detectability in this model.

sMLSBM Code on github

2. Network Compression

Collaborators: Roland Kwitt, Marc Niethammer, Peter Mucha

Community detection becomes challenging in large networks. To facilitate these tasks, we are investigating effective ways to initially compress the network by combining individual nodes into ‘super nodes’ in a principled way. This approach is analogous to and inspired by superpixels  in the image segmentation literature, which aims to pre-process images before applying image segmentation.

3. Classification of the Urinary Metabolome 

Collaborators: Jeff Henderson, Lindsey Steinberg , Peter Mucha

We focus on how to profile and understand differences in the urinary metabolomes of different groups of patients.

4. Understanding Microbial Interactions in the Lung Microbiome

Collaborators: Dana Walsh

From metagenomic sequence data in a collection of burn patients with injury to the lungs/airways, we focus on how to study changes in the microbiome composition of certain subsets of patients. Specifically, we have been studying changes in species co-occurence and microbial interaction networks in groups of patients. 

5. Attributed Stochastic Block Model

Collaborators: (See #2)

We extend the stochastic block model to a setting where nodes have a vector of continuous attributes. To find communities, we use leverage both sources of information in the inference of the stochastic block model parameters. 

6. Longitudinal Network Analysis Applied to Brain Connectivity Data

Collaborators: (See #2,6)

I am applying a variety of machine learning techniques to understand similarities between brain connectivity networks across subjects and how they change over time.