[Literature Review] Hypergraphs & Topological Data Analysis for Biomedical Research

This is an experiment. Comments and feedback are welcome.

Scientists produce a variety of literature reviews throughout the course of their work. The content and shape of those literature reviews are determined by their research needs and personal interests. Literature reviews are a valuable intellectual good that we currently share only in the form of review papers, which represent enormous efforts and do not surface actionable project details or note which studies have been replicated and which have not. I think we could publish more rough notes and compare them--the key is to reduce the curator's cost in sharing. This is an experiment in publishing the bare bones of a literature review I did last winter following my curiosity about the potential use of hyper networks and topological data analysis in single cell RNA sequencing data. Below is a Table of Contents linking to each paper included in this review, where I have used the Conversation tab to post my Obsidian .md notes for most papers. Note that the formatting of these .md notes will need some clean-up if you want to grab it.

It should be noted that this literature review did not result in any actionable changes to my research or plans for it, but it was very interesting reading and it reinforces that--at a sufficiently high dimensionality of data--count data can be represented in a variety of formats to learn different features: sparse matrix, simplicial complex, spectrum, or network with different tradeoffs inherent to each. It should be noted that matrix- and network-based techniques are the most widely-used and best-described, although other tools, such as the Singh Mapper algorithm (PDF link), are seeing more use as the volume of single cell data grows.

High-Level Background: This quick literature review covers hypernetworks and topological data analysis. Hypernetworks sound complicated and scary but they're not. A hyper network is just a standard graph but with a key addition: edges are no longer restricted to connecting just 2 nodes but can instead connect multiple nodes, connect to other edges, or represent other higher-order structures. Topological data analysis borrows from algebraic topology to model various kinds of complex data as collections of sets and surfaces upon which various operations can reveal underlying structure, the persistence of that structure, or abrupt changes in how the structure is generated.

Disclaimer: The following literature review is not exhaustive and each note attached varies in depth--some are just abstracts, some are in depth. I don't regard this literature review as comprehensive enough to base a project or review paper on.

2016 Bassett - Simplex Primer: This is a great introduction to simplicial complexes with key terms and perspectives although it quickly pivots into neuroscience-specific applications.
2019 Artyomov - Deconvolution of Cell Mixtures Based on Linearity of Signatures: This is an interesting mutual linearity detection technique using topological data analysis but, unfortunately, the tool's Github repo appears to be dead.
2019 Ritz - Hypergraph Connectivity for Pathway Topology: This work nicely reviews different types of graphs to introduce a new technique for finding robust hypergraph edges.
2021 Fetaya - Learning Pareto Fronts with Hypernetworks: This pre-print applies the idea of Pareto fronts in multi-objective optimization problems as introduced by Breiman & Cutler in 1994 to a machine learning approach using hyper networks. Note: I did not follow this reference up to see if it had been published beyond this pre-print.
2021 Jin - Evolutionary Algorithms in Irregular Pareto Fronts: This is a brief math- and ML-focused review of different multi-objective optimization approaches for dealing with discontinuous transitions in data.
2021 McDermott Purine - Hypergraph Models for Viral Response: This is really cool work out of Pacific Northwest National Labs that introduces a relatively straightforward way to learn hyper networks from data--scanning across the connectivity threshold to identify hyper edges with persistence across thresholds (will remind you of a simplicial filtration for persistent homology if you're familiar)--and a measure of hyper network centrality that can be used to start studying the structure of hyper networks. They apply this to viral response genes with interesting recapitulation of known biology.
2022 Adler Medzhitov - Network Hypermotifs: This is a cool review of feedback circuits and their combinations in biological functions. To be quite honest I downloaded it because of the word “hyper motifs” and because it's from Dr. Medzhitov but it turned out to not involve hyper networks or topological data analysis. It's still interesting and a great introduction to combining dynamic circuits for getting complex emergent patterns of metastability and logic gates.
2022 Bacco - Hyperedge & Community Inference in Hypergraphs: This paper introduces a new method for the detection of hyper edges, which is important in this field as we don't yet have many comparative methods to use. This doesn't include application to any sc-level biological data but does explore several example datasets, although it's worth noting that how this works will be heavily affected by how you count relatedness in the network you're studying. Notably the Github repo is still active.
2022 Battiston - Higher-Order Hypergraph Motifs: This paper introduces a new method for the detection of order-3 and -4 “hyper motifs”, or recurring patterns in hyper networks. Github repo appears to be at rest.
2022 Lefevre - Hypergraphs & Centrality in Gene Expression Data: This is a great introduction to hypergraphs and a showcase of how to apply various aspects of hypergraph construction and interpretation to differential gene expression analysis.
2022 Lin - sc Topological Simplicial Analysis: This is a cool demonstration of how to apply simplicial filtration to single cell gene expression data, but is also very dense. The Github repo appears to be dormant and the tool is not set up for other users to pull and apply unless you're ready to understand all of the simplicial complex construction terms.
2022 Sandhu - Hypergraph Geometry Mirrors PPI Dynamics: This reference blends hypergraphs and topological data analysis to construct hyper networks in 2D simplicial complexes. Note the reliance on network curvature to identify biologically interesting results--this speaks to the earliness of these techniques. I'm not sure I'd call the results presented here “dynamics” as they don't appear to have a measure of time-dependence or order, but the identification of higher-order hypernetwork motifs across datasets is interesting on its own.
2023 Lio - Hypergraph Factorization for Multi-Tissue Gene Expression: This is such a cool idea: to use hypergraphs as a way to predict expression profiles but I thought that the eQTL focus was potentially misplaced--identifying cross-tissue predictions may be higher-impact in terms of guiding study resources. However it does show that hypergraphs are well-suited for various ML approaches and I'm looking forward to seeing how this area develops.
2023 Nitzan - scPrisma Topological Spectral: What I like about this paper is that it really demonstrates the relationship between topological structure and spectral properties, showing that one can apply various spectral analysis techniques to find conserved topological structures. However the reliance on imputed pseudo time is a bit tricky and I was left wondering about the implicit bias of choosing which topology to focus on (linear, circular) instead of doing a persistent homology filtration to identify which topological features could be fit to their spectral analysis methods. Active Github repo.

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[Literature Review] Hypergraphs & Topological Data Analysis for Biomedical Research