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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Hypergraph Models of Biological Networks to Identify Genes Critical to Pathogenic Viral Response

Motivation: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way relationships present among genes and proteins in biological systems such as protein complexes, metabolic reactions, and signal transduction pathways. Hypergraphs are generalizations of graphs that naturally model multi-way interactions in data, and we therefore seek to understand how they can more faithfully identify, and potentially predict, complex relationships in genomic expression data sets. Results: We compiled a novel data set of transcriptional host response to pathogenic viral infections and formulated relationships between genes as a hypergraph where hyperedges are differentially expressed genes and vertices represent conditions. We find that hypergraph betweenness centrality is a superior method for identification of genes important to viral response when compared with graph centrality. Our results demonstrate the utility of using hypergraphs to represent complex biological systems, and highlight potentially interesting biological results about host response to highly pathogenic viruses.

systems biology, hypergraph, viral infection, biol↗
DOE OSTI2020

A Scalable Parallel Hypergraph Generator (HyGen)

Graphs are extensively used to model real-world complex systems. An edge in a graph can model pairwise relationships. However, multiway relationships (connections between three or more vertices) are common in many complex systems such as cellular process, image segmentation, and circuit design. A graph edge cannot model multiway relationships. A hypergraph, which can connect more than two vertices, is thus a better option to model multiway relationships. A large-scale hypergraph analysis has the potential to find useful insights from a complex system and assist in knowledge discovery. Currently a limited number of hypergraphs exists that are representative of real-world datasets. Moreover, real-world hypergraph datasets are small in size and inadequate to incorporate future needs. A graph generator that can produce large-scale synthetic hypergraphs can solve the above mentioned problems. In this paper, we present a scalable parallel hypergraph generator (HyGen) based on the Message Passing Interface (MPI) standard. To generate hypergraphs, HyGen takes the following parameter values as inputs: i) number of vertices, ii) number of hyperedges, iii) number of clusters, iv) vertex distribution, v) hyperedge distribution, vi) local cluster cardinality, and vii) global cluster cardinality. We have demonstrated that HyGen can generate hypergraphs of various sizes in a scalable fashion. HyGen takes approximately four minutes to generate a hypergraph with 4.8 million vertices, 1.6 million hyperedges, and 800 clusters using 1,024 processes on a leadership class computing platform. Our strong and weak scaling experiments on supercomputers demonstrate that HyGen can quickly create large-scale hypergraphs in a parallel manner, thus providing a useful capability for hypergraph analysis.

Hasan, S M Shamimul↗
DOE OSTI2023

Topological Analysis of Temporal Hypergraphs

In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of network science. A common use of hypergraphs is to model events as hyperedges in which the event can involve many elements as nodes. This provides a more complete picture of the event in comparison to the standard dyadic connection limitation of a graph. However, a common attribution to events is temporal information as an interval for when the event occurred. Consequently, a temporal hypergraph is born which accurately captures both the temporal information of events as well as their multi-way connections. Common tools for studying these temporal hypergraphs typically use summary statistics of snapshots from a sliding window procedure to capture changes in the underlying dynamics. However, these do not provide insight into how the changing structure of the hypergraph evolves and which components of the temporal hypergraph persist and are influential to the underlying system. To alleviate this need we leverage zigzag persistence from the field of Topological Data Analysis (TDA) to study the change in topological structure of time-evolving hypergraphs. We apply our pipeline to both a cyber security and social network dataset and show how the topological structure of their temporal hypergraphs change and can be used to understand the underlying dynamics.

hypergraphs, topological data analysis, zigzag per↗
DOE OSTI2020

Hypernetwork science via high-order hypergraph walks

We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).

hypergraph algorithms, graph algorithms, parallel ↗
DOE OSTI2019

Modeling Complex Relationships in Large-Scale Data using Hypergraphs (LDRD Final Report)

This SAND report documents the findings of the LDRD project, "Modeling Complex Relationships in Large-Scale Data using Hypergraphs". The project ran from October 2017 through September 2019. The focus of the project was the development and application of hypergraph data analytics to Sandia relational data applications. In this project, we attempted to apply a hypergraph data analysis method—specifically, hypergraph eigenvector centrality—to Sandia mission problems to identify influential entities (people, location, times, etc.) in the data. Unfortunately, the application data led to graph and hypergraph representations containing disconnected components. To date, there are no well-established techniques for applying eigenvector centrality to such graphs and hypergraphs. In this report, we present several heuristics for computing eigenvector centrality for disconnected graphs. We believe this is an important start to understanding how to approach the similar problem for hypergraphs, but this project concluded before we made progress on that problem. The ideas, methods, and suggestions presented here can be used for further research into this challenging problem. We also present our ideas for generating graphs with known degree and centrality distributions. The goal in presenting this work is to identify a procedure for analyzing such graphs once the problem of addressing disconnected components has been addressed. When working with a single data set, this generator can be used to create many instances of graphs that can be used to analyze the robustness of the centrality computations for the original data set. Although the results did not match perfectly in the case of the Facebook Ego dataset used in the experiments presented here, this again represents a good start in the direction of a graph generator for such problems. We note that there are potential trade-offs between how the degree and centrality distributions are fit to the original data and suggested several possible avenues for follow-on research efforts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Hypergraph Analytics of Domain Name System Relationships

We report on the use of novel mathematical methods in hypergraph analytice over a large quantity of DNS data. Hypergraphs generalize graphs, as used in network science, to better model complex multiway relations in cyber data. Specifically, casting DNS data from Georgia Tech's ActiveDNS repository as hypergraphs allows us to fully represent the interactions between {\em collections} of domains and IP addresses. To facilitate large-scale analytics, we fielded an analytical pipeline of two capabilities. HyperNetX (HNX) is a Python package for the exploration and visualization of hypergraphs, acting as a frontend. For the backend, the Chapel HyperGraph Library (CHGL) is a library for high performance hypergraph analytics written in the exascale programming language Chapel. CHGL was used to process gigascale DNS data, performing compute-intensive calculations for data reduction and segmentation. Identified portions are then sent to HNX for both exploratory analysis and knowledge discovery targeting known tactics, techniques, and procedures.

Joslyn, Cliff A.↗
DOE OSTI2022

Topological Simplifications of Hypergraphs

Here we study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph into its graph representations, known as the line graph and clique expansion. A topological simplification of such a graph representation induces a simplification of the hypergraph. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Our proposed approaches are general and mathematically justifiable, and put vertex simplification and hyperedge simplification in a unifying framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Community detection in hypergraphs via mutual information maximization

Abstract The hypergraph community detection problem seeks to identify groups of related vertices in hypergraph data. We propose an information-theoretic hypergraph community detection algorithm which compresses the observed data in terms of community labels and community-edge intersections. This algorithm can also be viewed as maximum-likelihood inference in a degree-corrected microcanonical stochastic blockmodel. We perform the compression/inference step via simulated annealing. Unlike several recent algorithms based on canonical models, our microcanonical algorithm does not require inference of statistical parameters such as vertex degrees or pairwise group connection rates. Through synthetic experiments, we find that our algorithm succeeds down to recently-conjectured thresholds for sparse random hypergraphs. We also find competitive performance in cluster recovery tasks on several hypergraph data sets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Visual Analytics of Heterogeneous Data Using Hypergraph Learning

For real-world learning tasks (e.g., classification), graph-based models are commonly used to fuse the information distributed in diverse data sources, which can be heterogeneous, redundant, and incomplete. Thesemodels represent the relations in different datasets as pairwise links. However, these links cannot deal with high-order relations which connect multiple objects (e.g., in public health datasets, more than two patient groups admitted by the same hospital in 2014). In this article, we propose a visual analytics approach forthe classification on heterogeneous datasets using the hypergraph model. The hypergraph is an extension to traditional graphs in which a hyperedge connects multiple vertices instead of just two. We model various high-order relations in heterogeneous datasets as hyperedges and fuse different datasets with a unified hypergraph structure. We use the hypergraph learning algorithm for predicting missing labels in the datasets.To allow users to inject their domain knowledge into the model-learning process, we augment the traditional learning algorithm in a number of ways. In addition, we also propose a set of visualizations which enable the user to construct the hypergraph structure and the parameters of the learning model interactively during the analysis. Here, we demonstrate the capability of our approach via two real-world cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Hypergraph Random Walks, Laplacians, and Clustering

We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-dependent vertex weights (EDVW), a weight is associated with each vertex-hyperedge pair, yielding a weighted incidence matrix of the hypergraph. Such weightings have been utilized in term-document representations of text data sets. We explain how random walks with EDVW serve to construct different hypergraph Laplacian matrices, and then develop a suite of clustering methods that use these incidence matrices and Laplacians for hypergraph clustering. Using 20Newsgroup, U.S. patent, Reuters' Corpus Volume 1, and genetics data sets, we compare the performance of these clustering algorithms experimentally against a variety of existing hypergraph clustering methods. We show that the proposed methods produce higher-quality clusters.

hypergraphs, clustering, laplacian, random walk, M↗
DOE OSTI2021

Phoenix: A Scalable Streaming Hypergraph Analysis Framework

We present Phoenix, a scalable hypergraph analytics framework for data analytics and knowledge discovery that was implemented on the leadership class computing platforms at Oak Ridge National Laboratory (ORNL). Our software framework comprises a distributed implementation of a streaming server architecture which acts as a gateway for various hypergraph generators/external sources to connect. Phoenix has the capability to utilize diverse hypergraph generators, including HyGen, a very large-scale hypergraph generator developed by ORNL. Phoenix incorporates specific algorithms for efficient data representation by exploiting hidden structures of the hypergraphs. Our experimental results demonstrate Phoenix’s scalable and stable performance on massively parallel computing platforms. Phoenix’s superior performance is due to the merging of high-performance computing with data analytic.

Kurte, Kuldeep↗
DOE OSTI2020

The quantum entropy cone of hypergraphs

In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone. This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs. In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks. We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy. We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction. To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

The connection between the chromatic numbers of a hypergraph and its 1-intersection graph

A well known problem from an excellent book of Lovász states that any hypergraph with the property that no pair of hyperedges intersect in exactly one vertex can be properly 2-colored. Motivated by this as well as recent works of Keszegh and of Gyárfás et al. we study the 1-intersection graph of a hypergraph. The 1-intersection graph encodes those pairs of hyperedges in a hypergraph that intersect in exactly one vertex. We prove for k ϵ {2, 4} that all hypergraphs whose 1-intersection graph is k-partite can be properly k-colored.

1-intersection graph of hypergraphs↗
DOE OSTI2024

Scalable Tensor Methods for Nonuniform Hypergraphs

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is applicable to nonuniform hypergraphs, but is prohibitively costly to form and analyze in practice. We develop tensor times same vector (TTSV) algorithms for this tensor which improve complexity from $O(n^r)$ to a low-degree polynomial in $r$, where $n$ is the number of vertices and $r$ is the maximum hyperedge size. Our algorithms are implicit, avoiding formation of the order $r$ adjacency tensor. Here, we demonstrate the flexibility and utility of our approach in practice by developing tensor-based hypergraph centrality and clustering algorithms. We also show these tensor measures offer complementary information to analogous graph-reduction approaches on data, and are also able to detect higher-order structure that many existing matrix-based approaches provably cannot.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast Parallel Tensor Times Same Vector for Hypergraphs

Hypergraphs are a popular paradigm to rep- resent complex real-world networks exhibiting multi-way relationships of varying sizes. Mining centrality in hyper- graphs via symmetric adjacency tensors has only recently become computationally feasible for large and complex datasets. To enable scalable computation of these and related hypergraph analytics, here we focus on the Sparse Symmetric Tensor Times Same Vector (S3TTVC) oper- ation. We introduce the Compound Compressed Sparse Symmetric (CCSS) format, an extension of the compact CSS format for hypergraphs of varying hyperedge sizes and present a shared-memory parallel algorithm to compute S3TTVC. We experimentally show S3TTVC computation using the CCSS format achieves better performance than the naive baseline, and is subsequently more performant for hypergraph H-eigenvector centrality.

Shivakumar, Shruti↗
DOE OSTI2018

Chapel HyperGraph Library (CHGL)

We present the Chapel Hpergraph Library (CHGL), a library for hypergraph computation in the emerging Chapel language. Hypergraphs generalize graphs, where a hypergraph edge can connect any number of vertices. Thus, hypergraphs capture high-order, high-dimensional interactions between mulitple entities that are not directly expressible in graphs. CHGL is designed to provide HPC-class computation with high-level abstractions and modern language support for parallel comptuing on shared memory and distributed memory systems.

Jenkins, Louis P.↗