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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Exploring the Landscape of Distributed Graph Clustering on Leadership Supercomputers

The rapid growth of large-scale datasets in fields like biology and social networks has driven the need for advanced graph analytics techniques. Community detection, a fundamental task in graph analytics, identifies closely connected groups of nodes within a network, providing valuable insights across various disciplines. This study focuses on two classic community detection methods, the Louvain algorithm and Markov Clustering (MCL), and evaluates the performance of two prominent distributed community detection algorithms: HiPDPL-GPU, our prior implementation, and HipMCL. We conduct experiments on GPU-accelerated heterogeneous HPC systems, Summit and Frontier, to assess their performance under varying conditions. Our objective is to identify the strengths and weaknesses of these algorithms in terms of scalability, and quality of solutions. We evaluate these algorithms on a diverse set of 70+ networks spanning 13 domains, with sizes ranging up to 4.2 billion edges. Our results demonstrate that HiPDPL-GPU consistently outperforms HipMCL, especially for large-scale networks. HiPDPL-GPU achieves significantly faster runtimes (47x to 1439x), higher modularity scores, and improved scalability. These findings highlight HiPDPL-GPU as a promising solution for efficient and effective large-scale graph analytics in diverse application domains, and provide insights into the feasibility of using MCL-based approaches for certain application domains.

Community detection, graph algorithms↗
DOE OSTI2016

Multilayer spectral graph clustering via convex layer aggregation

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theoretical framework for multilayer spectral graph clustering of the nodes via convex layer aggregation. Under a novel multilayer signal plus noise model, we provide a phase transition analysis that establishes the existence of a critical value on the noise level that permits reliable cluster separation. The analysis also specifies analytical upper and lower bounds on the critical value, where the bounds become exact when the clusters have identical sizes. Numerical experiments on synthetic multilayer graphs are conducted to validate the phase transition analysis and study the effect of layer weights and noise levels on clustering reliability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Scaling and Quality of Modularity Optimization Methods for Graph Clustering

Real-world graphs exhibit structures known as “communities” or “clusters” consisting of a group of vertices with relatively high connectivity between them, as compared to the rest of the vertices in the network. Graph clustering or community detection is a fundamental graph operation used to analyze real-world graphs occurring in the areas of computational biology, cybersecurity, electrical grids, etc. Similar to other graph algorithms, owing to irregular memory accesses and inherently sequential nature, current algorithms for community detection are challenging to parallelize. However, in order to analyze large networks, it is important to develop scalable parallel implementations of graph clustering that are capable of exploiting the architectural features of modern supercomputers. In response to the 2019 Streaming Graph Challenge, we present quality and performance analysis of our distributed- memory community detection using Vite, which is our distributed memory implementation of the popular Louvain method, on the ALCF Theta supercomputer. Clustering methods such as Louvain that rely on modularity maximization are known to suffer from the resolution limit problem, preventing identification of clusters of certain sizes. Hence, we also include quality analysis of our shared-memory implementation of the Fast-tracking Resistance method, in comparison with Louvain on the challenge datasets. Furthermore, we introduce an edge-balanced graph distribution for our distributed memory implementation, that significantly reduces communication, offering up to 80% improvement in the overall execution time. In addition to performance/quality analysis, we also include details on the power/energy consumption, and memory traffic of the distributed-memory clustering implementation using real-world graphs with over a billion edges.

Ghosh, Sayan↗
DOE OSTI2024

Identifying Sample Provenance From SEM/EDS Automated Particle Analysis via Few-Shot Learning Coupled With Similarity Graph Clustering

Automated particle analysis (APA) provides a vast amount of compositional data via energy-dispersive X-ray spectroscopy along with size and shape data via scanning electron microscopy for individual particles in a sample. In many instances, APA data are leveraged to support identification of the source of a sample based on the detection of particles of a specific composition. Often, the particles that provide context make up a minuscule portion of the sample. Additionally, the interpretation of complex samples can be difficult due to the diversity of compositions both in the mixture and within a particle. In this work, we demonstrate a method to compute and cluster similarity graphs that describe inter-particle relationships within a sample using a multi-modal few-shot learning neural network. Here, as a proof-of-concept, we show that samples known to have been exposed to gunshot residue can be distinguished from samples occasionally mistaken for gunshot residue. Our workflow builds upon standard APA techniques and data processing methods to unveil additional information in a readily interpretable and quantitatively comparable format.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Phase Transitions and a Model Order Selection Criterion for Spectral Graph Clustering

One of the longstanding open problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. Here, we propose automated model order selection (AMOS), a solution to the SGC model selection problem under a random interconnection model (RIM) using a novel selection criterion that is based on an asymptotic phase transition analysis. AMOS can more generally be applied to discovering hidden block diagonal structure in symmetric non-negative matrices. Numerical experiments on simulated graphs validate the phase transition analysis, and real-world network data is used to validate the performance of the proposed model selection procedure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Hyperspectral Image Classification Using Graph Clustering Methods

Hyperspectral imagery is a challenging modality due to the dimension of the pixels which can range from hundreds to over a thousand frequencies depending on the sensor. Most methods in the literature reduce the dimension of the data using a method such as principal component analysis, however this procedure can lose information. More recently methods have been developed to address classification of large datasets in high dimensions. This paper presents two classes of graph-based classification methods for hyperspectral imagery. Using the full dimensionality of the data, we consider a similarity graph based on pairwise comparisons of pixels. The graph is segmented using a pseudospectral algorithm for graph clustering that requires information about the eigenfunctions of the graph Laplacian but does not require computation of the full graph. We develop a parallel version of the Nyström extension method to randomly sample the graph to construct a low rank approximation of the graph Laplacian. With at most a few hundred eigenfunctions, we can implement the clustering method designed to solve a variational problem for a graph-cut-based semi-supervised or unsupervised classification problem. We implement OpenMP directive-based parallelism in our algorithms and show performance improvement and strong, almost ideal, scaling behavior. The method can handle very large datasets including a video sequence with over a million pixels, and the problem of segmenting a data set into a pre-determined number of classes.

47 OTHER INSTRUMENTATION↗
DOE OSTI2018

Simulated Half-Precision Implementation of Blocked QR Factorization and Graph Clustering Applications

We explored half-precision implementation of blocked QR algorithms with the following motivations: 1. New GPUs perform fast half-precision arithmetic (4 to 16 times as fast as doubleprecision). 2. QR factorization is a basic linear algebra tool useful for many physics and data analysis applications. 3. Communication-avoiding, parallelizable QR algorithms already exist for talland- skinny matrices. While the standard QR algorithms are highly unstable in half-precision, our numerical simulations show that the Tall-and-Skinny QR (TSQR) algorithm can improve the backward error of QR factorization. When using subspace iteration for graph clustering applications, half-precision accuracy in forming the eigenspace is sufficient for clustering with high precision and recall for some medium-scale benchmark problems. Note that all half-precision arithmetic were simulated with conversions to single-precision floats. Therefore, the results from this work are somewhat optimistic.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A Clustering Graph Generator

In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Leveraging graph clustering techniques for cyber‐physical system analysis to enhance disturbance characterisation

Abstract Cyber‐physical systems have behaviour that crosses domain boundaries during events such as planned operational changes and malicious disturbances. Traditionally, the cyber and physical systems are monitored separately and use very different toolsets and analysis paradigms. The security and privacy of these cyber‐physical systems requires improved understanding of the combined cyber‐physical system behaviour and methods for holistic analysis. Therefore, the authors propose leveraging clustering techniques on cyber‐physical data from smart grid systems to analyse differences and similarities in behaviour during cyber‐, physical‐, and cyber‐physical disturbances. Since clustering methods are commonly used in data science to examine statistical similarities in order to sort large datasets, these algorithms can assist in identifying useful relationships in cyber‐physical systems. Through this analysis, deeper insights can be shared with decision‐makers on what cyber and physical components are strongly or weakly linked, what cyber‐physical pathways are most traversed, and the criticality of certain cyber‐physical nodes or edges. This paper presents several types of clustering methods for cyber‐physical graphs of smart grid systems and their application in assessing different types of disturbances for informing cyber‐physical situational awareness. The collection of these clustering techniques provide a foundational basis for cyber‐physical graph interdependency analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Cluster-Graph Fingerprinting: A Framework for Quantitative Analysis of Machine-Learned Interatomic Model Training and Simulation Data

Machine-learned interatomic models represent a significant advancement in simulation methods, extending the predictive ability of first-principles methods to previously inaccessible length and time scales. However, the data-driven nature of these models can lead to difficult-to-detect errors that can compromise prediction accuracy. To address this challenge, we introduce a novel fingerprinting approach based on the Chebyshev Interaction Model for Efficient Simulation (ChIMES) ML-IAM graph-based descriptor. Our strategy enables efficient and statistically rigorous analysis of system configurations used in ML-IAM training and those generated by their application, e.g., in molecular dynamics simulations. We demonstrate that these fingerprints can effectively assess novelty of a configuration relative to an existing data set and determine dissimilarity among individual configurations, which are two key tasks in workflows for active learning-based ML-IAM training, data set curation, and on-the-fly uncertainty quantification.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Skew-Symmetric adjacency matrices for clustering directed graphs

Graph clustering methods often critically rely on the symmetry of graph matrices. Developing analogous methods for digraphs often proves more challenging, because digraph matrices are typically asymmetric and not orthogonally diagonalizable. However, researchers have recently proposed several complex-valued Hermitian digraph matrices. In particular, one such representation has been utilized as an input to an algorithm for finding imbalanced cuts. In this work, we establish an algebraic relationship between this matrix and an associated real-valued matrix. We show using this real-valued matrix for imbalanced cut-finding algorithms is not only sufficient but advantageous. Our algorithm uses less memory and asymptotically less computation while provably preserving solution quality. We also show our method can be easily implemented using standing computational building blocks, possesses better numerical properties, and loans itself to a natural interpretation via an objective function relaxation argument. We empirically demonstrate these advantages on real world data sets and show how our algorithm can uncover meaningful cluster structure.

Hayashi, Koby↗
DOE OSTI2019

Bootstrap AMG for spectral clustering

Graph Laplacian is a popular tool for analyzing graphs, particularly in graph partitioning and clustering. Given a notion of similarity (via an adjacency matrix), graph clustering refers to identifying different groups such that vertices in the same group are more similar compared to vertices across different groups. Data clustering can be reformulated in terms of a graph clustering problem when the given set of data is represented as a graph, also known as similarity graph. In this context, eigenvectors of the graph Laplacian are often used to obtain a new geometric representation of the original data set that generally enhances cluster properties and improves cluster detection. Here, we apply a bootstrap algebraic multigrid (AMG) method that constructs a set of vectors associated with the graph Laplacian. These vectors, referred to as algebraically smooth ones, span a low-dimensional Euclidean space, which we use to represent the data, enabling cluster detection both in synthetic and in realistic well-clustered graphs. We show that, in the case of a good quality bootstrap AMG, the computed smooth vectors employed in the construction of the final AMG operator, which by construction is spectrally equivalent to the originally given graph Laplacian, accurately approximate the space in the lower portion of the spectrum of the preconditioned operator. Thus, our approach can be viewed as a spectral clustering technique associated with the generalized spectral problem (Laplace operator versus the final AMG operator), and hence, it can be seen as an extension of the classical spectral clustering that employs a standard eigenvalue problem.

97 MATHEMATICS AND COMPUTING↗