Trends in Combinatorial Analysis: Complex Data, Machine Learning, and High-Performance Computing
Résumé
Discrete algorithms and combinatorial analysis were well represented at the 2019 SIAM Conference on Computational Science and Engineering (CSE19), which took place earlier this year in Spokane, Wash. Over 15 talks-dispersed among five minisymposia-covered topics ranging from graph algorithms and machine learning to scientific computing. Like many other communities in applied mathematics and computational science, the SIAM Activity Group on Applied and Computational Discrete Algorithms (SIAG/ACDA)-founded this spring-is innovating techniques to learn from large-scale combinatorial data. Challenges that accompany learning from data include increasing data volumes and complexity, the need for novel algorithms, and efficient employment of high-performance computing resources. Researchers at CSE19 presented ongoing work that addressed these challenges and captured the following four trends. Scientific Data and Combinatorial Representation Several presenters spoke about combinatorial models they have developed to represent scientific datasets, and algorithms they have designed for efficient solution of the aforementioned problems. Possible application areas include astrophysics, biology, agriculture, and neuroscience. In some cases, researchers used complex networks to model the data. For example, Ariful Azad (Indiana University Bloomington) utilized correlated brain segments, as measured by functional magnetic resonance imaging (fMRI), to create a brain connectivity network. Ananth Kalyanaraman (Washington State University) analyzed agricultural phenomics data via persistent homology techniques. And Francesca Arrigo (University of Strathclyde) modeled complex datasets as multilayer networks, where different layers of each network capture various features or modalities. Overall, members of SIAG/ACDA are actively finding innovative ways to model increasingly complex scientific and business datasets. Algorithmic Innovation After representing data with a sound mathematical model, the next step often involves developing algorithms to solve problems of scientific interest. New scientific and business challenges lead to the creation of novel, efficient algorithms in the SIAG/ACDA community. For example, Arrigo also discussed an eigenvector-based centrality measure in multilayer networks capable of calculating centrality in a network with several different types of interactions among various entities. Syed M. Ferdous (Purdue University) described the design of parallel approximation algorithms for computing edge covers using the primal dual linear programming framework, with applications to semi-supervised classification.
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