Date: Thursday, July 2nd (7/2), 2026
Time: 12:00-2:00pm ET
Location: Coda C1315 (Grant Park)
Zoom: https://gatech.zoom.us/j/95337401341?pwd=UA3HGBasOpWtv4JIanQFoBKtyovP9y.1
Benjamin Cobb
Computer Science Ph.D. Candidate
School of Computational Science and Engineering
Georgia Institute of Technology
Committee:
Dr. Richard W. Vuduc (co-advisor), CSE, Georgia Institute of Technology
Dr. Haesun Park (co-advisor), CSE, Georgia Institute of Technology
Dr. Edmond Chow, CSE, Georgia Institute of Technology
Dr. Grey M. Ballard, CS, Wake Forest University
Dr. Ramakrishnan Kannan, Discrete Algorithms, Oak Ridge National Laboratory
Abstract:
As our capacity to collect and generate data continues to outpace our capacity to store and analyze said data, low-rank tensor factorizations offer a solution to alleviate this issue for tensorized data. The process of computing low-rank tensor factorizations is computationally expensive and requires efficiently leveraging computational resources to enable feasibility. This thesis proposes several novel algorithms for low-rank tensor factorizations to enable interpretable analysis and compression of massive multiway datasets. To this end, we focus on three overarching themes: efficiently leveraging computational resources to compute large-scale tensor decompositions, efficiently enforcing nonnegativity constraints to improve interpretability, and incorporating additional information into the factorization to improve solution quality.
We start by proposing the Fused In-place Sequentially Truncated Higher Order Singular Value Decomposition (FIST-HOSVD) algorithm as the first in-place method for computing the dense Tucker decomposition, increasing the problem size that can be factorized by up to 3x. We demonstrate the effectiveness of the proposed FIST-HOSVD algorithm by decreasing the auxiliary memory consumption by over 135x when computing the dense Tucker decomposition on two combustion simulation compression applications. We then provide an in-depth study of several state-of-the-art methods for Nonnegative Matrix Factorization (NMF). As part of this, we provide a comprehensive survey of Nonnegative Least Squares (NNLS) solvers used to enforce the nonnegativity of the factors. In doing so, we propose a Fast Active-Set Thresholding NNLS (FAST-NNLS) solver which outperforms existing NNLS methods for broad classes of problems. We then introduce a GPU-accelerated Hierarchical NMF K-Means initialization method for large-scale protein clustering on commodity-grade hardware. We then propose the Low Rank Approximations with Constraints at Exascale (LORACX) framework for computing large-scale distributed NMF. We demonstrate that LORACX yields unprecedented performance and scalability by achieving 0.67 exaflops in double-precision on 8,192 nodes of the Frontier supercomputer when computing NMF of a 2.1 petabyte matrix. We then extend the NMF objective function to incorporate additional multiway data, culminating in a Joint Nonnegative Coupled Matrix-Tensor Factorization (Joint-NCMTF) framework. We demonstrate that the proposed Joint-NCMTF method yields improved clustering quality and additional dimensions of insight relative to traditional matrix-based methods.
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