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DOE OSTI2025

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗

DOE OSTI2025

Dynamical Sketching for Enhanced Communication Efficiency in Federated Learning

Federated learning (FL) has revolutionized distributed machine learning by enabling collaborative model training without sharing local data. However, communication efficiency and privacy guarantees remain significant challenges. This paper introduces a dynamic sketching mechanism in FL, optimizing the trade-off between communication efficiency and model accuracy. By dynamically selecting the sketch matrix size, our approach adapts to the evolving characteristics of the data and the model, ensuring optimal performance across diverse scenarios. We leverage Bayesian optimization to systematically tune the sketch parameters, achieving an effective balance between resource efficiency and model performance. Experimental results on the MNIST dataset using a convolutional neural network (CNN) architecture validate the proposed method's efficiency and scalability. Our dynamic sketching approach significantly outperforms fixed-size sketching techniques, achieving higher compression ratios (up to 62x) and providing better privacy guarantees while maintaining high model accuracy. These findings highlight the robustness and versatility of our approach and make it a valuable solution for privacy-preserving, communication-efficient federated learning.

Afrose, Sharmin [ORNL]↗

DOE OSTI2026

Augmenting subspace optimization methods with linear bandits

In this work, we consider the framework of methods for unconstrained minimization that are, in each iteration, restricted to a model that is only a valid approximation to the objective function on some affine subspace containing an incumbent point. These methods are of practical interest in computational settings where derivative information is either expensive or impossible to obtain. Recent attention has been paid in the literature to employing randomized matrix sketching for generating the affine subspaces within this framework. We consider a relatively straightforward, deterministic augmentation of such a generic subspace optimization method. In particular, we consider a sequential optimization framework where actions consist of one-dimensional linear subspaces and rewards consist of (approximations to) the magnitudes of directional derivatives computed in the direction of the action subspace. Reward maximization in this context is consistent with maximizing lower bounds on descent guaranteed by first-order Taylor models. This sequential optimization problem can be analysed through the lens of dynamic regret. We modify an existing linear upper confidence bound (UCB) bandit method and prove sublinear dynamic regret in the subspace optimization setting. We demonstrate the efficacy of employing this linear UCB method in a setting where forward-mode algorithmic differentiation can provide directional derivatives in arbitrary directions and in a derivative-free setting. For the derivative-free setting, we propose SS-POUNDers, an extension of the derivative-free optimization method POUNDers that employs the linear UCB mechanism to identify promising subspaces. Our numerical experiments suggest a preference, in either computational setting, for employing a linear UCB mechanism within a subspace optimization method.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2013

Peter Waterman and T-Matrix Methods

This paper summarizes the scientific legacy of Peter C. Waterman (1928-2012) who introduced concepts and theoretical techniques that have had a major impact on the fields of scattering by particles and particle groups, optical particletcharacterization, radiative transfer, and remote sensing. A biographical sketch is also included.

electromagnetic scattering↗

NASA NTRS1989

On polynomial preconditioning for indefinite Hermitian matrices

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Freund, Roland W.↗

NASA NTRS2005

Recent Advances in Radar Polarimetry and Polarimetric SAR Interferometry

The development of Radar Polarimetry and Radar Interferometry is advancing rapidly, and these novel radar technologies are revamping Synthetic Aperture Radar Imaging decisively. In this exposition the successive advancements are sketched; beginning with the fundamental formulations and high-lighting the salient points of these diverse remote sensing techniques. Whereas with radar polarimetry the textural fine-structure, target-orientation and shape, symmetries and material constituents can be recovered with considerable improvements above that of standard amplitude-only Polarization Radar ; with radar interferometry the spatial (in depth) structure can be explored. In Polarimetric-Interferometric Synthetic Aperture Radar (POL-IN-SAR) Imaging it is possible to recover such co-registered textural plus spatial properties simultaneously. This includes the extraction of Digital Elevation Maps (DEM) from either fully Polarimetric (scattering matrix) or Interferometric (dual antenna) SAR image data takes with the additional benefit of obtaining co-registered three-dimensional POL-IN-DEM information. Extra-Wide-Band POL-IN-SAR Imaging - when applied to Repeat-Pass Image Overlay Interferometry - provides differential background validation and measurement, stress assessment, and environmental stress-change monitoring capabilities with hitherto unattained accuracy, which are essential tools for improved global biomass estimation. More recently, by applying multiple parallel repeat-pass EWB-POL-D(RP)-IN-SAR imaging along stacked (altitudinal) or displaced (horizontal) flight-lines will result in Tomographic (Multi- Interferometric) Polarimetric SAR Stereo-Imaging , including foliage and ground penetrating capabilities. It is shown that the accelerated advancement of these modern EWB-POL-D(RP)-IN-SAR imaging techniques is of direct relevance and of paramount priority to wide-area dynamic homeland security surveillance and local-to-global environmental ground-truth measurement and validation, stress assessment, and stress-change monitoring of the terrestrial and planetary covers. In addition, various closely related topics of (i) acquiring additional and protecting existing spectral windows of the Natural Electromagnetic Spectrum (NES) pertinent to Remote Sensing; (ii) mitigating against common "Radio Frequency Interference (RFI)" and intentional Directive Jamming of Airborne & Space borne POL-IN-SAR Imaging Platforms are appraised.

Boerner, Wolfgang-Martin↗