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Non-negative matrix factorization (NMF) is a matrix decomposition problem with applications in unsupervised learning. The general form of this problem (along with many of its variants) is NP-hard in nature. In our work, we explore how this…

Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for understanding uncertainty and structure in matrix data. However, a large volume of applied work optimizes traditional non-Bayesian NMF objectives that fail to…

Machine Learning · Statistics 2018-03-19 M. Arjumand Masood , Finale Doshi-Velez

Traditional nonnegative matrix factorization (NMF) learns a new feature representation on the whole data space, which means treating all features equally. However, a subspace is often sufficient for accurate representation in practical…

Computer Vision and Pattern Recognition · Computer Science 2022-04-19 Junhang Li , Jiao Wei , Can Tong , Tingting Shen , Yuchen Liu , Chen Li , Shouliang Qi , Yudong Yao , Yueyang Teng

Generative AI models, such as score-based diffusion models, have recently advanced the field of computational materials science by enabling the generation of new materials with desired properties. In addition, these models could also be…

Materials Science · Physics 2026-01-06 Timo Reents , Arianna Cantarella , Marnik Bercx , Pietro Bonfà , Giovanni Pizzi

High-quality crystals without inversion symmetry are the conventional platform to achieve optical frequency conversion via three wave-mixing. In bulk crystals, efficient wave-mixing relies on phase-matching configurations, while at the…

We demonstrate how the mixed dynamic form factor (MDFF) can be interpreted as a quadratic form. This makes it possible to use matrix diagonalization methods to reduce the number of terms that need to be taken into account when calculating…

Materials Science · Physics 2017-02-16 Stefan Löffler , Viktoria Motsch , Peter Schattschneider

Ptychography is an imaging technique which involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the…

Numerical Analysis · Mathematics 2023-01-31 Mark Iwen , Michael Perlmutter , Mark Philip Roach

Materials property predictions have improved from advances in machine learning algorithms, delivering materials discoveries and novel insights through data-driven models of structure-property relationships. Nearly all available models rely…

Materials Science · Physics 2022-04-13 Yiqun Wang , Xiao-Jie Zhang , Fei Xia , Elsa A. Olivetti , Ram Seshadri , James M. Rondinelli

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more…

Machine Learning · Computer Science 2024-12-02 Koby Hayashi , Sinan G. Aksoy , Grey Ballard , Haesun Park

A suite of acquisition applications related to the 4D-STEM technique is presented as a software package written within the Digital Micrograph environment, which is a widely used software platform in worldwide electron microscopy…

Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between $-\pi$…

Plasma Physics · Physics 2022-10-20 Pierre-Alexandre Gourdain , Aidan Bachmann

Non-Negative Matrix Factorization (NMF) is a widely used dimension reduction method that factorizes a non-negative data matrix into two lower dimensional non-negative matrices: One is the basis or feature matrix which consists of the…

Applications · Statistics 2022-11-03 Yun Cai , Hong Gu , Toby Kenney

The displacement field in highly non uniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign…

Materials Science · Physics 2009-11-11 A. A. Minkevich , M. Gailhanou , J. -S. Micha , B. Charlet , V. Chamard , O. Thomas

The development of photonic integrated circuits would benefit from a wider selection of materials that can strongly-control near-infrared (NIR) light. Transition metal dichalcogenides (TMDs) have been explored extensively for visible…

Mesoscale and Nanoscale Physics · Physics 2019-10-18 Akshay Singh , Yifei Li , Balint Fodor , Laszlo Makai , Jian Zhou , Haowei Xu , Austin Akey , Ju Li , R. Jaramillo

Directed atomic fabrication using an aberration-corrected scanning transmission electron microscope (STEM) opens new pathways for atomic engineering of functional materials. In this approach, the electron beam is used to actively alter the…

We present a pipeline for geomorphological analysis that uses structure from motion (SfM) and deep learning on close-range aerial imagery to estimate spatial distributions of rock traits (size, roundness, and orientation) along a tectonic…

Recent advances in materials discovery have been driven by structure-based models, particularly those using crystal graphs. While effective for computational datasets, these models are impractical for real-world applications where atomic…

Machine Learning · Computer Science 2025-07-03 Jithendaraa Subramanian , Linda Hung , Daniel Schweigert , Santosh Suram , Weike Ye

Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the original NTF methods…

Machine Learning · Computer Science 2024-01-04 Jianyu Wang , Linruize Tang

Coherent Diffractive Imaging is a lensless technique that allows imaging of matter at a spatial resolution not limited by lens aberrations. This technique exploits the measured diffraction pattern of a coherent beam scattered by periodic…

Computational Physics · Physics 2025-08-27 Alessandro Colombo , Davide Emilio Galli , Liberato De Caro , Francesco Scattarella , Elvio Carlino

Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…

Numerical Analysis · Computer Science 2017-12-07 Gabriele Torre , Michael Graber
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