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Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…

Optimization and Control · Mathematics 2025-01-10 Valentin Leplat , Yurii Nesterov , Nicolas Gillis , François Glineur

We introduce a Generalized Randomized QR-decomposition that may be applied to arbitrary products of matrices and their inverses, without needing to explicitly compute the products or inverses. This factorization is a critical part of a…

Numerical Analysis · Mathematics 2019-09-17 Grey Ballard , James Demmel , Ioana Dumitriu , Alexander Rusciano

Although quantum computing holds promise for solving Combinatorial Optimization Problems (COPs), the limited qubit capacity of NISQ hardware makes large-scale instances intractable. Conventional methods attempt to bridge this gap through…

Quantum Physics · Physics 2026-01-21 Yuhan Huang , Siyuan Jin , Yichi Zhang , Qi Zhao , Jun Qi , Qiming Shao

Neutral atoms have emerged as a promising technology for implementing quantum computers due to their scalability and long coherence times. However, the execution frequency of neutral atom quantum computers is constrained by image processing…

Quantum Physics · Physics 2024-11-21 Xiaorang Guo , Jonas Winklmann , Dirk Stober , Amr Elsharkawy , Martin Schulz

We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower…

Machine Learning · Computer Science 2011-12-19 Youngmin Cho , Lawrence K. Saul

In this paper, we propose a distributed framework for reducing the dimensionality of high-dimensional, large-scale, heterogeneous matrix-variate time series data using a factor model. The data are first partitioned column-wise (or row-wise)…

Machine Learning · Statistics 2026-01-19 Hangjin Jiang , Yuzhou Li , Zhaoxing Gao

Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for…

Machine Learning · Computer Science 2018-11-15 Zhihui Zhu , Xiao Li , Kai Liu , Qiuwei Li

Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing.…

Machine Learning · Statistics 2015-04-02 Nicolas Gillis , Stephen A. Vavasis

This paper investigates the efficacy of quantum computing in two distinct machine learning tasks: feature selection for credit risk assessment and image classification for handwritten digit recognition. For the first task, we address the…

Quantum Physics · Physics 2025-11-05 JiaNing Long , Xuechen Liang

It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…

Quantum Physics · Physics 2007-05-23 Piotr Badziag , Pawel Horodecki , Ryszard Horodecki

The low-rank matrix factorization as a L1 norm minimization problem has recently attracted much attention due to its intrinsic robustness to the presence of outliers and missing data. In this paper, we propose a new method, called the…

Numerical Analysis · Computer Science 2012-04-26 Deyu Meng , Zongben Xu

Discriminative Canonical Correlation Analysis (DCCA) is a powerful supervised feature extraction technique for two sets of multivariate data, which has wide applications in pattern recognition. DCCA consists of two parts: (i) mean-centering…

Quantum Physics · Physics 2022-06-14 Yong-Mei Li , Hai-Ling Liu , Shi-Jie Pan , Su-Juan Qin , Fei Gao , Qiao-Yan Wen

Quantum computing and machine learning are state-of-the-art technologies that have been investigated intensively in both academia and industry. The hybrid technology of these two ingredients is expected to be a powerful tool to solve…

Quantum Physics · Physics 2026-03-05 Yusuke Hama , Tadashi Kadowaki

The RSA cryptosystem, which relies on the computational difficulty of prime factorization, faces growing challenges with the advancement of quantum computing. In this study, we propose a quantum annealing based approach to integer…

Quantum Physics · Physics 2025-06-23 Arim Ryou , Kiwoong Kim , Kyungtaek Jun

Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to…

Entanglement is widely believed to lie at the heart of the advantages offered by a quantum computer. This belief is supported by the discovery that a noiseless (pure) state quantum computer must generate a large amount of entanglement in…

Quantum Physics · Physics 2008-11-16 B. P. Lanyon , M. Barbieri , M. P. Almeida , A. G. White

Traditional methods in quantum chemistry rely on Hartree-Fock-based Slater-determinant (SD) representations, whose underlying zeroth-order picture assumes separability by particle. Here, we explore a radically different approach, based on…

Quantum Physics · Physics 2022-03-02 Bill Poirier , Jonathan Jerke

In this article we want to demonstrate the effectiveness of the new D-Wave quantum annealer, D-Wave 2000Q, in dealing with real world problems. In particular, it is shown how the quantum annealing process is able to find global optima even…

Quantum Physics · Physics 2018-08-28 Daniele Ottaviani , Alfonso Amendola

Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…

Quantum Physics · Physics 2021-01-21 Gian Giacomo Guerreschi

The qubit mapping problem (QMP) focuses on the mapping and routing of qubits in quantum circuits so that the strict connectivity constraints imposed by near-term quantum hardware are satisfied. QMP is a pivotal task for quantum circuit…

Quantum Physics · Physics 2024-09-10 Yunqi Huang , Xiangzhen Zhou , Fanxu Meng , Sanjiang Li