数据采掘中的许多基本问题可以归结为一个或多个NP难的组合优化问题。与使用通用计算机时相比，诸如量子和受量子启发的硬件之类的新技术的最新进展承诺了用于解决这些问题的显著加速，但是通常需要以特殊形式（诸如伊辛或二次无约束二进制优化（QUBO）模型）对问题进行建模，以便利用这些设备。在这项工作中，我们专注于重要的二进制矩阵分解（BMF）问题，有许多应用在数据采掘。我们提出了两个QUBO配方BMF。我们展示了如何聚类约束可以很容易地纳入这些配方。我们考虑的专用硬件在它可以处理的变量数量上是有限的，这在分解大型矩阵时提出了挑战。我们提出了一种基于采样的方法来克服这一挑战，使我们能够因式分解大型矩形矩阵。除了这些方法之外，我们还提出了一个简单的基线算法，它在某些情况下优于我们更复杂的方法。我们在Fujitsu Digital Annealer（一种量子启发的互补金属氧化物半导体（CMOS）退火机）上对合成和真实数据（包括基因表达数据）进行了实验。这些实验表明，我们的方法是能够产生更准确的BMF比竞争的方法。
英文摘要：
Many fundamental problems in data mining can be reduced to one or more NP-hard combinatorial optimization problems. Recent advances in novel technologies such as quantum and quantum-inspired hardware promise a substantial speedup for solving these problems compared to when using general purpose computers but often require the problem to be modeled in a special form, such as an Ising or quadratic unconstrained binary optimization (QUBO) model, in order to take advantage of these devices. In this work, we focus on the important binary matrix factorization (BMF) problem which has many applications in data mining. We propose two QUBO formulations for BMF. We show how clustering constraints can easily be incorporated into these formulations. The special purpose hardware we consider is limited in the number of variables it can handle which presents a challenge when factorizing large matrices. We propose a sampling based approach to overcome this challenge, allowing us to factorize large rectangular matrices. In addition to these methods, we also propose a simple baseline algorithm which outperforms our more sophisticated methods in a few situations. We run experiments on the Fujitsu Digital Annealer, a quantum-inspired complementary metal-oxide-semiconductor (CMOS) annealer, on both synthetic and real data, including gene expression data. These experiments show that our approach is able to produce more accurate BMFs than competing methods.
Interpretable factorization of clinical questionnaires to identify latent factors of psychopathology
Machine Learning Core, National Institute of Mental Health, National Institutes of Health（机器学习核心，国家心理健康研究所，国立卫生研究院）；Section on Developmental Neurogenomics, Human Genetics Branch, National Institute of Mental Health, National Institutes of Health（发育神经基因组学部门，人类遗传学分支，国家心理健康研究所，国立卫生研究院）；National Institute of Mental Health, National Institutes of Health（国家心理健康研究所，国立卫生研究院）
Implementation of Trained Factorization Machine Recommendation System on Quantum Annealer
Hon Hai (Foxconn) Research Institute（鸿海（富士康）研究院）；Graduate Institute of Applied Physics, National Taiwan University（国立台湾大学应用物理研究所）；Department of Finance, National Taiwan University（国立台湾大学财务金融学系）；Department of Mathematics, National Taiwan University（国立台湾大学数学系）；Department of Mathematics, National Cheng Kung University（国立成功大学数学系）
Department of Computer Science and Technology, University of Cambridge, United Kingdom（计算机科学与技术系，剑桥大学，英国）；Robotics and Biology Laboratory, Technische Universität Berlin（机器人与生物学实验室，柏林技术大学）；Science of Intelligence (SCIoI), Cluster of Excellence, Berlin, Germany（智能科学（SCIoI），卓越中心，柏林，德国）；Robotics Institute Germany（德国机器人研究所）
