We present new results on Boolean matrix factorization and a new algorithm based on these results. The results emphasize the significance of factorizations that provide from-below approximations of the input matrix. While the previously proposed algorithms do not consider the possibly different significance of different matrix entries, our results help measure such significance and suggest where to focus when computing factors. An experimental evaluation of the new algorithm on both synthetic and real data demonstrates its good performance in terms of good coverage by the first k factors as well as a small number of factors needed for exact decomposition and indicates that the algorithm outperforms the available ones in these terms. We also propose future research topics.
From-Below Boolean Matrix Factorization Algorithm Based on MDL
National Research University Higher School of Economics（国家研究型高等经济大学）；LORIA（洛林计算机科学及其应用实验室）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；University of Lorraine（洛林大学）；Palacký University Olomouc（奥洛穆茨帕拉茨基大学）
A Bayesian Boolean Matrix Factorization with Application to Copy Number Analysis in Cancer
Department of Data Science, Dana-Farber Cancer Institute（数据科学部，达纳-法伯癌症研究所）；Department of Biostatistics, Harvard T.H. Chan School of Public Health（生物统计学部，哈佛T.H. 潘克学校公共卫生学院）
布尔矩阵已被广泛应用于银行交易、犯罪记录、自然语言处理、蛋白质相互作用等领域。布尔矩阵分解（BMF）旨在寻找一个二元矩阵近似为两个低秩布尔矩阵的布尔积，从而产生大量的特征与样本之间关系模式的信息。受二进制矩阵置换理论和几何分割的启发，我们开发了一种快速有效的BMF方法，称为MEBF（Median Expansion for Boolean Factorization）。总的来说，MEBF采用了一种启发式的方法来定位二进制模式表示为密集的1的子矩阵。在每次迭代中，MEBF置换行和列，使得置换矩阵近似于上三角形（UTL），具有所谓的同时连续一属性（SC1P）。在1中稠密的最大子矩阵将位于置换矩阵的上三角区域，并且其位置基于三角形的几何分割来确定。我们比较了MEBF与其他国家的最先进的方法在不同的稀疏性和噪声水平的数据场景。MEBF在重建误差小、计算效率高、稀疏模式精度高等方面优于ASSO、PANDA和MP等主流方法。我们展示了MEBF在二进制和非二进制数据集上的应用，并揭示了其在知识检索和数据去噪方面的进一步潜力。
Matrix Factorization for Inferring Associations and Missing Links
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；Institute for Clarity in Documentation（文献清晰度研究所）；Inria Paris-Rocquencourt（法国国家信息与自动化研究所巴黎-罗康校区）；Rajiv Gandhi University（拉吉夫·甘地大学）；Tsinghua University（清华大学）；Palmer Research Laboratories（帕尔默研究实验室）
Federated Binary Matrix Factorization using Proximal Optimization
KTH Royal Institute of Technology（瑞典皇家理工学院）；CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）；Institute for AI in Medicine, UK Essen（埃森大学医院人工智能医学研究所）；Ruhr University Bochum（波鸿鲁尔大学）；Monash University（莫纳什大学）
Topic Modeling and Link-Prediction for Material Property Discovery
Theoretical Division, Los Alamos National Laboratory Los Alamos New Mexico USA；CSEE, University of Maryland, Baltimore County Baltimore Maryland USA；Modeling, Los Alamos National Laboratory Los Alamos New Mexico USA；Department of Material Science \& Engineering, University of Maryland College Park Maryland USA；Theoretical Division, Los Alamos National Laboratory；CSEE, University of Maryland, Baltimore County；Modeling, Los Alamos National Laboratory；Department of Material Science \& Engineering, University of Maryland
Matrix Completion in Group Testing: Bounds and Simulations
Faculty of Information Technology, University of Science, Ho Chi Minh city, Vietnam（信息科技学院，科学大学，胡志明市，越南）；Vietnam National University, Ho Chi Minh City, Vietnam（越南国家大学，胡志明市，越南）
