The aim of matrix decomposition is to express a provided matrix as the outcome of multiplying two or more factor matrices. In this situation, we possess the Y matrix of dimensions m×q, representing labels that we intend to break down into the m × q′ Y′ latent label matrix and the second q′ × q M factor matrix, which is required to reconstruct the initial labels (refer to table 1). Since the matrix being decomposed for labels is Boolean, it is essential for all the factor matrices to be Boolean as well. The multiplication of the factor matrices is executed in the Boolean field, where 0s and 1s indicate truth values, implying that the sum of 1 + 1 equals 1. It is a well-known and researched problem with a wide range of applications, e.g. in multi-label classiﬁcation, clustering, bioinformatics, or pattern minin
XOR-based Boolean Matrix Decomposition Proceedings Article
In: Wang, Jianyong; Shim, Kyuseok; Wu, Xindong (Ed.): 2019 IEEE International Conference on Data Mining (ICDM), pp. 638-647, IEEE, 2019, ISBN: 978-1-7281-4604-1.
BMaD — A Boolean Matrix Decomposition Framework Proceedings Article
In: Calders, Toon; Esposito, Floriana; Hüllermeier, Eyke; Meo, Rosa (Ed.): Machine Learning and Knowledge Discovery in Databases, pp. 481-484, Springer Berlin Heidelberg, 2014, ISBN: 978-3-662-44844-1.
Multi-label Classification Using Boolean Matrix Decomposition Proceedings Article
In: Proceedings of the 27th Annual ACM Symposium on Applied Computing, pp. 179–186, ACM, 2012, ISBN: 978-1-4503-0857-1.