@inproceedings{Wicker2019,
title = {XOR-based Boolean Matrix Decomposition},
author = {Jörg Wicker and Yan Cathy Hua and Rayner Rebello and Bernhard Pfahringer},
year = {2019},
date = {2019-11-08},
booktitle = {International Conference on Data Mining},
publisher = {IEEE},
abstract = {Boolean matrix factorization (BMF) is a data summarizing and dimension-reduction technique. Existing BMF methods build on matrix properties defined by Boolean algebra, where the addition operator is the logical inclusive OR and the multiplication operator the logical AND. As a consequence, this leads to the lack of an additive inverse in all Boolean matrix operations, which produces
an indelible type of approximation error. Previous research adopted various methods to address such an issue and produced reasonably accurate approximation. However, an exact factorization is rarely found in the literature. In this paper, we introduce a new algorithm named XBMaD (Xor-based Boolean Matrix Decomposition) where the addition operator is defined as the exclusive OR (Xor). This change completely removes the error-mitigation issue of OR-based BMF methods, and allows for an exact error-free factorization. An evaluation comparing XBMaD and classic OR-based methods suggested that XBMAD performed equal or in most cases more accurately and faster.
},
keywords = {Boolean matrix decomposition, data mining},
pubstate = {forthcoming},
tppubtype = {inproceedings}
}

Boolean matrix factorization (BMF) is a data summarizing and dimension-reduction technique. Existing BMF methods build on matrix properties defined by Boolean algebra, where the addition operator is the logical inclusive OR and the multiplication operator the logical AND. As a consequence, this leads to the lack of an additive inverse in all Boolean matrix operations, which produces
an indelible type of approximation error. Previous research adopted various methods to address such an issue and produced reasonably accurate approximation. However, an exact factorization is rarely found in the literature. In this paper, we introduce a new algorithm named XBMaD (Xor-based Boolean Matrix Decomposition) where the addition operator is defined as the exclusive OR (Xor). This change completely removes the error-mitigation issue of OR-based BMF methods, and allows for an exact error-free factorization. An evaluation comparing XBMaD and classic OR-based methods suggested that XBMAD performed equal or in most cases more accurately and faster.

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.

@inproceedings{tyukin2014bmad,
title = {BMaD -- A Boolean Matrix Decomposition Framework},
author = {Andrey Tyukin and Stefan Kramer and Jörg Wicker},
editor = {Toon Calders and Floriana Esposito and Eyke Hüllermeier and Rosa Meo},
url = {http://dx.doi.org/10.1007/978-3-662-44845-8_40},
doi = {10.1007/978-3-662-44845-8_40},
isbn = {978-3-662-44844-1},
year = {2014},
date = {2014-01-01},
booktitle = {Machine Learning and Knowledge Discovery in Databases},
volume = {8726},
pages = {481-484},
publisher = {Springer Berlin Heidelberg},
series = {Lecture Notes in Computer Science},
abstract = {Boolean matrix decomposition is a method to obtain a compressed
representation of a matrix with Boolean entries. We present a modular
framework that unifies several Boolean matrix decomposition algorithms, and
provide methods to evaluate their performance. The main advantages of
the framework are its modular approach and hence the flexible
combination of the steps of a Boolean matrix decomposition and the
capability of handling missing values. The framework is licensed under
the GPLv3 and can be downloaded freely at
urlhttp://projects.informatik.uni-mainz.de/bmad.},
keywords = {Boolean matrix decomposition, data mining, framework},
pubstate = {published},
tppubtype = {inproceedings}
}

Boolean matrix decomposition is a method to obtain a compressed
representation of a matrix with Boolean entries. We present a modular
framework that unifies several Boolean matrix decomposition algorithms, and
provide methods to evaluate their performance. The main advantages of
the framework are its modular approach and hence the flexible
combination of the steps of a Boolean matrix decomposition and the
capability of handling missing values. The framework is licensed under
the GPLv3 and can be downloaded freely at
urlhttp://projects.informatik.uni-mainz.de/bmad.

@inproceedings{wicker2012multi,
title = {Multi-label Classification Using Boolean Matrix Decomposition},
author = {Jörg Wicker and Bernhard Pfahringer and Stefan Kramer},
url = {https://wicker.nz/nwp-acm/authorize.php?id=N10032
http://doi.acm.org/10.1145/2245276.2245311},
doi = {10.1145/2245276.2245311},
isbn = {978-1-4503-0857-1},
year = {2012},
date = {2012-01-01},
booktitle = {Proceedings of the 27th Annual ACM Symposium on Applied Computing},
pages = {179--186},
publisher = {ACM},
series = {SAC '12},
abstract = {This paper introduces a new multi-label classifier based on Boolean matrix decomposition. Boolean matrix decomposition is used to extract, from the full label matrix, latent labels representing useful Boolean combinations of the original labels. Base level models predict latent labels, which are subsequently transformed into the actual labels by Boolean matrix multiplication with the second matrix from the decomposition. The new method is tested on six publicly available datasets with varying numbers of labels. The experimental evaluation shows that the new method works particularly well on datasets with a large number of labels and strong dependencies among them.},
keywords = {associations, Boolean matrix decomposition, machine learning, multi-label classification},
pubstate = {published},
tppubtype = {inproceedings}
}

This paper introduces a new multi-label classifier based on Boolean matrix decomposition. Boolean matrix decomposition is used to extract, from the full label matrix, latent labels representing useful Boolean combinations of the original labels. Base level models predict latent labels, which are subsequently transformed into the actual labels by Boolean matrix multiplication with the second matrix from the decomposition. The new method is tested on six publicly available datasets with varying numbers of labels. The experimental evaluation shows that the new method works particularly well on datasets with a large number of labels and strong dependencies among them.