Projected Hierarchical ALS for Generalized Boolean Matrix Factorization

We introduce a versatile approach for Boolean factorization of binary data matrices based on a projected hierarchical alternating least squares method. The general model considered in this work allows for an arbitrary Boolean combination of the binary rank-1 terms. The underlying approximation probl...

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Bibliographic Details
Published inICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 1 - 5
Main Authors Farias, Rodrigo Cabral, Miron, Sebastian
Format Conference Proceeding
LanguageEnglish
Published IEEE 04.06.2023
Subjects
Acoustics
Alternating least squares
Approximation algorithms
Binary data
Boolean matrix factorizations
Clustering algorithms
Data mining
Mixture models
Signal processing
Signal processing algorithms
Speech processing
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Summary:We introduce a versatile approach for Boolean factorization of binary data matrices based on a projected hierarchical alternating least squares method. The general model considered in this work allows for an arbitrary Boolean combination of the binary rank-1 terms. The underlying approximation problem is tackled by relaxing the binary constraints and representing the combining function by a multivariate polynomial. This leads to closed-form and simple to implement updates of the alternating algorithm. Performance comparisons with other methods from the literature are presented for the standard Boolean ('OR') mixture model. We also pro-vide results on real data, as well as factorization examples using XOR and 3-term majority logical operators as combining functions.
ISSN:2379-190X
DOI:10.1109/ICASSP49357.2023.10094568