Boolean Matrix Factorization via Nonnegative Auxiliary Optimization

@article{Truong2021BooleanMF,
  title={Boolean Matrix Factorization via Nonnegative Auxiliary Optimization},
  author={Duc P. Truong and Erik West Skau and Derek DeSantis and Boian S. Alexandrov},
  journal={IEEE Access},
  year={2021},
  volume={9},
  pages={117169-117177}
}
A novel approach to Boolean matrix factorization (BMF) is presented. Instead of solving the BMF problem directly, this approach solves a nonnegative optimization problem with an additional constraint over an auxiliary matrix whose Boolean structure is identical to the initial Boolean data. This additional auxiliary matrix constraint forces the support of the NMF solution to adhere to that of a BMF solution. The solution of the nonnegative auxiliary optimization problem is thresholded to provide… 
Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition
TLDR
A method for robust Boolean model selection, called BMFk, is introduced, and it is shown on numerical examples that BMFK not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.

References

SHOWING 1-10 OF 16 REFERENCES
Binary Matrix Factorization with Applications
TLDR
This paper extends the standard NMF to binary matrix factorization (BMF for short), and proposes and proves a fundamental boundedness property of NMF which provides a natural normalization scheme that eliminates the bias of factor matrices.
Factorizations of Binary Matrices - Rank Relations and the Uniqueness of Boolean Decompositions
TLDR
This work examines the minimal rank factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and Z2) and discusses when the factorizations are unique.
Boolean Matrix Factorization and Noisy Completion via Message Passing
TLDR
This empirical study demonstrates that message passing is able to recover low-rank Boolean matrices, in the boundaries of theoretically possible recovery and compares favorably with state-of-the-art in real-world applications, such collaborative filtering with large-scale Boolean data.
Discovery of optimal factors in binary data via a novel method of matrix decomposition
Bayesian Boolean Matrix Factorisation
TLDR
This is the first method to provide full posterior inference for Boolean Matrix factorisation which is relevant in applications, e.g. for controlling false positive rates in collaborative filtering and, crucially, improves the interpretability of the inferred patterns.
Learning the parts of objects by non-negative matrix factorization
TLDR
An algorithm for non-negative matrix factorization is demonstrated that is able to learn parts of faces and semantic features of text and is in contrast to other methods that learn holistic, not parts-based, representations.
Mining Top-K Patterns from Binary Datasets in Presence of Noise
TLDR
This paper proposes a greedy algorithm for the discovery of Patterns in Noisy Datasets, named PaNDa, and shows that it outperforms related techniques on both synthetic and realworld data.
Boolean decomposition of binary matrices using a post-nonlinear mixture approach
The Discrete Basis Problem
TLDR
This paper describes a matrix decomposition formulation for Boolean data, the Discrete Basis Problem, and gives a simple greedy algorithm for solving it and shows how it can be solved using existing methods.
General Intelligence
...
...