Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

Article Statistics & Probability

From-below Boolean matrix factorization algorithm based on MDL

Tatiana Makhalova et al.

Summary: In this paper, a novel BMF algorithm based on formal concept analysis is proposed, utilizing the MDL principle for factor selection. The algorithm outperforms existing state-of-the-art BMF algorithms in various experiments.

ADVANCES IN DATA ANALYSIS AND CLASSIFICATION (2021)

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Article Engineering, Electrical & Electronic

Boolean decomposition of binary matrices using a post-nonlinear mixture approach

Sebastian Miron et al.

Summary: The novel binary matrix factorization approach based on a post-nonlinear mixture model provides interpretable results in the presence of overlapping sources and generates more accurate low-rank binary matrix approximations compared to existing techniques.

SIGNAL PROCESSING (2021)

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Article Computer Science, Artificial Intelligence

Model order selection for approximate Boolean matrix factorization problem

Martin Trnecka et al.

Summary: A key step in applying Boolean matrix factorization (BMF) is to establish the correct model order for the data by determining the proper number of factors. There are two main approaches to BMF, namely, Discrete Basis Problem (DBP) and Approximation Factorization Problem (AFP). While there are techniques for model order selection for DBP, there is no tailored technique for AFP.

KNOWLEDGE-BASED SYSTEMS (2021)

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Article Computer Science, Information Systems

Boolean Matrix Factorization via Nonnegative Auxiliary Optimization

Duc P. Truong et al.

Summary: A novel approach to Boolean matrix factorization is presented, which solves a nonnegative optimization problem with an additional constraint over an auxiliary matrix. The equivalence of the two solution spaces is proved, and the nonincreasing property of the algorithm is also demonstrated. Experiments on synthetic and real datasets show the effectiveness and complexity of the algorithm compared to other methods.

IEEE ACCESS (2021)

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Article Computer Science, Information Systems

Finding the Number of Latent Topics With Semantic Non-Negative Matrix Factorization

Raviteja Vangara et al.

Summary: Topic modeling is a key objective in text mining, with the challenge of determining the correct number of topics. This paper introduces the SeNMFk model, based on KL divergence, which shows stable extraction of latent topics. Through performance comparison, it is demonstrated that this method accurately identifies the number of topics and extracts highly coherent topics.

IEEE ACCESS (2021)

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Article Mathematics, Applied