Boolean Matrix Factorization and Biclustering in Framework of Formal Concept Analysis

Bc. Roman VYJÍDÁČEK

Doctoral thesis

Algorithms of formal concept analysis

Abstract:

This dissertation thesis studies algorithms for Boolean Matrix Factorization (BMF) and the connection between BMF and biclustering in the framework of Formal concept analysis. Namely, we revise the GreCon algorithm for BMF, addressing its previously slow execution time. Experimental results show that the revised GreCon is competitive with the original algorithm in terms of running time and, in some cases, outperforms the state-of-the-art GreConD algorithm. Then, we present a new factor extension technique that successfully generates biclusters that are overlooked by other biclusters enumerating methods. Finally, we present a new BMF algorithm that utilizes biclusters as a starting point in the factor construction process. The algorithm selects the formal concepts or biclusters as factors based on their advantages. The new algorithm is fast, straightforward, and outperforms more sophisticated BMF algorithms. We also present various experimental results performed on real datasets.

Abstract:

This dissertation thesis studies algorithms for Boolean Matrix Factorization (BMF) and the connection between BMF and biclustering in the framework of Formal concept analysis. Namely, we revise the GreCon algorithm for BMF, addressing its previously slow execution time. Experimental results show that the revised GreCon is competitive with the original algorithm in terms of running time and, in some cases, outperforms the state-of-the-art GreConD algorithm. Then, we present a new factor extension technique that successfully generates biclusters that are overlooked by other biclusters enumerating methods. Finally, we present a new BMF algorithm that utilizes biclusters as a starting point in the factor construction process. The algorithm selects the formal concepts or biclusters as factors based on their advantages. The new algorithm is fast, straightforward, and outperforms more sophisticated BMF algorithms. We also present various experimental results performed on real datasets.

Keywords

Boolean Matrix Factorization, Biclustering, Formal concept analysis

Language used: English

Date on which the thesis was submitted / produced: 25. 7. 2024

Thesis defence

• Supervisor: doc. Mgr. Jan Outrata, Ph.D.

Palacký University Olomouc

Faculty of Science

Doctoral programme / field:
Computer Science / Computer Science