A public habilitation lecture by RNDr. Martin Trnečka, Ph.D., was held

On Wednesday, March 25, 2026, RNDr. Martin Trnečka, Ph.D. delivered his public habilitation lecture at FIT, Brno University of Technology. The title? “Boolean Matrix Factorization.”

Martin Trnečka specializes in the field of data analysis. The key topic of his work is Boolean matrix factorization, which is a method of data analysis. Trnečka earned his Ph.D. in 2017 at the Faculty of Science at Palacký University in Olomouc and has been working at the local Department of Computer Science for many years. He has worked on dozens of projects and completed research stays abroad at institutions such as the French INRIA (Nancy) and the American University of Texas (El Paso). The habilitation process has now brought him to our Faculty of Information Technology. Why here, specifically? “I think it’s good if the habilitation process takes place at a different institution; it’s a challenge. And the choice of FIT? Throughout my career, I’ve specialized at the intersection of computer science and information technology, so that choice felt natural to me,” Trnečka comments on his decision.

How to Draw Deeper Conclusions from Complex Matrices

Boolean matrix factorization is a method for uncovering deeper patterns, regularities, or common denominators in binary matrices, which often carry extensive data represented by the values 0/1 (true/false). Similar data can be found, for example, when we are determining whether a certain object has or lacks a particular property—typically, we have patients (imagine them as data in the rows of a matrix) exhibiting symptoms (data in the columns). The summary of symptoms can subsequently represent a specific disease; however, this is information that is not immediately apparent from the matrix itself but must be derived through another method. For example, through the method of matrix factorization (decomposition). The purpose of this method is to replace a complex matrix with a smaller number of more comprehensible factors, which constitute the hidden structure of the data. The method itself has its origins in psychology—psychologists generally deal with smaller datasets, and understanding them is key.

In his research and in his habilitation thesis, Martin Trnečka focuses on developing algorithms that perform factorization better than existing methods. He is also interested in the practical aspects of application. For example, adjusting parameters to ensure the best possible results. A significant part of his work consists of improving known methods: Trnečka specifically mentions formal conceptual analysis, which is frequently used when seeking matrix factorization: “This is a classical mathematical method that typically allows for the description of all patterns in the data. I would describe my contribution here roughly as follows: while the aforementioned method was not originally intended for big data, I am shifting it in precisely this direction.”

Among the main results of Trnečka’s work are several new or significantly modified algorithms, which achieved better decomposition quality or higher computation speed in a series of experiments. Another significant contribution is computational parallelization, i.e., dividing the task among multiple processes, which has accelerated computations. A strength of Trnečka’s research is also his emphasis on interpretability. The author demonstrates that it is not enough to find merely a technically sound decomposition of the data; rather, it is crucial that the resulting factors be as comprehensible as possible to the user. “Factors can be visualized as rectangles in the data. All algorithms solve the problem by attempting to explain as much of the data as possible. But the goal is to present the results to the user who requested the analysis. And that user often wants to see interesting factors.” That is why Trnečka addresses the question of whether the “comprehensibility” of factors can be measured in any way, and proposes methods that favor factors that are more easily grasped from the user’s perspective. This is particularly important where data analysis is not intended solely for machine processing, but also to help experts better understand the phenomenon under investigation.

Psychology, education, data mining. There are plenty of opportunities

The practical applications of the research results are wide-ranging. They can be used, for example, to gain insights from large datasets, to reduce the number of variables before further machine learning, or in bioinformatics. Trnečka himself speaks primarily about research in psychology and machine learning. “It’s a tool for classical data analysis and can be used in classification instead of the original attributes. The result is more accurate classification.” He describes one practical experience: “We analyzed educational data—students—where the attributes were test results. We were determining what characterized these tests; the factor we were looking for was, for example, their focus on logical thinking.”

And how does Martin Trnečka view his habilitation in the context of his professional career so far? “Back in my bachelor’s program, I hoped to become a traditional programmer. But during my master’s studies, I began to enjoy the theory related to algorithms more. And I still enjoy it today. I view habilitation as a natural career step that gives me a certain degree of autonomy. I can build a research group and define the direction.” According to him, the research topic he has been working on for a long time still has many open questions and offers considerable scope for further research. In the near future, Trnečka would like to move toward broader data mining, where he would like to apply his methods. “I would certainly like to thank Professor Radim Bělohlávek, my advisor, colleague, and friend, who has motivated me and pushed me forward throughout my career,” concludes Martin Trnečka in his reflection on the current state of his scientific career. Come hear about his main achievements.

A recording of the lecture can be viewed at the link HERE.