Our Research

Research on specific applications of AI was coupled with the development of inference and learning theories for uncertain and incomplete information (including Bayesian networks and Dempster-Shafer theory), the development of optimization methods inspired by nature (including immune networks, herd, genetic and extreme optimization algorithms), methods of extracting knowledge from numerical data, text and hypertext (new algorithms for cluster analysis and classification, including in the field of graph spectral analysis, new methods for extracting relationships of hierarchical concepts and simple relationships from natural language texts) and others. Currently, the Team has undertaken the hottest and most important challenge of developing Explainable Artificial Intelligence (XAI) methods. XAI is a response to industry objections that artificial intelligence methods such as deep neural networks, evolutionary algorithms and other operate on the principle of a "black box", while only transparent methods are trusted by business. Our Team took on a particularly difficult challenge, i.e. achieving explainability in the field of cluster analysis of text documents, especially those clustered using spectral methods. The basic difficulty lies in the lack of a coherent axiomatic system for cluster analysis. What is more, grievvant, ​spectral methods detach the representation of clusters from the textual content of documents. Our achievements in this area include:

• An non-cotradictory axiomatic system, including, among others, k-means algorithm, which is the basis of spectral methods,
• Classification method based on Laplacian spectra of document sets,
• Incremental clustering method based on the above-mentioned spectra,
• Clustering method based on kernelization of the similarity matrix,
• A method of explaining hashtags by hashtags based on the above-mentioned spectra,
• Method of assigning text labels to groups from spectral clustering,
• Explaining the nature of the kernel k-means clustering results for non-Euclidean spaces
• Deepen understanding and selection of non-dominated solutions in nature-inspired optimization systems
• And other.

A Couple of Publications

1. Borkowski P, Kłopotek MA, Starosta B, Wierzchoń ST, Sydow M (2023) Eigenvalue based spectral classification. PLoS ONE 18(4): e0283413. https://doi.org/10.1371/journal.pone.0283413
2. Bartłomiej Starosta: Set-theoretic relations for metasets. Journal of Experimental & Theoretical Artificial Intelligence, 2022, Vol. online, s. 1-15 , LINK.
3. Mieczyslaw A. Klopotek, Robert A. Klopotek: Towards Continuous Consistency Axiom. Applied Intelligence (2022) DOI https://doi.org/10.1007/s10489-022-03710-1 Springer Verlag, Earlier version: CoRR abs/2202.06015 (2022) [i45]

Our Books