arXiv subjects
Publications and source records attributed to José Luis Balcázar.
We state the graph-theoretic computational problem of finding tight paths in a directed, edge-weighted graph, as well as its simplification of finding tight pairs. These problems are motivated by the need of algorithms that find so-called basic antecedents in closure spaces, in one specific approach to data analysis. We discuss and compare several algorithms to approach these problems.
We argue that the existing knowledge about modular decomposition of graphs and clan decomposition of 2-structures can be put to use advantageously in a context of data analysis. We show how to obtain visual descriptions of co-occurrence patterns by employing these decompositions on possibly generalized Gaifman graphs associated to datasets. We provide both theoretical advances that connect the proposed process to other data mining aspects (namely, closed set mining), as well as implemented algorithmics leading to an open-source tool that demonstrates our approach.
We argue the usefulness of Gaifman graphs of first-order relational structures as an exploratory data analysis tool. We illustrate our approach with cases where the modular decompositions of these graphs reveal interesting facts about the data. Then, we introduce generalized notions of Gaifman graphs, enhanced with quantitative information, to which we can apply more general, existing decomposition notions via 2-structures; thus enlarging the analytical capabilities of the scheme. The very essence of Gaifman graphs makes this approach immediately appropriate for the multirelational data framework.