Knowledge & Data Engineering Group (KDE), EECS, University of Kassel

• 1.

  Draude, C., Engert, S., Hess, T., Hirth, J., Horn, V., Kropf, J., Lamla, J., Stumme, G., Uhlmann, M., Zwingmann, N.: Verrechnung – Design – Kultivierung: Instrumentenkasten für die Gestaltung fairer Geschäftsmodelle durch Ko-Valuation, https://www.forum-privatheit.de/wp-content/uploads/Forschungsberichte-1-2024-WP-Fairdienste.pdf, (2024). https://doi.org/10.24406/publica-2497.

  URLBibTeXEndNoteDOI

  @misc{claude2024verrechnung,
  address = {Karlsruhe},
  author = {Draude, Claude and Engert, Simon and Hess, Thomas and Hirth, Johannes and Horn, Viktoria and Kropf, Jonathan and Lamla, Jörn and Stumme, Gerd and Uhlmann, Markus and Zwingmann, Nina},
  edition = 1,
  editor = {Friedewald, Michael and Roßnagel, Alexander and Geminn, Christian and Karaboga, Murat},
  howpublished = {White Paper},
  keywords = {itegpub},
  month = {03},
  publisher = {Fraunhofer-Institut für System- und Innovationsforschung ISI},
  series = {Plattform Privatheit},
  title = {Verrechnung – Design – Kultivierung: Instrumentenkasten für die Gestaltung fairer Geschäftsmodelle durch Ko-Valuation},
  year = 2024
  }
  

  %0 Generic
  %1 claude2024verrechnung
  %A Draude, Claude
  %A Engert, Simon
  %A Hess, Thomas
  %A Hirth, Johannes
  %A Horn, Viktoria
  %A Kropf, Jonathan
  %A Lamla, Jörn
  %A Stumme, Gerd
  %A Uhlmann, Markus
  %A Zwingmann, Nina
  %B Plattform Privatheit
  %C Karlsruhe
  %D 2024
  %E Friedewald, Michael
  %E Roßnagel, Alexander
  %E Geminn, Christian
  %E Karaboga, Murat
  %I Fraunhofer-Institut für System- und Innovationsforschung ISI
  %R 10.24406/publica-2497
  %T Verrechnung – Design – Kultivierung: Instrumentenkasten für die Gestaltung fairer Geschäftsmodelle durch Ko-Valuation
  %U https://www.forum-privatheit.de/wp-content/uploads/Forschungsberichte-1-2024-WP-Fairdienste.pdf
  %7 1
  

• 1.

  Draude, C., Dürrschnabel, D., Hirth, J., Horn, V., Kropf, J., Lamla, J., Stumme, G., Uhlmann, M.: Conceptual Mapping of Controversies. (2024).

  BibTeXEndNote

  With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our experiments, we analyze two maps from different news journals with methods from ordinal data science. We show how these methods can be used to assess the diversity, complexity and potential bias of controversies. In addition to that, we discuss how the diagrams of concept lattices can be used to navigate between news articles

  @article{draude2024conceptual,
  abstract = {With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our experiments, we analyze two maps from different news journals with methods from ordinal data science. We show how these methods can be used to assess the diversity, complexity and potential bias of controversies. In addition to that, we discuss how the diagrams of concept lattices can be used to navigate between news articles},
  author = {Draude, Claude and Dürrschnabel, Dominik and Hirth, Johannes and Horn, Viktoria and Kropf, Jonathan and Lamla, Jörn and Stumme, Gerd and Uhlmann, Markus},
  keywords = {myown},
  title = {Conceptual Mapping of Controversies},
  year = 2024
  }
  

  %0 Journal Article
  %1 draude2024conceptual
  %A Draude, Claude
  %A Dürrschnabel, Dominik
  %A Hirth, Johannes
  %A Horn, Viktoria
  %A Kropf, Jonathan
  %A Lamla, Jörn
  %A Stumme, Gerd
  %A Uhlmann, Markus
  %D 2024
  %T Conceptual Mapping of Controversies
  %X With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our experiments, we analyze two maps from different news journals with methods from ordinal data science. We show how these methods can be used to assess the diversity, complexity and potential bias of controversies. In addition to that, we discuss how the diagrams of concept lattices can be used to navigate between news articles
  

• 1.

  Hille, T., Stubbemann, M., Hanika, T.: Reproducibility and Geometric Intrinsic Dimensionality: An Investigation on Graph Neural Network Research, (2024).

  BibTeXEndNote

  @preprint{hille2024reproducibility,
  author = {Hille, Tobias and Stubbemann, Maximilian and Hanika, Tom},
  keywords = {kde},
  title = {Reproducibility and Geometric Intrinsic Dimensionality: An Investigation on Graph Neural Network Research},
  year = 2024
  }
  

  %0 Generic
  %1 hille2024reproducibility
  %A Hille, Tobias
  %A Stubbemann, Maximilian
  %A Hanika, Tom
  %D 2024
  %T Reproducibility and Geometric Intrinsic Dimensionality: An Investigation on Graph Neural Network Research
  

• 1.

  Hirth, J., Hanika, T.: The Geometric Structure of Topic Models, (2024).

  BibTeXEndNote

  Topic models are a popular tool for clustering and analyzing textual data. They allow texts to be classified on the basis of their affiliation to the previously calculated topics. Despite their widespread use in research and application, an in-depth analysis of topic models is still an open research topic. State-of-the-art methods for interpreting topic models are based on simple visualizations, such as similarity matrices, top-term lists or embeddings, which are limited to a maximum of three dimensions. In this paper, we propose an incidence-geometric method for deriving an ordinal structure from flat topic models, such as non-negative matrix factorization. These enable the analysis of the topic model in a higher (order) dimension and the possibility of extracting conceptual relationships between several topics at once. Due to the use of conceptual scaling, our approach does not introduce any artificial topical relationships, such as artifacts of feature compression. Based on our findings, we present a new visualization paradigm for concept hierarchies based on ordinal motifs. These allow for a top-down view on topic spaces. We introduce and demonstrate the applicability of our approach based on a topic model derived from a corpus of scientific papers taken from 32 top machine learning venues.

  @preprint{hirth2024geometric,
  abstract = {Topic models are a popular tool for clustering and analyzing textual data. They allow texts to be classified on the basis of their affiliation to the previously calculated topics. Despite their widespread use in research and application, an in-depth analysis of topic models is still an open research topic. State-of-the-art methods for interpreting topic models are based on simple visualizations, such as similarity matrices, top-term lists or embeddings, which are limited to a maximum of three dimensions. In this paper, we propose an incidence-geometric method for deriving an ordinal structure from flat topic models, such as non-negative matrix factorization. These enable the analysis of the topic model in a higher (order) dimension and the possibility of extracting conceptual relationships between several topics at once. Due to the use of conceptual scaling, our approach does not introduce any artificial topical relationships, such as artifacts of feature compression. Based on our findings, we present a new visualization paradigm for concept hierarchies based on ordinal motifs. These allow for a top-down view on topic spaces. We introduce and demonstrate the applicability of our approach based on a topic model derived from a corpus of scientific papers taken from 32 top machine learning venues.},
  author = {Hirth, Johannes and Hanika, Tom},
  keywords = {kde},
  title = {The Geometric Structure of Topic Models},
  year = 2024
  }
  

  %0 Generic
  %1 hirth2024geometric
  %A Hirth, Johannes
  %A Hanika, Tom
  %D 2024
  %T The Geometric Structure of Topic Models
  %X Topic models are a popular tool for clustering and analyzing textual data. They allow texts to be classified on the basis of their affiliation to the previously calculated topics. Despite their widespread use in research and application, an in-depth analysis of topic models is still an open research topic. State-of-the-art methods for interpreting topic models are based on simple visualizations, such as similarity matrices, top-term lists or embeddings, which are limited to a maximum of three dimensions. In this paper, we propose an incidence-geometric method for deriving an ordinal structure from flat topic models, such as non-negative matrix factorization. These enable the analysis of the topic model in a higher (order) dimension and the possibility of extracting conceptual relationships between several topics at once. Due to the use of conceptual scaling, our approach does not introduce any artificial topical relationships, such as artifacts of feature compression. Based on our findings, we present a new visualization paradigm for concept hierarchies based on ordinal motifs. These allow for a top-down view on topic spaces. We introduce and demonstrate the applicability of our approach based on a topic model derived from a corpus of scientific papers taken from 32 top machine learning venues.
  

• 1.

  Abdulla, M., Hirth, J., Stumme, G.: The Birkhoff completion of finite lattices. (2024).

  BibTeXEndNote

  We introduce the Birkhoff completion as the smallest dis- tributive lattice in which a given finite lattice can be embedded as semi- lattice. We discuss its relationship to implicational theories, in particular to R. Wille’s simply-implicational theories. By an example, we show how the Birkhoff completion can be used as a tool for ordinal data science.

  @article{abdulla2024birkhoff,
  abstract = {We introduce the Birkhoff completion as the smallest dis- tributive lattice in which a given finite lattice can be embedded as semi- lattice. We discuss its relationship to implicational theories, in particular to R. Wille’s simply-implicational theories. By an example, we show how the Birkhoff completion can be used as a tool for ordinal data science.},
  author = {Abdulla, Mohammad and Hirth, Johannes and Stumme, Gerd},
  keywords = {fca},
  title = {The Birkhoff completion of finite lattices},
  year = 2024
  }
  

  %0 Journal Article
  %1 abdulla2024birkhoff
  %A Abdulla, Mohammad
  %A Hirth, Johannes
  %A Stumme, Gerd
  %D 2024
  %T The Birkhoff completion of finite lattices
  %X We introduce the Birkhoff completion as the smallest dis- tributive lattice in which a given finite lattice can be embedded as semi- lattice. We discuss its relationship to implicational theories, in particular to R. Wille’s simply-implicational theories. By an example, we show how the Birkhoff completion can be used as a tool for ordinal data science.
  

• 1.

  Hirth, J., Horn, V., Stumme, G., Hanika, T.: Ordinal motifs in lattices. Information Sciences. 659, 120009 (2024). https://doi.org/https://doi.org/10.1016/j.ins.2023.120009.

  URLBibTeXEndNoteDOI

  @article{HIRTH2024120009,
  author = {Hirth, Johannes and Horn, Viktoria and Stumme, Gerd and Hanika, Tom},
  journal = {Information Sciences},
  keywords = {itegpub},
  pages = 120009,
  title = {Ordinal motifs in lattices},
  volume = 659,
  year = 2024
  }
  

  %0 Journal Article
  %1 HIRTH2024120009
  %A Hirth, Johannes
  %A Horn, Viktoria
  %A Stumme, Gerd
  %A Hanika, Tom
  %D 2024
  %J Information Sciences
  %P 120009
  %R https://doi.org/10.1016/j.ins.2023.120009
  %T Ordinal motifs in lattices
  %U https://www.sciencedirect.com/science/article/pii/S0020025523015943
  %V 659
  

• 1.

  Dürrschnabel, D., Hanika, T., Stumme, G.: Drawing Order Diagrams Through Two-Dimension Extension. Journal of Graph Algorithms and Applications. 27, 783–802 (2023). https://doi.org/10.7155/jgaa.00645.

  URLBibTeXEndNoteDOI

  @article{drrschnabel2023drawing,
  author = {Dürrschnabel, Dominik and Hanika, Tom and Stumme, Gerd},
  journal = {Journal of Graph Algorithms and Applications},
  keywords = {linear_extension},
  number = 9,
  pages = {783–802},
  publisher = {Journal of Graph Algorithms and Applications},
  title = {Drawing Order Diagrams Through Two-Dimension Extension},
  volume = 27,
  year = 2023
  }
  

  %0 Journal Article
  %1 drrschnabel2023drawing
  %A Dürrschnabel, Dominik
  %A Hanika, Tom
  %A Stumme, Gerd
  %D 2023
  %I Journal of Graph Algorithms and Applications
  %J Journal of Graph Algorithms and Applications
  %N 9
  %P 783–802
  %R 10.7155/jgaa.00645
  %T Drawing Order Diagrams Through Two-Dimension Extension
  %U http://dx.doi.org/10.7155/jgaa.00645
  %V 27
  

• 1.

  Budde, K.B., Rellstab, C., Heuertz, M., Gugerli, F., Hanika, T., Verdú, M., Pausas, J.G., González-Martínez, S.C.: Divergent selection in a Mediterranean pine on local spatial scales. Journal of Ecology. n/a, (2023). https://doi.org/https://doi.org/10.1111/1365-2745.14231.

  URLBibTeXEndNoteDOI

  Abstract The effects of selection on an organism's genome are hard to detect on small spatial scales, as gene flow can swamp signatures of local adaptation. Therefore, most genome scans to detect signatures of environmental selection are performed on large spatial scales; however, divergent selection on the local scale (e.g. between contrasting soil conditions) has also been demonstrated, in particular for herbaceous plants. Here, we hypothesised that in topographically complex landscapes, microenvironment variability is strong enough to leave a selective footprint in the genomes of long-lived organisms. To test this, we investigated paired south- versus north-facing Pinus pinaster stands on the local scale, with trees growing in close vicinity (≤820 m distance between paired south- and north-facing stands), in a Mediterranean mountain area. While trees on north-facing slopes experience less radiation, trees on south-facing slopes suffer from especially harsh conditions, particularly during the dry summer season. Two outlier analyses consistently revealed five putatively adaptive loci (out of 4034), in candidate genes two of which encoded non-synonymous substitutions. Additionally, one locus showed consistent allele frequency differences in all three stand pairs indicating divergent selection despite high gene flow on the local scale. Permutation tests demonstrated that our findings were robust. Functional annotation of these candidate genes revealed biological functions related to abiotic stress response, such as water availability, in other plant species. Synthesis. Our study highlights how divergent selection in heterogeneous microenvironments shapes and maintains the functional genetic variation within populations of long-lived forest tree species, being the first to focus on adaptive genetic divergence between south- and north-facing slopes within continuous forest stands. This is especially relevant in the current context of climate change, as this variation is at the base of plant population responses to future climate.

  @article{https://doi.org/10.1111/1365-2745.14231,
  abstract = {Abstract The effects of selection on an organism's genome are hard to detect on small spatial scales, as gene flow can swamp signatures of local adaptation. Therefore, most genome scans to detect signatures of environmental selection are performed on large spatial scales; however, divergent selection on the local scale (e.g. between contrasting soil conditions) has also been demonstrated, in particular for herbaceous plants. Here, we hypothesised that in topographically complex landscapes, microenvironment variability is strong enough to leave a selective footprint in the genomes of long-lived organisms. To test this, we investigated paired south- versus north-facing Pinus pinaster stands on the local scale, with trees growing in close vicinity (≤820 m distance between paired south- and north-facing stands), in a Mediterranean mountain area. While trees on north-facing slopes experience less radiation, trees on south-facing slopes suffer from especially harsh conditions, particularly during the dry summer season. Two outlier analyses consistently revealed five putatively adaptive loci (out of 4034), in candidate genes two of which encoded non-synonymous substitutions. Additionally, one locus showed consistent allele frequency differences in all three stand pairs indicating divergent selection despite high gene flow on the local scale. Permutation tests demonstrated that our findings were robust. Functional annotation of these candidate genes revealed biological functions related to abiotic stress response, such as water availability, in other plant species. Synthesis. Our study highlights how divergent selection in heterogeneous microenvironments shapes and maintains the functional genetic variation within populations of long-lived forest tree species, being the first to focus on adaptive genetic divergence between south- and north-facing slopes within continuous forest stands. This is especially relevant in the current context of climate change, as this variation is at the base of plant population responses to future climate.},
  author = {Budde, Katharina B. and Rellstab, Christian and Heuertz, Myriam and Gugerli, Felix and Hanika, Tom and Verdú, Miguel and Pausas, Juli G. and González-Martínez, Santiago C.},
  journal = {Journal of Ecology},
  keywords = {itegpub},
  number = {n/a},
  title = {Divergent selection in a Mediterranean pine on local spatial scales},
  volume = {n/a},
  year = 2023
  }
  

  %0 Journal Article
  %1 https://doi.org/10.1111/1365-2745.14231
  %A Budde, Katharina B.
  %A Rellstab, Christian
  %A Heuertz, Myriam
  %A Gugerli, Felix
  %A Hanika, Tom
  %A Verdú, Miguel
  %A Pausas, Juli G.
  %A González-Martínez, Santiago C.
  %D 2023
  %J Journal of Ecology
  %N n/a
  %R https://doi.org/10.1111/1365-2745.14231
  %T Divergent selection in a Mediterranean pine on local spatial scales
  %U https://besjournals.onlinelibrary.wiley.com/doi/abs/10.1111/1365-2745.14231
  %V n/a
  %X Abstract The effects of selection on an organism's genome are hard to detect on small spatial scales, as gene flow can swamp signatures of local adaptation. Therefore, most genome scans to detect signatures of environmental selection are performed on large spatial scales; however, divergent selection on the local scale (e.g. between contrasting soil conditions) has also been demonstrated, in particular for herbaceous plants. Here, we hypothesised that in topographically complex landscapes, microenvironment variability is strong enough to leave a selective footprint in the genomes of long-lived organisms. To test this, we investigated paired south- versus north-facing Pinus pinaster stands on the local scale, with trees growing in close vicinity (≤820 m distance between paired south- and north-facing stands), in a Mediterranean mountain area. While trees on north-facing slopes experience less radiation, trees on south-facing slopes suffer from especially harsh conditions, particularly during the dry summer season. Two outlier analyses consistently revealed five putatively adaptive loci (out of 4034), in candidate genes two of which encoded non-synonymous substitutions. Additionally, one locus showed consistent allele frequency differences in all three stand pairs indicating divergent selection despite high gene flow on the local scale. Permutation tests demonstrated that our findings were robust. Functional annotation of these candidate genes revealed biological functions related to abiotic stress response, such as water availability, in other plant species. Synthesis. Our study highlights how divergent selection in heterogeneous microenvironments shapes and maintains the functional genetic variation within populations of long-lived forest tree species, being the first to focus on adaptive genetic divergence between south- and north-facing slopes within continuous forest stands. This is especially relevant in the current context of climate change, as this variation is at the base of plant population responses to future climate.
  

• 1.

  Stubbemann, M., Hille, T., Hanika, T.: Selecting Features by their Resilience to the Curse of Dimensionality. (2023).

  BibTeXEndNote

  @article{stubbemann2023selecting,
  author = {Stubbemann, Maximilian and Hille, Tobias and Hanika, Tom},
  keywords = {selecting},
  title = {Selecting Features by their Resilience to the Curse of Dimensionality},
  year = 2023
  }
  

  %0 Journal Article
  %1 stubbemann2023selecting
  %A Stubbemann, Maximilian
  %A Hille, Tobias
  %A Hanika, Tom
  %D 2023
  %T Selecting Features by their Resilience to the Curse of Dimensionality
  

• 1.

  Hirth, J., Horn, V., Stumme, G., Hanika, T.: Automatic Textual Explanations of Concept Lattices. In: Ojeda{-}Aciego, M., Sauerwald, K., and Jäschke, R. (eds.) Graph-Based Representation and Reasoning - 28th International Conference on Conceptual Structures, {ICCS} 2023, Berlin, Germany, September 11-13, 2023, Proceedings. pp. 138–152 (2023). https://doi.org/doi.org/10.1007/978-3-031-40960-8_12.

  URLBibTeXEndNoteDOI

  Lattices and their order diagrams are an essential tool for communicating knowledge and insights about data. This is in particular true when applying Formal Concept Analysis. Such representations, however, are difficult to comprehend by untrained users and in general in cases where lattices are large. We tackle this problem by automatically generating textual explanations for lattices using standard scales. Our method is based on the general notion of ordinal motifs in lattices for the special case of standard scales. We show the computational complexity of identifying a small number of standard scales that cover most of the lattice structure. For these, we provide textual explanation templates, which can be applied to any occurrence of a scale in any data domain. These templates are derived using principles from human-computer interaction and allow for a comprehensive textual explanation of lattices. We demonstrate our approach on the spices planner data set, which is a medium sized formal context comprised of fifty-six meals (objects) and thirty-seven spices (attributes). The resulting 531 formal concepts can be covered by means of about 100 standard scales.

  @inproceedings{hirth2023automatic,
  abstract = {Lattices and their order diagrams are an essential tool for communicating knowledge and insights about data. This is in particular true when applying Formal Concept Analysis. Such representations, however, are difficult to comprehend by untrained users and in general in cases where lattices are large. We tackle this problem by automatically generating textual explanations for lattices using standard scales. Our method is based on the general notion of ordinal motifs in lattices for the special case of standard scales. We show the computational complexity of identifying a small number of standard scales that cover most of the lattice structure. For these, we provide textual explanation templates, which can be applied to any occurrence of a scale in any data domain. These templates are derived using principles from human-computer interaction and allow for a comprehensive textual explanation of lattices. We demonstrate our approach on the spices planner data set, which is a medium sized formal context comprised of fifty-six meals (objects) and thirty-seven spices (attributes). The resulting 531 formal concepts can be covered by means of about 100 standard scales.},
  author = {Hirth, Johannes and Horn, Viktoria and Stumme, Gerd and Hanika, Tom},
  booktitle = {Graph-Based Representation and Reasoning - 28th International Conference on Conceptual Structures, {ICCS} 2023, Berlin, Germany, September 11-13, 2023, Proceedings},
  editor = {Ojeda{-}Aciego, Manuel and Sauerwald, Kai and Jäschke, Robert},
  keywords = {itegpub},
  pages = {138--152},
  title = {Automatic Textual Explanations of Concept Lattices},
  volume = 14133,
  year = 2023
  }
  

  %0 Conference Paper
  %1 hirth2023automatic
  %A Hirth, Johannes
  %A Horn, Viktoria
  %A Stumme, Gerd
  %A Hanika, Tom
  %B Graph-Based Representation and Reasoning - 28th International Conference on Conceptual Structures, {ICCS} 2023, Berlin, Germany, September 11-13, 2023, Proceedings
  %D 2023
  %E Ojeda{-}Aciego, Manuel
  %E Sauerwald, Kai
  %E Jäschke, Robert
  %P 138--152
  %R doi.org/10.1007/978-3-031-40960-8_12
  %T Automatic Textual Explanations of Concept Lattices
  %U http://arxiv.org/abs/2304.08093
  %V 14133
  %X Lattices and their order diagrams are an essential tool for communicating knowledge and insights about data. This is in particular true when applying Formal Concept Analysis. Such representations, however, are difficult to comprehend by untrained users and in general in cases where lattices are large. We tackle this problem by automatically generating textual explanations for lattices using standard scales. Our method is based on the general notion of ordinal motifs in lattices for the special case of standard scales. We show the computational complexity of identifying a small number of standard scales that cover most of the lattice structure. For these, we provide textual explanation templates, which can be applied to any occurrence of a scale in any data domain. These templates are derived using principles from human-computer interaction and allow for a comprehensive textual explanation of lattices. We demonstrate our approach on the spices planner data set, which is a medium sized formal context comprised of fifty-six meals (objects) and thirty-seven spices (attributes). The resulting 531 formal concepts can be covered by means of about 100 standard scales.
  

• 1.

  Stumme, G., Dürrschnabel, D., Hanika, T.: Towards Ordinal Data Science, (2023).

  BibTeXEndNote

  @misc{stumme2023ordinal,
  author = {Stumme, Gerd and Dürrschnabel, Dominik and Hanika, Tom},
  keywords = {lattices},
  title = {Towards Ordinal Data Science},
  year = 2023
  }
  

  %0 Generic
  %1 stumme2023ordinal
  %A Stumme, Gerd
  %A Dürrschnabel, Dominik
  %A Hanika, Tom
  %D 2023
  %T Towards Ordinal Data Science
  

• 1.

  Hirth, J., Horn, V., Stumme, G., Hanika, T.: Ordinal Motifs in Lattices. Information Sciences. 120009 (2023). https://doi.org/https://doi.org/10.1016/j.ins.2023.120009.

  URLBibTeXEndNoteDOI

  Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of understandably large parts. With the present work we propose /ordinal motifs/ as analytical units of meaning. We study these ordinal substructures (or standard scales) through (full) scale-measures of formal contexts from the field of formal concept analysis. We show that the underlying decision problems are NP-complete and provide results on how one can incrementally identify ordinal motifs to save computational effort. Accompanying our theoretical results, we demonstrate how ordinal motifs can be leveraged to retrieve basic meaning from a medium sized ordinal data set.

  @article{hirth2023ordinal,
  abstract = {Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of understandably large parts. With the present work we propose /ordinal motifs/ as analytical units of meaning. We study these ordinal substructures (or standard scales) through (full) scale-measures of formal contexts from the field of formal concept analysis. We show that the underlying decision problems are NP-complete and provide results on how one can incrementally identify ordinal motifs to save computational effort. Accompanying our theoretical results, we demonstrate how ordinal motifs can be leveraged to retrieve basic meaning from a medium sized ordinal data set.},
  author = {Hirth, Johannes and Horn, Viktoria and Stumme, Gerd and Hanika, Tom},
  journal = {Information Sciences},
  keywords = {sai},
  pages = 120009,
  title = {Ordinal Motifs in Lattices},
  year = 2023
  }
  

  %0 Journal Article
  %1 hirth2023ordinal
  %A Hirth, Johannes
  %A Horn, Viktoria
  %A Stumme, Gerd
  %A Hanika, Tom
  %D 2023
  %J Information Sciences
  %P 120009
  %R https://doi.org/10.1016/j.ins.2023.120009
  %T Ordinal Motifs in Lattices
  %U https://www.sciencedirect.com/science/article/pii/S0020025523015943
  %X Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of understandably large parts. With the present work we propose /ordinal motifs/ as analytical units of meaning. We study these ordinal substructures (or standard scales) through (full) scale-measures of formal contexts from the field of formal concept analysis. We show that the underlying decision problems are NP-complete and provide results on how one can incrementally identify ordinal motifs to save computational effort. Accompanying our theoretical results, we demonstrate how ordinal motifs can be leveraged to retrieve basic meaning from a medium sized ordinal data set.
  

• 1.

  Dürrschnabel, D., Stumme, G.: Maximal Ordinal Two-Factorizations. In: Ojeda-Aciego, M., Sauerwald, K., and Jäschke, R. (eds.) Graph-Based Representation and Reasoning. pp. 41–55. Springer Nature Switzerland, Cham (2023).

  BibTeXEndNote

  Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and Glodeanu proposed a biplot based on two ordinal factors. For the biplot to be useful, it is important that these factors comprise as much data points as possible, i.e., that they cover a large part of the incidence relation. In this work, we investigate such ordinal two-factorizations. First, we investigate for formal contexts that omit ordinal two-factorizations the disjointness of the two factors. Then, we show that deciding on the existence of two-factorizations of a given size is an {\$}{\$}{\backslash}textsf{\{}NP{\}}{\$}{\$}NP-complete problem which makes computing maximal factorizations computationally expensive. Finally, we provide the algorithm Ord2Factor that allows us to compute large ordinal two-factorizations.

  @inproceedings{10.1007/978-3-031-40960-8_5,
  abstract = {Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and Glodeanu proposed a biplot based on two ordinal factors. For the biplot to be useful, it is important that these factors comprise as much data points as possible, i.e., that they cover a large part of the incidence relation. In this work, we investigate such ordinal two-factorizations. First, we investigate for formal contexts that omit ordinal two-factorizations the disjointness of the two factors. Then, we show that deciding on the existence of two-factorizations of a given size is an {\$}{\$}{\backslash}textsf{\{}NP{\}}{\$}{\$}NP-complete problem which makes computing maximal factorizations computationally expensive. Finally, we provide the algorithm Ord2Factor that allows us to compute large ordinal two-factorizations.},
  address = {Cham},
  author = {Dürrschnabel, Dominik and Stumme, Gerd},
  booktitle = {Graph-Based Representation and Reasoning},
  editor = {Ojeda-Aciego, Manuel and Sauerwald, Kai and Jäschke, Robert},
  keywords = {factorization},
  pages = {41--55},
  publisher = {Springer Nature Switzerland},
  title = {Maximal Ordinal Two-Factorizations},
  year = 2023
  }
  

  %0 Conference Paper
  %1 10.1007/978-3-031-40960-8_5
  %A Dürrschnabel, Dominik
  %A Stumme, Gerd
  %B Graph-Based Representation and Reasoning
  %C Cham
  %D 2023
  %E Ojeda-Aciego, Manuel
  %E Sauerwald, Kai
  %E Jäschke, Robert
  %I Springer Nature Switzerland
  %P 41--55
  %T Maximal Ordinal Two-Factorizations
  %X Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and Glodeanu proposed a biplot based on two ordinal factors. For the biplot to be useful, it is important that these factors comprise as much data points as possible, i.e., that they cover a large part of the incidence relation. In this work, we investigate such ordinal two-factorizations. First, we investigate for formal contexts that omit ordinal two-factorizations the disjointness of the two factors. Then, we show that deciding on the existence of two-factorizations of a given size is an {\$}{\$}{\backslash}textsf{\{}NP{\}}{\$}{\$}NP-complete problem which makes computing maximal factorizations computationally expensive. Finally, we provide the algorithm Ord2Factor that allows us to compute large ordinal two-factorizations.
  %@ 978-3-031-40960-8
  

• 1.

  Stubbemann, M., Hanika, T., Schneider, F.M.: Intrinsic Dimension for Large-Scale Geometric Learning. Transactions on Machine Learning Research. (2023).

  URLBibTeXEndNote

  @article{stubbemann2022intrinsic,
  author = {Stubbemann, Maximilian and Hanika, Tom and Schneider, Friedrich Martin},
  journal = {Transactions on Machine Learning Research},
  keywords = {itegpub},
  title = {Intrinsic Dimension for Large-Scale Geometric Learning},
  year = 2023
  }
  

  %0 Journal Article
  %1 stubbemann2022intrinsic
  %A Stubbemann, Maximilian
  %A Hanika, Tom
  %A Schneider, Friedrich Martin
  %D 2023
  %J Transactions on Machine Learning Research
  %T Intrinsic Dimension for Large-Scale Geometric Learning
  %U https://openreview.net/forum?id=85BfDdYMBY
  

• 1.

  Felde, M., Koyda, M.: Interval-dismantling for lattices. International Journal of Approximate Reasoning. 159, 108931 (2023). https://doi.org/10.1016/j.ijar.2023.108931.

  URLBibTeXEndNoteDOI

  Dismantling allows for the removal of elements from a poset, or in our case lattice, without disturbing the remaining structure. In this paper we have extended the notion of dismantling by single elements to the dismantling by intervals in a lattice. We utilize theory from Formal Concept Analysis (FCA) to show that lattices dismantled by intervals correspond to closed subrelations in the respective formal context, and that there exists a unique core with respect to dismantling by intervals. Furthermore, we show that dismantling intervals can be identified directly in the formal context utilizing a characterization via arrow relations and provide an algorithm to compute all dismantling intervals.

  @article{FELDE2023108931,
  abstract = {Dismantling allows for the removal of elements from a poset, or in our case lattice, without disturbing the remaining structure. In this paper we have extended the notion of dismantling by single elements to the dismantling by intervals in a lattice. We utilize theory from Formal Concept Analysis (FCA) to show that lattices dismantled by intervals correspond to closed subrelations in the respective formal context, and that there exists a unique core with respect to dismantling by intervals. Furthermore, we show that dismantling intervals can be identified directly in the formal context utilizing a characterization via arrow relations and provide an algorithm to compute all dismantling intervals.},
  author = {Felde, Maximilian and Koyda, Maren},
  journal = {International Journal of Approximate Reasoning},
  keywords = {Concept_lattice},
  pages = 108931,
  title = {Interval-dismantling for lattices},
  volume = 159,
  year = 2023
  }
  

  %0 Journal Article
  %1 FELDE2023108931
  %A Felde, Maximilian
  %A Koyda, Maren
  %D 2023
  %J International Journal of Approximate Reasoning
  %P 108931
  %R 10.1016/j.ijar.2023.108931
  %T Interval-dismantling for lattices
  %U https://www.sciencedirect.com/science/article/pii/S0888613X23000622
  %V 159
  %X Dismantling allows for the removal of elements from a poset, or in our case lattice, without disturbing the remaining structure. In this paper we have extended the notion of dismantling by single elements to the dismantling by intervals in a lattice. We utilize theory from Formal Concept Analysis (FCA) to show that lattices dismantled by intervals correspond to closed subrelations in the respective formal context, and that there exists a unique core with respect to dismantling by intervals. Furthermore, we show that dismantling intervals can be identified directly in the formal context utilizing a characterization via arrow relations and provide an algorithm to compute all dismantling intervals.
  

• 1.

  Stubbemann, M., Stumme, G.: The Mont Blanc of Twitter: Identifying Hierarchies of Outstanding Peaks in Social Networks. In: Machine Learning and Knowledge Discovery in Databases: Research Track - European Conference, {ECML} {PKDD} 2023, Turin, Italy, September 18-22, 2023, Proceedings, Part {III}. pp. 177–192. Springer (2023). https://doi.org/10.1007/978-3-031-43418-1\_11.

  URLBibTeXEndNoteDOI

  @inproceedings{DBLP:conf/pkdd/StubbemannS23,
  author = {Stubbemann, Maximilian and Stumme, Gerd},
  booktitle = {Machine Learning and Knowledge Discovery in Databases: Research Track - European Conference, {ECML} {PKDD} 2023, Turin, Italy, September 18-22, 2023, Proceedings, Part {III}},
  keywords = {itegpub},
  pages = {177--192},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {The Mont Blanc of Twitter: Identifying Hierarchies of Outstanding Peaks in Social Networks},
  volume = 14171,
  year = 2023
  }
  

  %0 Conference Paper
  %1 DBLP:conf/pkdd/StubbemannS23
  %A Stubbemann, Maximilian
  %A Stumme, Gerd
  %B Machine Learning and Knowledge Discovery in Databases: Research Track - European Conference, {ECML} {PKDD} 2023, Turin, Italy, September 18-22, 2023, Proceedings, Part {III}
  %D 2023
  %I Springer
  %P 177--192
  %R 10.1007/978-3-031-43418-1\_11
  %T The Mont Blanc of Twitter: Identifying Hierarchies of Outstanding Peaks in Social Networks
  %U https://doi.org/10.1007/978-3-031-43418-1_11
  %V 14171
  

• 1.

  Felde, M., Stumme, G.: Interactive collaborative exploration using incomplete contexts. Data & Knowledge Engineering. 143, 102104 (2023). https://doi.org/10.1016/j.datak.2022.102104.

  URLBibTeXEndNoteDOI

  @article{Felde_2023,
  author = {Felde, Maximilian and Stumme, Gerd},
  journal = {Data & Knowledge Engineering},
  keywords = {attribute-exploration},
  month = {01},
  pages = 102104,
  publisher = {Elsevier {BV}},
  title = {Interactive collaborative exploration using incomplete contexts},
  volume = 143,
  year = 2023
  }
  

  %0 Journal Article
  %1 Felde_2023
  %A Felde, Maximilian
  %A Stumme, Gerd
  %D 2023
  %I Elsevier {BV}
  %J Data & Knowledge Engineering
  %P 102104
  %R 10.1016/j.datak.2022.102104
  %T Interactive collaborative exploration using incomplete contexts
  %U https://doi.org/10.1016%2Fj.datak.2022.102104
  %V 143
  

• 1.

  Schäfermeier, B., Hirth, J., Hanika, T.: Research Topic Flows in Co-Authorship Networks. Scientometrics. 128, 5051–5078 (2023). https://doi.org/10.1007/s11192-022-04529-w.

  BibTeXEndNoteDOI

  In scientometrics, scientific collaboration is often analyzed by means of co-authorships. An aspect which is often overlooked and more difficult to quantify is the flow of expertise between authors from different research topics, which is an important part of scientific progress. With the Topic Flow Network (TFN) we propose a graph structure for the analysis of research topic flows between scientific authors and their respective research fields. Based on a multi-graph and a topic model, our proposed network structure accounts for intratopic as well as intertopic flows. Our method requires for the construction of a TFN solely a corpus of publications (i.e., author and abstract information). From this, research topics are discovered automatically through non-negative matrix factorization. The thereof derived TFN allows for the application of social network analysis techniques, such as common metrics and community detection. Most importantly, it allows for the analysis of intertopic flows on a large, macroscopic scale, i.e., between research topic, as well as on a microscopic scale, i.e., between certain sets of authors. We demonstrate the utility of TFNs by applying our method to two comprehensive corpora of altogether 20 Mio. publications spanning more than 60 years of research in the fields computer science and mathematics. Our results give evidence that TFNs are suitable, e.g., for the analysis of topical communities, the discovery of important authors in different fields, and, most notably, the analysis of intertopic flows, i.e., the transfer of topical expertise. Besides that, our method opens new directions for future research, such as the investigation of influence relationships between research fields.

  @article{schafermeier2022research,
  abstract = {In scientometrics, scientific collaboration is often analyzed by means of co-authorships. An aspect which is often overlooked and more difficult to quantify is the flow of expertise between authors from different research topics, which is an important part of scientific progress. With the Topic Flow Network (TFN) we propose a graph structure for the analysis of research topic flows between scientific authors and their respective research fields. Based on a multi-graph and a topic model, our proposed network structure accounts for intratopic as well as intertopic flows. Our method requires for the construction of a TFN solely a corpus of publications (i.e., author and abstract information). From this, research topics are discovered automatically through non-negative matrix factorization. The thereof derived TFN allows for the application of social network analysis techniques, such as common metrics and community detection. Most importantly, it allows for the analysis of intertopic flows on a large, macroscopic scale, i.e., between research topic, as well as on a microscopic scale, i.e., between certain sets of authors. We demonstrate the utility of TFNs by applying our method to two comprehensive corpora of altogether 20 Mio. publications spanning more than 60 years of research in the fields computer science and mathematics. Our results give evidence that TFNs are suitable, e.g., for the analysis of topical communities, the discovery of important authors in different fields, and, most notably, the analysis of intertopic flows, i.e., the transfer of topical expertise. Besides that, our method opens new directions for future research, such as the investigation of influence relationships between research fields.},
  author = {Schäfermeier, Bastian and Hirth, Johannes and Hanika, Tom},
  journal = {Scientometrics},
  keywords = {co-authorships},
  month = {09},
  number = 9,
  pages = {5051--5078},
  title = {Research Topic Flows in Co-Authorship Networks},
  volume = 128,
  year = 2023
  }
  

  %0 Journal Article
  %1 schafermeier2022research
  %A Schäfermeier, Bastian
  %A Hirth, Johannes
  %A Hanika, Tom
  %D 2023
  %J Scientometrics
  %N 9
  %P 5051--5078
  %R 10.1007/s11192-022-04529-w
  %T Research Topic Flows in Co-Authorship Networks
  %V 128
  %X In scientometrics, scientific collaboration is often analyzed by means of co-authorships. An aspect which is often overlooked and more difficult to quantify is the flow of expertise between authors from different research topics, which is an important part of scientific progress. With the Topic Flow Network (TFN) we propose a graph structure for the analysis of research topic flows between scientific authors and their respective research fields. Based on a multi-graph and a topic model, our proposed network structure accounts for intratopic as well as intertopic flows. Our method requires for the construction of a TFN solely a corpus of publications (i.e., author and abstract information). From this, research topics are discovered automatically through non-negative matrix factorization. The thereof derived TFN allows for the application of social network analysis techniques, such as common metrics and community detection. Most importantly, it allows for the analysis of intertopic flows on a large, macroscopic scale, i.e., between research topic, as well as on a microscopic scale, i.e., between certain sets of authors. We demonstrate the utility of TFNs by applying our method to two comprehensive corpora of altogether 20 Mio. publications spanning more than 60 years of research in the fields computer science and mathematics. Our results give evidence that TFNs are suitable, e.g., for the analysis of topical communities, the discovery of important authors in different fields, and, most notably, the analysis of intertopic flows, i.e., the transfer of topical expertise. Besides that, our method opens new directions for future research, such as the investigation of influence relationships between research fields.
  

• 1.

  Ganter, B., Hanika, T., Hirth, J.: Scaling Dimension. In: Dürrschnabel, D. and López-Rodríguez, D. (eds.) Formal Concept Analysis - 17th International Conference, ICFCA 2023, Kassel, Germany, July 17-21, 2023, Proceedings. pp. 64–77. Springer (2023). https://doi.org/10.1007/978-3-031-35949-1_5.

  URLBibTeXEndNoteDOI

  @inproceedings{DBLP:conf/icfca/GanterHH23,
  author = {Ganter, Bernhard and Hanika, Tom and Hirth, Johannes},
  booktitle = {Formal Concept Analysis - 17th International Conference, ICFCA 2023, Kassel, Germany, July 17-21, 2023, Proceedings},
  editor = {Dürrschnabel, Dominik and López-Rodríguez, Domingo},
  keywords = {itegpub},
  pages = {64--77},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Scaling Dimension},
  volume = 13934,
  year = 2023
  }
  

  %0 Conference Paper
  %1 DBLP:conf/icfca/GanterHH23
  %A Ganter, Bernhard
  %A Hanika, Tom
  %A Hirth, Johannes
  %B Formal Concept Analysis - 17th International Conference, ICFCA 2023, Kassel, Germany, July 17-21, 2023, Proceedings
  %D 2023
  %E Dürrschnabel, Dominik
  %E López-Rodríguez, Domingo
  %I Springer
  %P 64--77
  %R 10.1007/978-3-031-35949-1_5
  %T Scaling Dimension
  %U https://doi.org/10.1007/978-3-031-35949-1_5
  %V 13934