
List of publications and preprints by Tom Hanika
2023
- Ganter, B., Hanika, T., Hirth, J.: Scaling Dimension, https://arxiv.org/abs/2302.09101, (2023).
@misc{https://doi.org/10.48550/arxiv.2302.09101,
author = {Ganter, Bernhard and Hanika, Tom and Hirth, Johannes},
keywords = {publist},
note = {Accepted for Publication at ICFCA 2023},
publisher = {arXiv},
title = {Scaling Dimension},
year = 2023
}%0 Generic
%1 https://doi.org/10.48550/arxiv.2302.09101
%A Ganter, Bernhard
%A Hanika, Tom
%A Hirth, Johannes
%D 2023
%I arXiv
%R 10.48550/ARXIV.2302.09101
%T Scaling Dimension
%U https://arxiv.org/abs/2302.09101 - Hirth, J., Horn, V., Stumme, G., Hanika, T.: Ordinal Motifs in Lattices, http://arxiv.org/abs/2304.04827, (2023).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.
@misc{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},
keywords = {publist},
title = {Ordinal Motifs in Lattices},
year = 2023
}%0 Generic
%1 hirth2023ordinal
%A Hirth, Johannes
%A Horn, Viktoria
%A Stumme, Gerd
%A Hanika, Tom
%D 2023
%R 10.48550/arXiv.2304.04827
%T Ordinal Motifs in Lattices
%U http://arxiv.org/abs/2304.04827
%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. - Hirth, J., Horn, V., Stumme, G., Hanika, T.: Automatic Textual Explanations of Concept Lattices, http://arxiv.org/abs/2304.08093, (2023).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.
@misc{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},
keywords = {xai},
title = {Automatic Textual Explanations of Concept Lattices},
year = 2023
}%0 Generic
%1 hirth2023automatic
%A Hirth, Johannes
%A Horn, Viktoria
%A Stumme, Gerd
%A Hanika, Tom
%D 2023
%R 10.48550/arXiv.2304.08093
%T Automatic Textual Explanations of Concept Lattices
%U http://arxiv.org/abs/2304.08093
%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. - Hanika, T., Hirth, J.: Conceptual Views on Tree Ensemble Classifiers CoRR. abs/2302.05270, (2023).
@article{DBLP:journals/corr/abs-2302-05270,
author = {Hanika, Tom and Hirth, Johannes},
journal = {CoRR},
keywords = {xai},
title = {Conceptual Views on Tree Ensemble Classifiers},
volume = {abs/2302.05270},
year = 2023
}%0 Journal Article
%1 DBLP:journals/corr/abs-2302-05270
%A Hanika, Tom
%A Hirth, Johannes
%D 2023
%J CoRR
%R 10.48550/arXiv.2302.05270
%T Conceptual Views on Tree Ensemble Classifiers
%U https://doi.org/10.48550/arXiv.2302.05270
%V abs/2302.05270 - Stubbemann, M., Hanika, T., Schneider, F.M.: Intrinsic Dimension for Large-Scale Geometric Learning Transactions on Machine Learning Research. (2023).The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID) that employs more complex feature functions, e.g., distances between data points. Yet, many of these approaches are based on empirical observations, cannot cope with the geometric character of contemporary datasets, and do lack an axiomatic foundation. A different approach was proposed by V. Pestov, who links the intrinsic dimension axiomatically to the mathematical concentration of measure phenomenon. First methods to compute this and related notions for ID were computationally intractable for large-scale real-world datasets. In the present work, we derive a computationally feasible method for determining said axiomatic ID functions. Moreover, we demonstrate how the geometric properties of complex data are accounted for in our modeling. In particular, we propose a principle way to incorporate neighborhood information, as in graph data, into the ID. This allows for new insights into common graph learning procedures, which we illustrate by experiments on the Open Graph Benchmark.
@article{stubbemann2022intrinsic,
abstract = {The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID) that employs more complex feature functions, e.g., distances between data points. Yet, many of these approaches are based on empirical observations, cannot cope with the geometric character of contemporary datasets, and do lack an axiomatic foundation. A different approach was proposed by V. Pestov, who links the intrinsic dimension axiomatically to the mathematical concentration of measure phenomenon. First methods to compute this and related notions for ID were computationally intractable for large-scale real-world datasets. In the present work, we derive a computationally feasible method for determining said axiomatic ID functions. Moreover, we demonstrate how the geometric properties of complex data are accounted for in our modeling. In particular, we propose a principle way to incorporate neighborhood information, as in graph data, into the ID. This allows for new insights into common graph learning procedures, which we illustrate by experiments on the Open Graph Benchmark.},
author = {Stubbemann, Maximilian and Hanika, Tom and Schneider, Friedrich Martin},
journal = {Transactions on Machine Learning Research},
keywords = {publist},
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
%X The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID) that employs more complex feature functions, e.g., distances between data points. Yet, many of these approaches are based on empirical observations, cannot cope with the geometric character of contemporary datasets, and do lack an axiomatic foundation. A different approach was proposed by V. Pestov, who links the intrinsic dimension axiomatically to the mathematical concentration of measure phenomenon. First methods to compute this and related notions for ID were computationally intractable for large-scale real-world datasets. In the present work, we derive a computationally feasible method for determining said axiomatic ID functions. Moreover, we demonstrate how the geometric properties of complex data are accounted for in our modeling. In particular, we propose a principle way to incorporate neighborhood information, as in graph data, into the ID. This allows for new insights into common graph learning procedures, which we illustrate by experiments on the Open Graph Benchmark. - Stubbemann, M., Hille, T., Hanika, T.: Selecting Features by their Resilience to the Curse of Dimensionality (2023).
@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