Abstract
In this paper we introduce and study description quivers as compact representations of concept lattices and respective ensembles of decision trees. Formally, description quivers are directed multigraphs where vertices represent concept intents and (multiple) edges represent generators of intents. We study some properties of description quivers and shed light on their use for describing state-of-the-art symbolic machine learning models based on decision trees. We also argue that a concept lattice can be considered as a cornerstone in constructing an efficient machine learning model. We show that the proposed description quivers allow us to fuse decision trees just as we can sum linear regressions, while proposing a way to select the most important rules in decision models, just as we can select the most important coefficients in regressions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Coenen, F. (2003), The LUCS-KDD Discretised/normalised ARM and CARM Data Library, http://www.csc.liv.ac.uk/~frans/KDD/Software/LUCS_KDD_DN/, Department of Computer Science, The University of Liverpool, UK.
References
Aldinucci, T., Civitelli, E., Di Gangi, L., Sestini, A.: Contextual Decision Trees. arXiv preprint arXiv:2207.06355 (2022)
Bělohlávek, R., De Baets, B., Outrata, J., Vychodil, V.: Characterizing trees in concept lattices. Internat. J. Uncertain. Fuzziness Knowl. Based Syst. 16, 1–15 (2008)
Bělohlávek, R., De Baets, B., Outrata, J., Vychodil, V.: Inducing decision trees via concept lattices. Int. J. Gen Syst 38(4), 455–467 (2009)
Breiman, L.: Random forests. Mach. Learn. 45, 5–32 (2001)
Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification and Regression Trees. Wadsworth, New York (1984)
Buzmakov, A., Dudyrev, E., Kuznetsov, S.O., Makhalova, T., Napoli, A.: Experimental study of concise representations of concepts and dependencies. In: Cordero, P., Krídlo, O. (eds.) Proceedings of the Sixteenth International Conference on Concept Lattices and Their Applications (CLA 2022), pp. 117–132. CEUR Workshop Proceedings 3308, CEUR-WS.org (2022)
Dudyrev, E., Kuznetsov, S.O.: Decision concept lattice vs. decision trees and random forests. In: Braud, A., Buzmakov, A., Hanika, T., Le Ber, F. (eds.) ICFCA 2021. LNCS (LNAI), vol. 12733, pp. 252–260. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77867-5_16
Dudyrev, E., Kuznetsov, S.O.: Summation of Decision Trees. In: Kuznetsov, S.O., Napoli, A., Rudolph, S. (eds.) Proceedings of the 9th International Workshop FCA4AI co-located with IJCAI 2021, pp. 99–104. CEUR Workshop Proceedings 2972, CEUR-WS.org (2021)
Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Berlin (1999). https://doi.org/10.1007/978-3-030-77867-5
Hanika, T., Hirth, J.: Conceptual Views on Tree Ensemble Classifiers. arXiv preprint arXiv:2302.05270 (2023)
Kuznetsov, S.O.: Machine learning and formal concept analysis. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 287–312. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24651-0_25
Strecht, P.: A survey of merging decision trees data mining approaches. In: Proceedings of the 10th Doctoral Symposium in Informatics Engineering (DSIE 2015), pp. 36–47 (2015)
Wille, R.: Line diagrams of hierarchical concept systems. Knowl. Organ. 11(2), 77–86 (1984). Nomos Verlagsgesellschaft mbH & Co. KG
Acknowledgments
The work on Sects. 1 and 2 was done by Sergei O. Kuznetsov under support of the Russian Science Foundation under grant 22-11-00323 and performed at HSE University, Moscow, Russia.
Egor Dudyrev and Amedeo Napoli are carrying out this research work as part of the French ANR-21-CE23-0023 SmartFCA Research Project.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Dudyrev, E., Kuznetsov, S.O., Napoli, A. (2023). Description Quivers for Compact Representation of Concept Lattices and Ensembles of Decision Trees. In: Dürrschnabel, D., López Rodríguez, D. (eds) Formal Concept Analysis. ICFCA 2023. Lecture Notes in Computer Science(), vol 13934. Springer, Cham. https://doi.org/10.1007/978-3-031-35949-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-35949-1_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-35948-4
Online ISBN: 978-3-031-35949-1
eBook Packages: Computer ScienceComputer Science (R0)