Abstract
In this chapter we present a network theoretic approach to linguistics. In particular, we introduce a network model of derivational morphology in languages. We focus on suffixation as a mechanism to derive new words from existing ones. We induce networks of natural language data consisting of words, derivation suffixes and parts of speech (PoS) as well as the relations between them. Measuring the entropy of these networks by means of so called information functionals we aim at capturing the variation between typologically different languages. In this way, we rely on the work of Dehmer (Appl Math Comput 201:82–94, 2008) who has introduced a framework for measuring the entropy of graphs. In addition, we compare several entropy measures recently presented for graphs. We check whether these measures allow us to distinguish between language networks on the one hand, and random networks on the other.We found out, that linguistic variation among languages can be captured by investigating the topology of the underlying networks. Further, information functionals based on distributions of topological properties turned out to be better discriminators than those that are based on properties of single vertices.
MSC2010 Primary 94C15; Secondary 90C35, 05C90.
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Notes
- 1.
In fact, only 4 nodes of 136 have a degree > 1.
- 2.
Dehmer [12] uses log to calculate the entropy. We use ln here for all functionals, which does not have any impact on the final results of the relative entropy (see the definition below) values.
- 3.
We selected these combinations since they performed best in the parameter study shown in Table 11.6.
- 4.
ER graphs are connected undirected random [15] graphs of the cardinality of German and English. BA [5] and WA [39] are randomly generated small world graphs of the cardinality of German. We generate ten graphs of each kind of random network (i.e., ten graphs for ER, ten for BA, etc.) and compare the averaged entropy values.
- 5.
See [21] for details.
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Acknowledgements
We would like to express our gratitude to Alexander Mehler and Kirill Medvedev for fruitful discussions and comments. Our special thanks goes to Matthias Dehmer whose useful hints and recommendations helped to improve this chapter.
This work is supported by the Linguisitc Networks project (http://www.linguistic- networks.net/) funded by the German Federal Ministry of Education and Research (BMBF), and by the German Research Foundation Deutsche Forschungsgemeinschaft (DFG) in the Collaborative Research Center 673 “Alignment in Communication.”
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Abramov, O., Lokot, T. (2011). Typology by Means of Language Networks: Applying Information Theoretic Measures to Morphological Derivation Networks. In: Dehmer, M., Emmert-Streib, F., Mehler, A. (eds) Towards an Information Theory of Complex Networks. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4904-3_11
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