Discovering Global Patterns in Linguistic Networks through Spectral Analysis: A Case Study of the Consonant Inventories

Proceedings of the 12th Conference of the European Chapter of the ACL, pages 585–593, Athens, Greece, 30 March – 3 April 2009. c⃝2009 Association for Computational Linguistics Discovering Global Patterns in Linguistic Networks through Spectral Analysis: A Case Study of the Consonant Inventories Animesh Mukherjee∗ Indian Institute of Technology, Kharagpur animeshm@cse.iitkgp.ernet.in Monojit Choudhury and Ravi Kannan Microsoft Research India {monojitc,kannan}@microsoft.com Abstract Recent research has shown that language and the socio-cognitive phenomena asso- ciated with it can be aptly modeled and visualized through networks of linguistic entities. However, most of the existing works on linguistic networks focus only on the local properties of the networks. This study is an attempt to analyze the structure of languages via a purely struc- tural technique, namely spectral analysis, which is ideally suited for discovering the global correlations in a network. Appli- cation of this technique to PhoNet, the co-occurrence network of consonants, not only reveals several natural linguistic prin- ciples governing the structure of the con- sonant inventories, but is also able to quan- tify their relative importance. We believe that this powerful technique can be suc- cessfully applied, in general, to study the structure of natural languages. 1 Introduction Language and the associated socio-cognitive phe- nomena can be modeled as networks, where the nodes correspond to linguistic entities and the edges denote the pairwise interaction or relation- ship between these entities. The study of lin- guistic networks has been quite popular in the re- cent times and has provided us with several in- teresting insights into the nature of language (see Choudhury and Mukherjee (to appear) for an ex- tensive survey). Examples include study of the WordNet (Sigman and Cecchi, 2002), syntactic dependency network of words (Ferrer-i-Cancho, 2005) and network of co-occurrence of conso- nants in sound inventories (Mukherjee et al., 2008; Mukherjee et al., 2007). ∗This research has been conducted during the author’s in- ternship at Microsoft Research India. Most of the existing studies on linguistic net- works, however, focus only on the local structural properties such as the degree and clustering coef- ficient of the nodes, and shortest paths between pairs of nodes. On the other hand, although it is a well known fact that the spectrum of a network can provide important information about its global structure, the use of this powerful mathematical machinery to infer global patterns in linguistic net- works is rarely found in the literature. Note that spectral analysis, however, has been successfully employed in the domains of biological and social networks (Farkas et al., 2001; Gkantsidis et al., 2003; Banerjee and Jost, 2007). In the context of linguistic networks, (Belkin and Goldsmith, 2002) is the only work we are aware of that analyzes the eigenvectors to obtain a two dimensional visualize of the network. Nevertheless, the work does not study the spectrum of the graph. The aim of the present work is to demonstrate the use of spectral analysis for discovering the global patterns in linguistic networks. These pat- terns, in turn, are then interpreted in …

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