Modeling the Structure and Dynamics of the Consonant Inventories: A Complex Network Approach Animesh Mukherjee1, Monojit Choudhury2, Anupam Basu1, Niloy Ganguly1 1Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India – 721302 2Microsoft Research India, Bangalore, India – 560080 animeshm,anupam,niloy @cse.iitkgp.ernet.in, { [email protected]} Abstract ior through certain general principles such as max- imal perceptual contrast (Liljencrants and Lind- We study the self-organization of the con- blom, 1972), ease of articulation (Lindblom and sonant inventories through a complex net- Maddieson, 1988; de Boer, 2000), and ease of work approach. We observe that the dis- learnability (de Boer, 2000). In fact, there are a tribution of occurrence as well as co- lot of studies that attempt to explain the emergence occurrence of the consonants across lan- of the vowel inventories through the application of guages follow a power-law behavior. The one or more of the above principles (Liljencrants co-occurrence network of consonants ex- and Lindblom, 1972; de Boer, 2000). Some studies hibits a high clustering coefficient. We have also been carried out in the area of linguistics propose four novel synthesis models for that seek to reason the observed patterns in the con- these networks (each of which is a refine- sonant inventories (Trubetzkoy, 1939; Lindblom ment of the earlier) so as to successively and Maddieson, 1988; Boersma, 1998; Clements, match with higher accuracy (a) the above 2008). Nevertheless, most of these works are con- mentioned topological properties as well fined to certain individual principles rather than as (b) the linguistic property of feature formulating a general theory describing the emer- economy exhibited by the consonant inven- gence of these regular patterns across the conso- tories. We conclude by arguing that a pos- nant inventories. sible interpretation of this mechanism of network growth is the process of child lan- The self-organization of the consonant inven- guage acquisition. Such models essentially tories emerges due to an interaction of different increase our understanding of the struc- forces acting upon them. In order to identify the ture of languages that is influenced by their nature of these interactions one has to understand evolutionary dynamics and this, in turn, the growth dynamics of these inventories. The the- can be extremely useful for building future ories of complex networks provide a number of NLP applications. growth models that have proved to be extremely successful in explaining the evolutionary dynam- 1 Introduction ics of various social (Newman, 2001; Ramasco et al., 2004), biological (Jeong et al., 2000) and other A large number of regular patterns are observed natural systems. The basic framework for the cur- across the sound inventories of human languages. rent study develops around two such complex net- These regularities are arguably a consequence of works namely, the Phoneme-Language Network the self-organization that is instrumental in the or PlaNet (Choudhury et al., 2006) and its one- emergence of these inventories (de Boer, 2000). mode projection, the Phoneme-Phoneme Network Many attempts have been made by functional pho- or PhoNet (Mukherjee et al.2007a). We begin by nologists for explaining this self-organizing behav- analyzing some of the structural properties (Sec. 2) c 2008. Licensed under the Creative Commons of the networks and observe that the consonant Attribution-Noncommercial-Share° Alike 3.0 Unported li- cense (http://creativecommons.org/licenses/by-nc-sa/3.0/). nodes in both PlaNet and PhoNet follow a power- Some rights reserved. law-like degree distribution. Moreover, PhoNet 601 Proceedings of the 22nd International Conference on Computational Linguistics (Coling 2008), pages 601–608 Manchester, August 2008 is characterized by a high clustering coefficient, a property that has been found to be prevalent in many other social networks (Newman, 2001; Ra- masco et al., 2004). We propose four synthesis models for PlaNet (Sec. 3), each of which employ a variant of a pref- erential attachment (Barabasi´ and Albert, 1999) based growth kernel1. While the first two mod- els are independent of the characteristic proper- ties of the (consonant) nodes, the following two use them. These models are successively refined not only to reproduce the topological properties of Figure 1: Illustration of the nodes and edges of PlaNet and PhoNet, but also to match the linguis- PlaNet and PhoNet. tic property of feature economy (Boersma, 1998; Clements, 2008) that is observed across the conso- is the set of edges running between and . nant inventories. The underlying growth rules for Epl VL VC There is an edge from a node to a each of these individual models helps us to inter- e Epl vl VL node iff the∈ consonant is present∈ in the pret the cause of the emergence of at least one (or vc VC c inventory∈ of language . more) of the aforementioned properties. We con- l clude (Sec. 4) by providing a possible interpreta- PhoNet is the one-mode projection of PlaNet tion of the proposed mathematical model that we onto the consonant nodes i.e., a network of con- finally develop in terms of child language acquisi- sonants in which two nodes are linked by an edge tion. with weight as many times as they co-occur across There are three major contributions of this work. languages. Hence, it can be represented by a graph G = V , E , where V is the set of conso- Firstly, it provides a fascinating account of the h C ph i C structure and the evolution of the human speech nant nodes and Eph is the set of edges connecting these nodes in G. There is an edge e E if the sound systems. Furthermore, the introduction of ∈ ph the node property based synthesis model is a sig- two nodes (read consonants) that are connected by nificant contribution to the field of complex net- e co-occur in at least one language and the number works. On a broader perspective, this work shows of languages they co-occur in defines the weight of how statistical mechanics can be applied in under- the edge e. Figure 1 shows the nodes and the edges standing the structure of a linguistic system, which of PlaNet and PhoNet. in turn can be extremely useful in developing fu- Data Source and Network Construction: Like ture NLP applications. many other earlier studies (Liljencrants and Lind- blom, 1972; Lindblom and Maddieson, 1988; de 2 Properties of the Consonant Boer, 2000; Hinskens and Weijer, 2003), we use Inventories the UCLA Phonological Segment Inventory Data- base (UPSID) (Maddieson, 1984) as the source of In this section, we briefly recapitulate the defi- our data. There are 317 languages in the data- nitions of PlaNet and PhoNet, the data source, base with a total of 541 consonants found across construction procedure for the networks and some them. Each consonant is characterized by a set of of their important structural properties. We also phonological features (Trubetzkoy, 1931), which revisit the concept of feature economy and the distinguishes it from others. UPSID uses articula- method used for its quantification. tory features to describe the consonants, which can be broadly categorized into three different types 2.1 Structural Properties of the Consonant namely the manner of articulation, the place of Networks articulation and phonation. Manner of articu- PlaNet is a bipartite graph G = V , V , E con- h L C pl i lation specifies how the flow of air takes place sisting of two sets of nodes namely, VL (labeled by in the vocal tract during articulation of a conso- the languages) and VC (labeled by the consonants); nant, whereas place of articulation specifies the 1The word kernel here refers to the function or mathemat- active speech organ and also the place where it ical formula that drives the growth of the network. acts. Phonation describes the vibration of the vo- 602 Manner of Articulation Place of Articulation Phonation suitably modified by the one presented in (Barrat tap velar voiced flap uvular voiceless et al., 2004). According to this definition, the clus- trill dental click palatal tering coefficient for a node i is, nasal glottal plosive bilabial 1 (wij + wil) r-sound alveolar ci = aijailajl fricative retroflex 2 affricate pharyngeal j wij (ki 1) j,l ∀ − X∀ implosive labial-velar ³ ´ (1) approximant labio-dental P ejective stop labial-palatal where j and l are neighbors of i; ki represents the affricated click dental-palatal ejective affricate dental-alveolar plain degree of the node i; wij, wjl and wil de- ejective fricative palato-alveolar note the weights of the edges connecting nodes i lateral approximant and j, j and l, and i and l respectively; aij, ail, Table 1: The table shows some of the important ajl are boolean variables, which are true iff there features listed in UPSID. Over 99% of the UPSID is an edge between the nodes i and j, i and l, and j languages have bilabial, dental-alveolar and velar and l respectively. The clustering coefficient of the plosives. Furthermore, voiceless plosives outnum- network (cav) is equal to the average clustering co- ber the voiced ones (92% vs. 67%). 93% of the efficient of the nodes. The value of cav for PhoNet languages have at least one fricative, 97% have at is 0.89, which is significantly higher than that of a least one nasal and 96% have at least one liquid. random graph with the same number of nodes and Approximants occur in fewer than 95% of the lan- edges (0.08). guages. 2.2 Linguistic Properties: Feature Economy and its Quantification cal cords during the articulation of a consonant. The principle of feature economy states that lan- Apart from these three major classes there are also guages tend to use a small number of distinctive some secondary articulatory features found in cer- features and maximize their combinatorial pos- tain languages.