Emergence of Community Structures in Vowel Inventories:An Analysis based on Complex Networks

Abstract

In this work, we attempt to capture patternsof co-occurrence across vowel systems andat the same time figure out the nature of theforce leading to the emergence of such pat-terns. For this purpose we define a weightednetwork where the vowels are the nodesand an edge between two nodes (read vow-els) signify their co-occurrence likelihoodover the vowel inventories. Through thisnetwork we identify communities of vow-els, which essentially reflect their patternsof co-occurrence across languages. We ob-serve that in the assortative vowel communi-ties the constituent nodes (read vowels) arelargely uncorrelated in terms of their fea-tures indicating that they are formed basedon the principle of maximal perceptual con-trast. However, in the rest of the communi-ties, strong correlations are reflected amongthe constituent vowels with respect to theirfeatures indicating that it is the principle offeature economy that binds them together.

1 Introduction

Linguistic research has documented a wide range ofregularities across the sound systems of the world’slanguages (Liljencrants and Lindblom, 1972; Lind-blom, 1986; de Boer, 2000; Choudhury et al., 2006;Mukherjee et al., 2006a; Mukherjee et al., 2006b).Functional phonologists argue that such regulari-ties are the consequences of certain general princi-ples likemaximal perceptual contrast(Liljencrants

and Lindblom, 1972), which is desirable betweenthe phonemes of a language for proper percep-tion of each individual phoneme in a noisy envi-ronment,ease of articulation(Lindblom and Mad-dieson, 1988; de Boer, 2000), which requires thatthe sound systems of all languages are formed ofcertain universal (and highly frequent) sounds, andease of learnability(de Boer, 2000), which is re-quired so that a speaker can learn the sounds ofa language with minimum effort. In the study ofvowel systems the optimizing principle, which hasa long tradition (Jakobson, 1941; Wang, 1968) inlinguistics, is maximal perceptual contrast. A num-ber of numerical studies based on this principle havebeen reported in literature (Liljencrants and Lind-blom, 1972; Lindblom, 1986; Schwartz et al., 1997).Of late, there have been some attempts to explain thevowel systems through multi agent simulations (deBoer, 2000) and genetic algorithms (Ke et al., 2003);all of these experiments also use the principle of per-ceptual contrast for optimization purposes.

An exception to the above trend is a school oflinguists (Boersma, 1998; Clements, 2004) who ar-gue that perceptual contrast-based theories fail to ac-count for certain fundamental aspects such as thepatterns of co-occurrence of vowels based on sim-ilar acoustic/articulatoryfeatures1 observed across

1In linguistics, features are the elements, which distinguishone phoneme from another. The features that describe thevowles can be broadly categorized into three different classesnamely theheight, the backnessand theroundedness. Heightrefers to the vertical position of the tongue relative to either theroof of the mouth or the aperture of the jaw. Backness refersto the horizontal tongue position during the articulation of avowel relative to the back of the mouth. Roundedness refers towhether the lips are rounded or not during the articulation of a

the vowel inventories. Instead, they posit that theobserved patterns, especially found in larger size in-ventories (Boersma, 1998), can be explained onlythrough the principle offeature economy(de Groot,1931; Martinet, 1955). According to this principle,languages tend to maximize the combinatorial pos-sibilities of a few distinctive features to generate alarge number of sounds.

The aforementioned ideas can be possibly linkedtogether through the example illustrated by Figure 1.As shown in the figure, the initial planeP constitutesof a set of three very frequently occurring vowels /i/,/a/ and /u/, which usually make up the smaller in-ventories and do not have any single feature in com-mon. Thus, smaller inventories are quite likely tohave vowels that exhibit a large extent of contrastin their constituent features. However, in bigger in-ventories, members from the higher planes (P ′ andP ′′) are also present and they in turn exhibit fea-ture economy. For instance, in the planeP ′ com-prising of the set of vowels /i/, /a/, /u/, we find anasal modification applied equally on all the threemembers of the set. This is actually indicative of aneconomic behavior that the larger inventories showwhile choosing a new feature in order to reduce thelearnability effort of the speakers. The third planeP ′′ reinforces this idea by showing that the largerthe size of the inventories the greater is the urge forthis economy in the choice of new features. An-other interesting facet of the figure are the relationsthat exist across the planes (indicated by the bro-ken lines). All these relations are representative of acommon linguistic concept ofrobustness(Clements,2004) in which one frequently occurring vowel (say/i/) implies the presence of the other (and not viceversa) less frequently occurring vowel (say /i/) in alanguage inventory. These cross-planar relations arealso indicative of feature economy since all the fea-tures present in the frequent vowel (e.g., /i/) are alsoshared by the less frequent one (e.g., /i/). In sum-mary, while the basis of organization of the vowelinventories is perceptual contrast as indicated bythe planeP in Figure 1, economic modifications ofthe perceptually distinct vowels takes place with the

vowel. There are however still more possible features of vowelquality, such as the velum position (e.g., nasality), type of vocalfold vibration (i.e., phonation), and tongue root position (i.e.,secondary place of articulation).

increase in the inventory size (as indicated by theplanesP ′ andP ′′ in Figure 1).

In this work we attempt to corroborate the aboveconjecture by automatically capturing the patterns ofco-occurrence that are prevalentin and acrosstheplanes illustrated in Figure 1. In order to do so,we define the “Vowel-Vowel Network” or VoNet,which is a weighted network where the vowels arethe nodes and an edge between two nodes (read vow-els) signify their co-occurrence likelihood over thevowel inventories. We conduct community struc-ture analysis of different versions of VoNet in or-der to capture the patterns of co-occurrence in andacross the planesP , P ′ andP ′′ shown in Figure 1.The planeP consists of the communities, whichare formed of those vowels that have a very highfrequency of occurrence (usuallyassortative(New-man, 2003) in nature). We observe that the con-stituent nodes (read vowels) of these assortativevowel communities are largely uncorrelated in termsof their features. On the other hand, the commu-nities obtained from VoNet, in which the links be-tween the assortative nodes are absent, correspondsto the co-occurrence patterns of the planesP ′ andP ′′. In these communities, strong correlations arereflected among the constituent vowels with respectto their features. Moreover, the co-occurrencesacross the planes can be captured by the communityanalysis of VoNet where only the connections be-tween the assortative and the non-assortative nodes,with the non-assortative node co-occurring very fre-quently with the assortative one, are retained whilethe rest of the connections are filtered out. We findthat these communities again exhibit a high correla-tion among the constituent vowels.

This article is organized as follows: Section 2 de-scribes the experimental setup in order to explorethe co-occurrence principles of the vowel inven-tories. In this section we formally define VoNet,outline its construction procedure, and present acommunity-finding algorithm in order to capture theco-occurrence patterns across the vowel systems. Insection 3 we report the experiments performed toobtain the community structures, which are repre-sentative of the co-occurrence patterns in and acrossthe planes discussed above. Finally, we conclude insection 4 by summarizing our contributions, point-ing out some of the implications of the current work

Figure 1: The organizational principles of the vowels (in decreasing frequency of occurrence) indicatedthrough different hypothetical planes.

and indicating the possible future directions.

2 Experimental Setup

In this section we systematically develop the ex-perimental setup in order to investigate the co-occurrence principles of the vowel inventories. Forthis purpose, we formally define VoNet, outlineits construction procedure, describe a community-finding algorithm to decompose VoNet to obtain thecommunity structures that essentially reflects the co-occurrence patterns of the vowel inventories.

2.1 Definition and Construction of VoNet

Definition of VoNet: We define VoNet as a networkof vowels, represented as G =〈 VV , E 〉 where VV

is the set of nodes labeled by the vowels and E isthe set of edges occurring in VoNet. There is anedgee ∈ E between two nodes, if and only if thereexists one or more language(s) where the nodes(read vowels) co-occur. The weight of the edgee(also edge-weight) is the number of languages inwhich the vowels connected bye co-occur. Theweight of a nodeu (alsonode-weight) is the numberof languages in which the vowel represented byuoccurs. In other words, if a vowelvi represented by

the nodeu occurs in the inventory ofn languagesthen the node-weight ofu is assigned the valuen. Also if the vowelvj is represented by the nodev and there arew languages in which vowelsvi

and vj occur together then the weight of the edgeconnectingu andv is assigned the valuev. Figure 2illustrates this structure by reproducing some of thenodes and edges of VoNet.

Construction of VoNet: Many typological stud-ies (Lindblom and Maddieson, 1988; Ladefogedand Maddieson, 1996; Hinskens and Weijer, 2003;Choudhury et al., 2006; Mukherjee et al., 2006a;Mukherjee et al., 2006b) of segmental inventorieshave been carried out in past on the UCLA Phono-logical Segment Inventory Database (UPSID) (Mad-dieson, 1984). Currently UPSID records the soundinventories of 451 languages covering all the ma-jor language families of the world. In this work wehave therefore used UPSID comprising of these 451languages and 180 vowels found across them, forconstructing VoNet. Consequently, the set VV com-prises of 180 elements (nodes) and the set E com-prises of 3135 elements (edges). Figure 3 presentsa partial illustration of VoNet as constructed from

Figure 3: A partial illustration of VoNet. All edges in this figure have an edge-weight greater than or equal to15. The number on each node corresponds to a particular vowel. For instance, node number 72 correspondsto /i/.

Figure 2: A partial illustration of the nodes andedges in VoNet. The labels of the nodes denote thevowels represented in IPA (International PhoneticAlphabet). The numerical values against the edgesand nodes represent their corresponding weights.For example /i/ occurs in 393 languages; /e/ occursin 124 languages while they co-occur in 117 lan-guages.

UPSID.

2.2 Finding Community Structures

We attempt to identify the communities appearingin VoNet by the extended Radicchi et al. (Radic-chi et al., 2003) algorithm for weighted networkspresented in (Mukherjee et al., 2006a). The ba-sic idea is that if the weights on the edges form-ing a triangle (loops of length three) are comparablethen the group of vowels represented by this trian-gle highly occur together rendering a pattern of co-occurrence while if these weights are not compara-ble then there is no such pattern. In order to capturethis property we define a strength metricS (in thelines of (Mukherjee et al., 2006a)) for each of theedges of VoNet as follows. Let the weight of theedge (u,v), whereu, v ∈ VC , be denoted bywuv.We defineS as,

S =wuv√∑

i∈VC−{u,v} (wui − wvi)2

(1)

if√∑

i∈VC−{u,v} (wui − wvi)2 > 0 elseS = ∞.

The denominator in this expression essentially triesto capture whether or not the weights on the edges

forming triangles are comparable (the higher thevalue of S the more comparable the weights are).The network can be then decomposed into clustersor communities by removing edges that haveS lessthan a specified threshold (sayη).

At this point it is worthwhile to clarify the sig-nificance of a vowel community. A community ofvowels actually refers to a set of vowels which occurtogether in the language inventories very frequently.In other words, there is a higher than expected prob-ability of finding a vowelv in an inventory which al-ready hosts the other members of the community towhichv belongs. For instance, if /i/, /a/ and /u/ forma vowel community and if /i/ and /a/ are present inany inventory then there is a very high chance thatthe third member /u/ is also present in the inventory.

3 Experiments and Results

In this section we describe the experiments per-formed and the results obtained from the analysis ofVoNet. In order to find the co-occurrence patternsin and across the planes of Figure 1 we define threeversions of VoNet namely VoNetassort, VoNetrest

and VoNetrest′ . The construction procedure foreach of these versions are presented below.

Construction of VoNetassort: VoNetassort com-prises of the assortative2 nodes having node-weightsabove 120 (i.e, vowels occurring in more than 120languages in UPSID), along with only the edgesinter-connecting these nodes. The rest of the nodes(having node-weight less than 120) and edges areremoved from the network. We make a choiceof this node-weight for classifying the assortativenodes from the non-assortative ones by observingthe distribution of the occurrence frequency of thevowels illustrated in Figure 4. The curve showsthe frequency of a vowel (y-axis) versus the rankof the vowel according to this frequency (x-axis)in log-log scale. The high frequency zone (markedby a circle in the figure) can be easily distinguishedfrom the low-frequency one since there is distinctgap featuring between the two in the curve.

Figure 5 illustrates how VoNetassort is con-

2The term “assortative node” here refers to the nodes havinga very high node-weight.

Figure 4: The frequency (y-axis) versus rank (x-axis) curve in log-log scale illustrating the distrib-ution of the occurrence of the vowels over the lan-guage inventories of UPSID.

Figure 5: The construction procedure of VoNetassort

from VoNet.

structed from VoNet. Presently, the number ofnodes in VoNetassort is 9 and the number of edgesis 36.

Construction of VoNetrest: VoNetrest comprisesof all the nodes as that of VoNet. It also has allthe edges of VoNet except for those edges thatinter-connect the assortative nodes. Figure 6 showshow VoNetrest can be constructed from VoNet. Thenumber of nodes and edges in VoNetrest are 180

Figure 6: The construction procedure of VoNetrest

from VoNet.

and 12933 respectively.

Construction of VoNetrest′ : VoNetrest′ againcomprises of all the nodes as that of VoNet. Itconsists of only the edges that connect an assor-tative node with a non-assortative one if the non-assortative node co-occurs more than ninety five per-cent of times with the assortative nodes. The basicidea behind such a construction is to capture the co-occurrence patterns based on robustness (Clements,2004) (discussed earlier in the introductory section)that actually defines the cross-planar relationships inFigure 1. Figure 7 shows how VoNetrest′ can beconstructed from VoNet. The number of nodes inVoNetrest′ is 180 while the number of edges is 1144.

We separately apply the community-finding al-gorithm (discussed earlier) on each of VoNetassort,VoNetrest and VoNetrest′ in order to obtain the re-spective vowel communities. We can obtain dif-ferent sets of communities by varying the thresholdη. A few assortative vowel communities (obtainedfrom VoNetassort) are noted in Table 1. Some of thecommunities obtained from VoNetrest are presented

3We have neglected nodes with node-weight less than 3since these nodes correspond to vowels that occur in less than 3languages in UPSID and the communities they form are there-fore statistically insignificant.

4The network does not get disconnected due to this construc-tion since, there is always a small fraction of edges that run be-tween assortative and low node-weight non-assortative nodes ofotherwise disjoint groups.

Figure 7: The construction procedure of VoNetrest′

from VoNet.

in Table 2. We also note some of the communitiesobtained from VoNetrest′ in Table 3.

Tables 1 , 2 and 3 indicate that the communi-ties in VoNetassort are formed based on the princi-ple of perceptual contrast whereas the formation ofthe communities in VoNetrest as well as VoNetrest′

is largely governed by feature economy. Hence,the smaller vowel inventories which are composedof mainly the members of VoNetassort are orga-nized based on the principle of maximal percep-tual contrast whereas the larger vowel inventories,which also contain members from VoNetrest andVoNetrest′ apart from VoNetassort, show a consid-erable extent of feature economy.

4 Conclusion

In this paper we explored the co-occurrence prin-ciples of the vowels, across the inventories of theworld’s languages. In order to do so we started witha concise review of the available literature on vowelinventories. We proposed an automatic procedureto extract the co-occurrence patterns of the vowelsacross languages.

Some of our important findings from this workare,

• The smaller vowel inventories (correspondingto the communities ofVoNetassort) tend to be organized based on theprinciple of maximal perceptual contrast;

Community Features in Contrast/i/, /a/, /u/ (low/high), (front/central/back), (unrounded/rounded)

/e/, /o/ (higher-mid/mid), (front/back), (unrounded/rounded)

Table 1: Assortative vowel communities. The contrastive features separated by slashes (/) are shown withinparentheses. Comma-separated entries represent the features that are in use from the three respective classesnamely the height, the backness, and the roundedness.

Community Features in Common

/i/, /a/, /u/ nasalized

/i:/, /a:/, /u:/ long, nasalized/i:/, /u:/, /a:/, /o:/, /e:/ long

Table 2: Some of the vowel communities obtained from VoNetrest.

Community Features in Common

/i/, /i/ high, front, unrounded/a/,/a/ low, central, unrounded/u/, /u/ high, back, rounded

Table 3: Some of the vowel communities obtained from VoNetrest′ . Comma-separated entries represent thefeatures that are in use from the three respective classes namely the height, the backness, and the rounded-ness.

• On the other hand, the larger vowel invento-ries (mainly comprising of the communities ofVoNetrest) reflect a considerable extent of fea-ture economy;

• Co-occurrences based on robustness are preva-lent across vowel inventories (captured throughthe communities of VoNetrest′) and their emer-gence is again a consequence of feature econ-omy.

Until now, we have concentrated mainly on themethodology that can be used to automatically cap-ture the co-occurrence patterns across the vowel sys-tems. However, it would be also interesting to in-vestigate the extent to which these patterns are gov-erned by the forces of maximal perceptual contrastand feature economy. Such an investigation callsfor quantitative definitions of the above forces anda thorough evaluation of the vowel communities interms of these definitions. We look forward to ac-complish the same as a part of our future work.

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