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<Paper uid="J03-1001">
  <Title>c(c) 2003 Association for Computational Linguistics Optimization Models of Sound Systems Using Genetic Algorithms</Title>
  <Section position="2" start_page="0" end_page="3" type="abstr">
    <SectionTitle>
1. Introduction
</SectionTitle>
    <Paragraph position="0"> Studies of the universal characteristics of sound systems in human languages can be pursued according to two different approaches, an inductive approach and a deductive one. The inductive approach involves analyzing the database built from a survey of a large number of languages to arrive at a list of &amp;quot;universal&amp;quot; features that can be widely observed in the database. The deductive approach hypothesizes a number of principles related to speech production and perception processes and predicts possible systems using these principles. These two approaches, however, are often interwoven.</Paragraph>
    <Paragraph position="1"> The principles hypothesized by the deductive approach are modified or falsified by comparing the predictions with the results from the inductive analysis of real language systems. At the same time, the ultimate aim for inductive analysis is to seek intrinsic mechanisms and principles of human speech to explain the universals found in real systems.</Paragraph>
    <Paragraph position="2"> For the inductive approach in phonological studies, there are two large-scale databases available. One is the Stanford Phonology Archiving (SPA) Project (Vihman 1977), which initially included 196 languages and was extended to 209 languages in  [?] Department of Electronic Engineering, City University of Hong Kong, Hong Kong. E-mail: jyke@ee. cityu.edu.hk + Linguistics Laboratory, Tsurumi University, Yokohama, Japan; Project on Linguistic Analysis, University of California at Berkeley. E-mail: ogura-m@tsurumi-u.ac.jp ++ Department of Electronic Engineering, City University of Hong Kong, Hong Kong; Project on  Computational Linguistics Volume 29, Number 1 1978. The other is the Phonological Segment Inventory Database (UPSID) (Maddieson 1984) at the University of California at Los Angeles, which initially included 371 languages and was later extended to 451 languages (Maddieson and Precoda 1990; Ladefoged and Maddieson 1996). Many typological studies have been carried out based on these two databases. For example, in studying vowel systems, Crothers (1978) reported an analysis using the SPA database. Ladefoged and Maddieson (1990) and Schwartz et al. (1997b) reported comprehensive analyses for the vowels systems in UPSID.</Paragraph>
    <Paragraph position="3"> Along with typological studies of the languages in these databases, explanatory models, which attempt to explore the intrinsic reasons for structures and universals, have also been proposed. In the study of vowel systems, the principle of maximal perceptual contrast has a long tradition in linguistics (Jakobson 1941; Wang 1968). This principle suggests that a vowel system tends to achieve a maximum contrast among the vowels in the system. A number of numerical studies adopting this principle have been proposed (Liljencrants and Lindblom 1972; Crothers 1978; Lindblom 1986). Lindblom (1986) proposed the sufficient perceptual contrast principle, under which more systems are predicted to be consistent with natural systems than is predicted by the maximal perceptual contrast principle. Bo&amp;quot;e, Schwartz, and Vall 'ee (1994) and Schwartz et al. (1997a) added a new consideration called the focalization principle that is based on the observation that vowels with strong formant convergence would be perceptually preferred. More recently, de Boer (1997, 2000, 2001) proposed a synthesized model in which agents interact with each other through iterative imitation games. With explicit optimization, agents can develop coherent vowel systems that are close to real systems. All of the works cited above are concerned with vowel systems. Far fewer studies are reported on other components of a sound system, including consonants, tones (in tone languages), and pitch accent (in non-tone languages), than on vowels. Lindblom and Maddieson (1988) reported a study on phonetic universals in consonant systems using data from UPSID. They proposed that the structure of consonant systems does not arise from a single principle such as the maximization of perceptual contrast. Instead, articulatory factors interact with perceptual factors. According to their proposal, consonant inventories tend to evolve so as to achieve maximal perceptual distinctiveness at minimum articulatory cost.</Paragraph>
    <Paragraph position="4"> There are some inductive studies on the universals of tone systems as well. For example, Maddieson (1978) reviewed the phonological universals of tones by analyzing data from SPA. Also, Cheng (1973) reported a detailed analysis of the tone systems in Chinese dialects. We have not, however, found any explanatory models that apply a deductive approach for tone systems in the way that such an approach has been applied for vowel systems.</Paragraph>
    <Paragraph position="5"> More recently, Redford, Chen, and Miikkulainen (2001) reported their studies on the universal and variations of syllable structures (i.e., the combinations of vowels and consonants). They developed a computational model based on a version of the genetic algorithm (GA) (Holland 1975) to simulate the emergence of syllable systems in a language. A set of functional constraints related to perceptual distinctiveness and articulatory ease are taken into account as optimization objectives.</Paragraph>
    <Paragraph position="6"> In this study, we report some optimization models using GAs to study optimal vowel and tone systems. In these models, the optimal systems are derived from the models based on various explicit optimization criteria and compared with observed systems. First, in the study of vowel systems, we compare two sets of criteria, one considering only the principle of maximal perceptual contrast (Liljencrants and Lindblom 1972), and the other considering both the intervowel perceptual distance and the intravowel spectral salience, that is, the dispersion-focalization principle proposed by Schwartz et al. (1997a). In the second set of criteria, the two objectives, that is, inter- null Ke, Ogura, and Wang Optimization Models of Sound Systems Using GA vowel perceptual distance and the intravowel spectral salience, are combined into a scalar function. In comparing our results with those of earlier studies, we find that the GA models demonstrate the effectiveness of the GA method in identifying the optimal vowel systems based on the above criteria.</Paragraph>
    <Paragraph position="7"> Second, we apply the GA method to study tone systems. In our application, two objectives (maximum perceptual contrast and minimum markedness complexity) are taken into account to predict the &amp;quot;optimal&amp;quot; tone systems. Instead of combining the two objectives into one fitness function, we use a multi-objective GA (MOGA) model in which a Pareto ranking method is applied for the fitness function. For comparison, we also try a simple GA model that uses only perceptual distance as the optimization criterion. The predicted systems are compared with the real systems for the two sets of criteria.</Paragraph>
    <Paragraph position="8"> In the following parts of the article, Section 2 gives a brief introduction to a simple GA and a MOGA. Section 3 reports the simulation we performed for vowel systems and comparisons with previous reports. Section 4 introduces our models for tone systems, together with a new analysis of an available tone systems database. Conclusions and discussion are given in Section 5.</Paragraph>
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