Goals Benefits New Harmony Patterns - Swarthmore Homethe calculation of the z-score (2 harmonic...
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Discovering new vowel harmony patterns using a pairwise statistical model Nathan Sanders and K. David Harrison (Swarthmore College) 20th Manchester Phonology Meeting, 24–26 May 2012 Goals Define a statistical measurement of vowel harmony over a corpus, in such a way that it can be meaningfully compared across corpora, languages, and harmonic features. Methods (1) Extract tier-adjacent vowel pairs from the corpus. For example, if the corpus contains the word krematoryum, the algorithm extracts ea, ao, and ou. For a given feature, like backness, compute the overall harmony percentage: the number of harmonic pairs divided by the total number of pairs. In this case, 2 out of 3 pairs are harmonic (ao, ou), so the percentage is 67%. (2) Using the total size of the corpus, the distributions of the vowels, and the distribution of word lengths, randomly generate a large number of corpora, and calculate the harmony percentage for each. (3) Compare the harmony of the original corpus to the distribution of harmony in the random corpora. e number of standard deviations the real corpus is from the mean of the random corpora is its z-score for harmony. Benefits e z-score is a normalized measure of statistical deviance, so it can be meaningfully compared from one case to any other, like the relative harmony between languages. Measures of whole-word harmony, like the h-index of Harrison et al.’s (2002–2004) Vowel Harmony Calculator (VHCalc), do not distinquish between different levels of disharmony, as in krematoryum versus eskavatör (both are categorically disharmonic), which contribute differently to the calculation of the z-score (2 harmonic pairs vs. 1). New Harmony Patterns First, there are bizarre cases of “anti-harmony”, where a language has a statistically significant negative z-score. For example, Swahili ’s pairwise backness harmony has a z-score of –11, well beyond the –2 needed for statistical significance. It’s not clear what anti-harmony might be… More importantly, many languages do not have harmony at the word level, but do have a large amount of pairwise harmony, and thus, have “hidden harmony”. For example, Estonian ’s h-index for backness harmony is 0.07, but it is very harmonic for vowel pairs (z = 24). In this case, the discrepancy is due to historical harmony that has leſt remnants in the lexicon. us, hidden harmony could be a diagnostic tool for reconstructing historical harmony. Hidden harmony may also have implications for the learnability of harmony or for development and/or loss of harmony over time. Comparison with VHCalc Despite the different underlying mathematics, the pairwise z-score and VHCalc’s whole-word h-index are strongly correlated, however there are still important differences: White regions are harmonic for both VHCalc and z-score (h-index > 0.3, |z-score| > 2). Gray regions are unharmonic for VHCalc, and blue regions are unharmonic for z-score. References Harrison, K.D., E. omforde, & M. O’Keefe. 2002–2004. e Vowel Harmony Calculator. http://www.swarthmore.edu/ SocSci/harmony/public_html/index.html pairwise z-score pairwise z-score VHCalc’s whole word h-index VHCalc’s whole word h-index VHCalc’s whole word h-index pairwise z-score backness (r ≈ 0.9) height (r ≈ 0.7) rounding (r ≈ 0.9) Estonian Estonian Spanish Indonesian Indonesian Japanese Japanese Uzbek Uzbek Estonian Indonesian Japanese Swahili Karakpalak Tuvan Spanish Turkish Finnish Swahili Swahili Zulu Zulu Zulu Ingrian Ingrian Ingrian Votic Votic Spanish Votic Azeri Kyrgyz Turkish Turkish Tuvan Tuvan Karakpalak Finnish Uzbek pairwise harmonic (|z| > 2) VHCalc harmonic (h-index > 0.3) Finnish Azeri Azeri Karakpalak Turkmen Turkmen Turkmen Kyrgyz Kyrgyz Old Turkic Old Turkic Old Turkic
Transcript of Goals Benefits New Harmony Patterns - Swarthmore Homethe calculation of the z-score (2 harmonic...
Discovering new vowel harmony patterns using a pairwise statistical model
Nathan Sanders and K. David Harrison (Swarthmore College)20th Manchester Phonology Meeting, 24–26 May 2012
Goals
De�ne a statistical measurement of vowelharmony over a corpus, in such a way that it can be meaningfully compared across corpora,languages, and harmonic features.
Methods
(1) Extract tier-adjacent vowel pairs from the corpus. For example, if the corpus contains the word krematoryum, the algorithm extracts ea, ao, and ou. For a given feature, like backness, compute the overall harmony percentage: the number of harmonic pairs divided by the total number of pairs. In this case, 2 out of 3 pairs are harmonic (ao, ou), so the percentage is 67%.
(2) Using the total size of the corpus, thedistributions of the vowels, and the distribution of word lengths, randomly generate a large number of corpora, and calculate the harmony percentage for each.
(3) Compare the harmony of the original corpus to the distribution of harmony in the random corpora. �e number of standarddeviations the real corpus is from the mean of the random corpora is its z-score for harmony.
Benefits
�e z-score is a normalized measure of statistical deviance, so it can be meaningfully compared from one case to any other, like the relative harmony between languages.
Measures of whole-word harmony, like the h-index ofHarrison et al.’s (2002–2004) Vowel Harmony Calculator (VHCalc), do not distinquish between di�erent levels of disharmony, as in krematoryum versus eskavatör (both are categorically disharmonic), which contribute di�erently to the calculation of the z-score (2 harmonic pairs vs. 1).
New Harmony Patterns
First, there are bizarre cases of “anti-harmony”, where a language has a statistically signi�cant negative z-score. For example, Swahili’s pairwise backness harmony has a z-score of –11, well beyond the –2 needed for statistical signi�cance. It’s not clear what anti-harmony might be…
More importantly, many languages do not have harmony at the word level, but do have a large amount of pairwise harmony, and thus, have “hidden harmony”. For example, Estonian’sh-index for backness harmony is 0.07, but it is very harmonic for vowel pairs (z = 24). In this case, the discrepancy is due to historicalharmony that has le� remnants in the lexicon. �us, hidden harmony could be a diagnostic tool for reconstructing historical harmony.
Hidden harmony may also have implications for the learnability of harmony or for development and/or loss of harmony over time.
Comparison with VHCalc
Despite the di�erent underlying mathematics, the pairwise z-score and VHCalc’s whole-word h-index are stronglycorrelated, however there are still important di�erences:
White regions are harmonic for both VHCalc and z-score (h-index > 0.3, |z-score| > 2). Gray regions are unharmonic for VHCalc, and blue regions are unharmonic for z-score.
ReferencesHarrison, K.D., E. �omforde, & M. O’Keefe. 2002–2004. �e Vowel Harmony Calculator. http://www.swarthmore.edu/ SocSci/harmony/public_html/index.html
pairwise z-scorepairwise z-score
VH
Cal
c’s w
hole
wor
d h-
inde
x
VH
Cal
c’s w
hole
wor
d h-
inde
x
VH
Cal
c’s w
hole
wor
d h-
inde
x
pairwise z-score
backness (r ≈ 0.9) height (r ≈ 0.7)rounding (r ≈ 0.9)
EstonianEsto
nian
Spanish
Indonesian
Indo
nesia
n
Japa
nese
Japanese
Uzb
ek
Uzbek
Estonian
IndonesianJapanese
SwahiliKarakpalak
Tuvan
Span
ish TurkishFinnish
Swah
ili
Swahili
Zulu Zulu
Zulu
Ingrian
Ingrian
Ingrian
Votic
Votic
Span
ish
Votic
Aze
riKy
rgyz
Turkish
Turkish
Tuvan
TuvanKarakpalak
FinnishUzbek
pairwise harmonic(|z| > 2)
VHCalc harmonic(h-index > 0.3) Finnish
Azeri
Azeri
Karakpalak
Turkmen
Turkmen
TurkmenKyrgyz
KyrgyzOld Turkic
Old Turkic Old Turkic
