Vowel Harmony
6.5 Generating the visualization
o a e ¨a o u i y
¨
o 0.0393 −0.0324 −0.0220 0.0911 −0.0211 −0.0268 −0.0178 0.0947 a −0.0487 0.1750 −0.1091 −0.1509 0.0429 0.0104 0.0185 −0.0693 e −0.0186 −0.0862 0.0098 0.0608 −0.0041 −0.0209 0.0639 −0.0124
¨
a 0.1475 −0.1406 −0.0261 0.2302 −0.0727 −0.0534 0.0397 0.0745 o −0.0301 0.0342 0.0373 −0.1021 −0.0161 −0.0034 0.0346 −0.0497 u −0.0356 0.0383 0.0077 −0.1117 0.0342 0.1437 −0.0611 −0.0604 i −0.0032 −0.0099 0.0801 0.0229 0.0171 −0.0382 −0.0580 −0.0058 y 0.0488 −0.1138 0.0049 0.1728 −0.0518 −0.0552 −0.0229 0.2248
At this point, it has to be remarked that the calculations of the φ coefficients are only a preliminary step for the visualizations and are therefore not tested for their statistical significance. The idea is that when looking at the visualizations the user can decide for themselves whether a certain vowel succession is considered to be significant (not in the statistical sense, but in the eye of the beholder) for a certain pattern to stand out. One of the advantages of the visual component is therefore that no arbitrary agreement on when something is considered to be significant has to be made in advance.
In addition, statistical significance is more likely to be achieved with more data, thus making it more difficult to compare their values across languages of different sample sizes.7 The main task of the visual component is to yield a representation of the data so that the decision whether a given pattern is salient enough to be looked into in more detail can be made by the user.
6.5 Generating the visualization
In Section 3.4.3, it was already described how to generate a matrix visualization from a table of numerical values such as the one given in Table 6.9. In this section, I want to describe the methodology with respect to the specific task of visualizing vowel successions in order to display VH patterns. The matrix ofφ coefficients in Table 6.9 already contains all the information that is needed for linguists to determine whether a language has VH or other interesting patterns of vowel distributions. However, picking out patterns among a forest of numbers is not an easy task for most humans.
Visualizations, on the other hand, remedy this problem by directing the attention of the user to possibly interesting patterns. This can best be seen when comparing the matrices ofφvalues in Tables 6.10 and 6.11 with their corresponding visualizations in Figure 6.1.
As described in more detail in Section 3.4.3, the generation of the visualizations in Figure 6.1 involves two major steps that will here be explained with respect to the task of visualizing VH. First, the numerical values of theφ matrices have to be mapped to visual variables. Mapping numerical values to suitable pre-attentive visual variables
7See Mayer et al. (2010a) for the minimum amount of data that is needed to obtain reliable results.
Table 6.10: The matrix of φvalues for Turkish.
¨
o ¨u e i o u a ı
¨
o −0.0023 0.4304 0.1052 −0.0906 −0.0271 −0.0455 −0.0837 −0.0886
¨
u −0.0033 0.5757 0.1110 −0.1227 0.0249 −0.0595 −0.1010 −0.1259 e −0.0026 −0.1105 0.3034 0.4225 −0.0826 −0.1440 −0.2374 −0.2903 i 0.0100 −0.0923 0.1387 0.3684 0.0918 −0.1203 −0.1692 −0.2477 o −0.0029 −0.0424 −0.0848 −0.1038 −0.0269 0.4522 0.0415 −0.1097 u 0.0038 −0.0538 −0.1215 −0.1479 0.0381 0.5470 0.0864 −0.1551 a −0.0002 −0.1365 −0.2473 −0.3046 −0.1000 −0.1479 0.2920 0.4392 ı −0.0056 −0.0832 −0.1690 −0.2196 0.1156 −0.1106 0.0976 0.3408
Table 6.11: The matrix of φvalues for Latin.
i u y a e o
i −0.017289 0.035255 −0.015904 0.053854 −0.041805 −0.037511 u 0.004586 −0.064273 −0.010554 0.067001 −0.007922 −0.005593 y 0.006081 −0.016576 −0.002558 0.008697 −0.015041 0.027216 a 0.063170 0.012152 0.010513 −0.084544 −0.018669 0.033249 e −0.028650 0.008915 −0.004610 −0.002376 0.028295 −0.003494 o −0.026121 −0.013378 0.022909 −0.017858 0.049924 0.010216
1/2/14 2:40 PM
Please select the association measure and order of symbols. You can also move individual columns or rows by dragging their label cell to the desired position.
Association measure: Phi Order: by phi values Size:
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Step1 - Step 2 - Step 3
Please select the association measure and order of symbols. You can also move individual columns or rows by dragging their label cell to the desired position.
Association measure: Phi Order: by phi values Size:
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Step1 - Step 2 - Step 3
Figure 6.1: The visualized φmatrix for Turkish (left) and Latin (right).
VOWEL HARMONY | 131
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Step 3: Visualization
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Please select the association measure and order of symbols. You can also move individual columns or rows by dragging their label cell to the desired position.
Association measure: Phi Order: by phi values Size:
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Figure 6.2: These visualizations show the matrix from Table 6.9 where numerical values have been mapped to color shades. The rows and columns of the matrix on the left are left unsorted. As a consequence, no interesting patterns with respect to VH can be detected from looking at the visualization. The visualization on the right represents the matrix from Table 6.9, but now in an automatically sorted manner.
can boost the analysis process as analysts can detect interesting relations without any cognitive overload. Second, the cells in the matrix have to be arranged in a meaningful way so that the resulting patterns emerge from the data.
6.5.1 Data mapping
The visualization matrix is based on theφvalues (Table 6.9) of vowel successions. The generation of the visualization for the φ values where two unipolar color scales (with red and blue) were used has already been described in Section 3.4.3. In comparison to unipolar color scales, bipolar color scales contain more distinguishable color shades.8 Vowel successions occurring more frequently than expected are colored in blue whereas successions that are less frequently observed than expected in the data are given a red color. In this case, the+and−symbols are redundant in giving the same information as the color. The higher the absoluteφvalue, the more saturated is the color. A square root function is applied before mapping the numerical values to color shades. Figure 6.2 (left) provides the visualization for the Finnishφ matrix.
6.5.2 Matrix arrangement
The matrices of numerical values that have been presented so far have been arranged in a way so that the patterns might already be visible by looking at their algebraic signs.
However, such an arrangement is not trivial as there are many possibilities for sorting
8See Gehlenborg and Wong (2012) for the choice of unipolar vs. bipolar color scales.
the rows and columns. The most conspicuous ordering with respect to the VH patterns is not known beforehand and must therefore be derived from the data as well. The sorting method that is used in these visualizations has been described in Section 3.4.3.
It has to be pointed out again that a meaningful arrangement of rows and columns in the matrix is crucial for the analysis process. Blocks of vowels that belong to the same harmony pattern can only be detected if the vowels are sorted properly. Figure 6.2 (right) shows the φmatrix of Figure 6.2 (left), but now with the proper arrangement of rows and columns. It can clearly be seen that the blocks of vowels that make up the harmony patterns in Finnish are now adjacent and no longer scattered throughout the matrix.