The World Color Survey as Similarity Judgments

Naming as Similarity Judgment:
Data from The World Color Survey (Kay, Berlin, and Merrifield).

Substantive question:

What is the nature of the similarities and differences among color classifications?

History:

Early studies treated color classification as an example of extreme cultural relativism:
- e.g., Conklin's study of Hanunoo color categories (attributes attended to include surface texture and sheen, not just hue, brightness, and saturation).
- Cultural relativism is expectable, given the nature of the domain.
  - Colors vary continuously from one another
    - hue (wavelength)
    - brightness (white — black)
    - saturation (mixture with the complement)
  - People in different cultures should cut the continuum up differently, if there is no intrinsic structure to the color space.
- But not at all right:
  - As Paul Kay in Tahiti and Brent Berlin in Tenejapa observed, it was not nearly as difficult to learn the meanings of the color terms of other languages as would be implied by a extreme relativist position.
Emergence of Universals and Evolution (UE) approach:

Berlin and Kay: Basic Color Terms (1969):
- 11 basic color terms (black, white, red, yellow, green, blue, brown, gray, pink, orange, purple)
- Pattern interpreted as the sequential encoding of foci in a limited number of combinations:
  - 2 terms: black, white
  - 3 terms: black, white, red
  - 4 terms: black, white, red, yellow or black, white, red, green
  - 5 terms: black, white, red, yellow, green
  - 6 terms: black, white, red, yellow, green, blue
  - 7 terms: black, white, red, yellow, green, blue, brown
  - 8 or more terms: black, white, red, yellow, green, blue, brown plus gray, pink, orange, purple in no particular order

But not quite right:
- "white" term in Dani focuses in white, yellow or red (warm/light)
- "green" term in Mayan and elsewhere focuses in green or blue (GRUE)
Kay and McDaniel: The Linguistic Significance of the Meanings of Basic Color Terms. (1978)

Pattern interpreted as the successive differentiation of existing color categories.
- Union of unique hue points
  - 2 terms: WRY / GBK
  - 3 terms: W / RY / GBK
  - 4 terms: W / R / Y / GBK or W / RY / GB / K
  - 5 terms: W / R / Y / GB / K
- Identity of unique hue points
  - 6 terms: W / R / Y / G / B / K
- Intersection of unique hue points
  - 7 + terms: + YxK + (WxK, WxR, RxY, or RxB)

IIIa: IIIb:

Argued that cross-cultural universals have their origin in the physiology of color vision.
- Lateral Geniculate Nucleii in hypothalamus: 'nerve junction box'
- Three families of opponent process cells:
  - RG channel: excited by red light, inhibited by green light (or vice versa)
  - YB channel: excited by yellow light, inhibited by blue light (or vice versa)
  - WK channel: responds to brightness levels independent of other two channels
- Explains why there might be universals in the classification of a structureless domain — (the structure is imposed by the neuro-physiology).

But not quite right:
- Anomalous composite categories found (YGB, YG, BK)
Kay, Berlin, and Merrifield: Biocultural Implications of Systems of Color Naming. (1991)
- World Color Survey: 111 languages, 2 hour interview with 25 native speakers in their own societies.
- Pattern interpreted with Composite Category Rule: "A possible composite category is any fuzzy union of a subset of fundamental neural response categories which, in Figure 2, forms an unbroken associational chain not crossing the diagonal line."
- Composite categories in Kay and McDaniel (1978): RWY, GBK, RY, GB
- Composite categories in Kay, Berlin, and Merrifield (1991): YGB, WY, YG, BK
- Allowed by rule, but not yet found: YGBK
- Kay, Berlin, and Merrifield (1991), Figure 2.

But not quite right:
- Composite category rule is arbitrary statement of permitted categories offering no statement of the logic of the rule.

Kay, Berlin, Maffi, and Merrifield: Color naming across languages (1997).
Kay and Maffi: Color Appearance and the Emergence and Evolution of Basic Color Lexicons (1999).
- Pattern interpreted as five evolutionary trajectories.
- Four Principles:
  - (0) Partition: In notational domains of universal or quasi-universal cultural salience (kin relations, living things, colors, etc.), languages tend to assign significata to lexical items in such a way as to partition the denotata of the domain.
  - (1) Black and White: Distinguish black and white.
  - (2) Warm and Cool: Distinguish the warm primaries (red and yellow) from the cool primaries (green and blue).
  - (3) Red: Distinguish red.

Remaining objection: Are these patterns a methodological artifact? (cf. Lucy, 1997).

Is the analysis contaminated by the color categories of the analyst's native language (e.g., English)?

Alternative method of analyzing naming data as similarity judgments.
- For each informant of the WCS, produce an inter-chip similarity matrix, with a 1 if the pair of chips receives the same name and an 0 if the pair of chips receive different names.
- For each language, sum the informant similarity matrices.

Results

Does language make a difference? Are the inter-chip similarity matrices of speakers of the same language more alike than those of speakers of different languages?
- Procedure:
  - Correlate the 2616 informants' inter-chip similarity matrices to produce an inter-informant correlation matrix.
  - Create an inter-informant model matrix, cells = 1 if speakers of same language, 0 if speakers of different languages.
  - Compare matrices with QAP (Hubert and Schultz, 1976).
  - QAP Z = 200.9, p < 10^-8000
- Answer: Yes.

Are languages related as predicted by the Kay, Berlin, Maffi, and Merrifield (1997) typology.

Procedure

Elicit classifications of 110 WCS languages from Paul Kay.
Produce hypothesized similarity matrix of systems based on the number of changes of the categorization of the unique hue points (WRYGBK). (Explanation)

II	15
IIIgbk	14	15
IIIgb	13	12	15
IIIygb	10	11	12	15
IVbk	12	13	12	11	15
IVgb	12	13	14	13	13	15
IVyg	10	11	12	13	13	13	15
V	11	12	13	12	14	14	14	15
	II	IIIgbk	IIIgb	IIIygb	IVbk	IVgb	IVyg	V

Correlate the 110 languages' inter-chip similarity matrices to produce an inter-language correlation matrix.
Create inter-language model matrix, cells = hypothesized similarity of languages of a given type.
Compare matrices with QAP (Hubert and Schultz, 1976).
QAP Z = 7.7, p < 10^-14

Answer: Yes, but the IIIygb and IVyg systems are more different from the others than hypothesized.

Is the KBMM classification the best of all possible classifications?

Procedure
- Produce an average-link hierarchical clustering of the languages by their overall similarity.
- Label the nodes of the clustering by their KBMM classification.
- Examine whether similarly classified languages fall together in the cluster diagram.
Answer: No, although there is a reasonable fit with the structure of the tree, there are a number of systems of one type that are most similar to systems of another type. (Note that late stage systems (H = V, F = IVgb) tend to cluster at the top of the tree, while early stage systems (A = II, B = IIIgbk, C = IIIgb, D = IIIyg) tend to cluster at the bottom.)

Is there a consensus among the informants of the WCS on the similarity of the chips?

Procedure
- Perform a principal components analysis of the inter-informant correlation matrix.
- Evaluate whether the first factor is large relative to other factors and whether there are any negative scores on the first factor.
- Do the same for the inter-language correlation matrix.

Answer: Yes, there is substantial agreement among speakers on the similarity structure.

The first factor is more than 7 times larger than the second factor.
There are no negative scores on the first factor.
Individuals differ as languages do: the factor structure of the individuals is virtually the same as the factor structure of the languages.
Correlation matrix of principal components for languages (columns) vs. average scores of individual speakers of languages (rows). (Note high correlations along the diagonal.)

	1	2	3	4
1	0.53	0.37	0.38	-0.05
2	-0.14	0.98	-0.02	0.06
3	0.02	-0.04	0.98	0.14
4	-0.47	-0.19	-0.12	0.95

But are there nevertheless patterned differences among languages (as demonstrated above)?
- Yes, (of course) but speakers of some languages disagree more with each other than speakers of other languages do. (Potentially due to the fact that languages undergoing evolution may include speakers at very different stages.)

95% confidence intervals around the centroids of the first (agreement) and second (differentiation) factor scores for speakers of the first 55 languages of the WCS sample.
Note that the ellipses differ greatly in size, reflecting greater variation in speakers of some languages than others.
95% confidence intervals around the centroids of the first (agreement) and second (differentiation) factor scores for speakers of the second 55 languages of the WCS sample.

The factor structure appears to reflect the differences among the stages:

ANOVAs on factors scores 1 through 10 all show significant differences among the different stage systems (all p < .005).

Factor	1	2	3	4	5	6	7	8	9	10
F	11.7	12.5	19.2	9.3	3.3	4.2	14.3	3.8	3.7	16.6

Factor 1 (Agreement) vs Factor 2 (Differentiation)
Factor 1 (Agreement) appears to distinguish the anomalous yellow-green systems (D = IIIygb, G = IVgb) from other systems.
Factor 2 (Differentiation) appears to distinguish non-anomalous early stage systems (A = II, B = IIIgbk, C = IIIgb) from later stage systems (E = IVbk, F = IVgb, H = V).
Factor 3 (Differentiation II) vs Factor 4 (Differentiation III)
Factor 3 (Differentiation II) appears to distinguish stage E = IVbk and stage H = V systems from other systems.
Factor 4 (Differentiation III) appears to distinguish stage A = II systems from other systems.

Can one infer something like the UE pattern without the intervention of the categories of the analyst?

Procedure
- Create mapping matrix: 330 columns correspond to 330 color chips, 2222 rows correspond to color terms in 110 languages, cells = frequency of the application of the term corresponding to the row to the chip corresponding to the column.
- Perform a correspondence analysis of the mapping matrix, simultaneously factoring the rows and columns of the mapping matrix.
- Examine dimensions of the infered similarity of the chips
Answer: Yes, the dimensions successively distinguish the unique hue points, more or less in the UE order.
- 1st dimension: Separate warm and cool colors.
- 2nd dimension: Separate white.
- 3rd dimension: Separate yellow.
- 4th dimension: Separate black.
- 5th dimension: Separate purple.
- 6th dimension: Separate green and blue.
The only anomaly is the separation of purple before the separation of green and blue. The rest of the dimensions are perfectly compatible with Kay and McDaniel (1978).

Alternate Procedure
- Create aggregate similarity by summing the cells of the 2616 individual similarity matrices.
- Perform an average link hierarchical clustering of the chips, based on this overall similarity.
- Examine the structure of the tree diagram.
Answer: Yes, the clustering algorithm successively distinguishes the unique hue points, more or less in the UE order.
- 1st distinction: Separate cool colors.
- 2nd distinction: Separate light colors.
- 3rd distinction: Separate red.
- 4th distinction: Separate black.
- 5th distinction: Separate purple.

Second Alternate Procedure
- For each informant of the WCS, discover how they have classified the 6 best examples of the unique hue points (W,R,Y,G,B,K).
- Sum the unique huepoint similarities to create an overall similarity matrix of the unique huepoints.
- Perform an average link hierarchical clustering of the unique hue points, based on this overall similarity.
- Examine the structure of the tree diagram.
Answer: Yes, the clustering algorithm successively distinguishes the unique hue points, more or less in the UE order.
- 1st distinction: Separate white.
- 2nd distinction: Separate warm from cool/dark.
- 3rd distinction: Separate red from yellow.
- 4th distinction: Separate black from cool.
- 5th distinction: Separate green and blue.

Conclusion

While the pattern of variation among the World Color Survey systems is far from tidy, the results of this analysis appear to confirm the major findings of the UE tradition using methods that are logically independent of those used by Kay, et al.