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Searching for patterns in the World Color Survey Gerhard J ager - - PowerPoint PPT Presentation

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Searching for patterns in the World Color Survey Gerhard J ager gerhard.jaeger@uni-tuebingen.de July 2, 2009 University of Frankfurt 1/115 Overview Structure of the talk the psychological color space Berlin and Kays 1969 study the

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Searching for patterns in the World Color Survey

Gerhard J¨ ager gerhard.jaeger@uni-tuebingen.de

July 2, 2009

University of Frankfurt

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Overview

Structure of the talk the psychological color space Berlin and Kay’s 1969 study the World Color Survey the distribution of focal colors categorization Principal Component Analysis clustering color categories are (more or less) convex

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The psychological color space

physical color space has infinite dimensionality — every wavelength within the visible spectrum is one dimension psychological color space is only 3-dimensional this fact is employed in technical devices like computer screens (additive color space) or color printers (subtractive color space) additive color space subtractive color space

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The psychological color space

psychologically correct color space should not only correctly represent the topology of, but also the distances between colors distance is inverse function of perceived similarity L*a*b* color space has this property three axes:

black — white red — green blue — yellow

irregularly shaped 3d color solid

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The color solid

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The Munsell chart

for psychological investigations, the Munsell chart is being used 2d-rendering of the surface of the color solid

8 levels of lightness 40 hues

plus: black–white axis with 8 shaded of grey in between neighboring chips differ in the minimally perceivable way

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Berlin and Kay 1969

pilot study how different languages carve up the color space into categories informants: speakers of 20 typologically distant languages (who happened to be around the Bay area at the time) questions (using the Munsell chart):

What are the basic color terms of your native language? What is the extension of these terms? What are the prototypical instances of these terms?

results are not random indicate that there are universal tendencies in color naming systems

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Berlin and Kay 1969

distribution of focal colors: essentially correspond to the centers of the English categories black, white, red, green, yellow, blue, purple, orange, brown, grey, pink

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Berlin and Kay 1969

extensions

Arabic 9/115

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Berlin and Kay 1969

extensions

Bahasa Indonesia 10/115

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Berlin and Kay 1969

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Bulgarian 11/115

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Berlin and Kay 1969

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Cantonese 12/115

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Berlin and Kay 1969

extensions

Catalan 13/115

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Berlin and Kay 1969

extensions

English 14/115

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Berlin and Kay 1969

extensions

Hebrew 15/115

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Berlin and Kay 1969

extensions

Hungarian 16/115

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Berlin and Kay 1969

extensions

Ibibo 17/115

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Berlin and Kay 1969

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Japanese 18/115

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Berlin and Kay 1969

extensions

Korean 19/115

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Berlin and Kay 1969

extensions

Mandarin 20/115

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Berlin and Kay 1969

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Mexican Spanish 21/115

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Berlin and Kay 1969

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Pomo 22/115

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Berlin and Kay 1969

extensions

Swahili 23/115

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Berlin and Kay 1969

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Tagalog 24/115

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Berlin and Kay 1969

extensions

Thai 25/115

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Berlin and Kay 1969

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Tzeltal 26/115

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Berlin and Kay 1969

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Urdu 27/115

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Berlin and Kay 1969

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Vietnamese 28/115

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Berlin and Kay 1969

identification of absolute and implicational universals, like

all languages have words for black and white if a language has a word for yellow, it has a word for red if a language has a word for pink, it has a word for blue ...

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The World Color Survey

B&K was criticized for methodological reasons in response, in 1976 Kay and co-workers launched the world color survey investigation of 110 non-written languages from around the world around 25 informants per language two tasks:

the 330 Munsell chips were presented to each test person one after the other in random order; they had to assign each chip to basic some color term from their native language for each native basic color term, each informant identified the prototypical instance(s)

data are publicly available under http://www.icsi.berkeley.edu/wcs/

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Data digging in the WCS

distribution of focal colors across all informants:

Distribution of focal colors

Munsell chips # named as focal color 20 50 200 1000

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Data digging in the WCS

distribution of focal colors across all informants:

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

partition of a randomly chosen informant from a randomly chosen language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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Data digging in the WCS

extension of a randomly chosen term from a randomly chosen language, averaged over all informants from that language

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What is the extension of categories?

data from individual informants are extremely noisy averaging over all informants from a language helps, but there is still noise, plus dialectal variation desirable: distinction between “genuine” variation and noise

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Principal Component Analysis

technique to reduce dimensionality of data input: set of vectors in an n-dimensional space first step: rotate the coordinate system, such that

the new n coordinates are orthogonal to each other the variations of the data along the new coordinates are stochastically independent

second step:

choose a suitable m < n project the data on those m new coordinates where the data have the highest variance

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Principal Component Analysis

alternative formulation:

choose an m-dimensional linear sub-manifold of your n-dimensional space project your data onto this manifold when doing so, pick your sub-manifold such that the average squared distance of the data points from the sub-manifold is minimized

intuition behind this formulation:

data are “actually” generated in an m-dimensional space

  • bservations are disturbed by n-dimensional noise

PCA is a way to reconstruct the underlying data distribution

applications: picture recognition, latent semantic analysis, statistical data analysis in general, data visualization, ...

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Applying PCA to WCS-categories

data: informant-category pairs 330 dimensions (each Munsell color is one dimension) each informant-category pair assigns 1 to the colors that belong to that category, and 0 else

principal components proportion of variance explained 0.00 0.05 0.10 0.15

first seven principal components jointly explain 60% of the variance in the data each PC after PC10 only marginally increases proportion of variance explained so let’s say m = 10

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PC1

green/blue vs. white/red/yellow

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PC2

white vs. red

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PC3

black vs. red/white

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PC4

yellow vs. black/white/blue/red

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PC5

black vs. red/green/blue

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PC6

blue/yellow vs. red/green

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PC7

purple vs. red/blue/black

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PC8

pink vs. red/yellow/white

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PC9

brown vs. black/pink

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PC10

brown vs. light blue/yellow/black

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Projecting observed data on 10d-manifold

noise removal: project observed data onto the lower-dimensional submanifold that was obtained via PCA in our case: noisy binary categories are mapped to smoothed fuzzy categories (= probability distributions over Munsell chips) some examples:

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Projecting observed data on 10d-manifold

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Smoothed partitions of the color space

vocabulary of a given language does not always form a partition many cases of (near) synonymy, hyponymy, and overlap for instance language 1 (Abidjy, Ivory Coast):

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Smoothed partitions of the color space

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Smoothed partitions of the color space

if two categories of one language have a correlation of at least .5, they are treated as synonyms process is repeated if remaining categories are independent or negatively correlated after this process, each Munsell chip c is assigned to the category that assigns the highest probability to c for Abidji, we get

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Smoothed partitions of the color space

some more examples: Waorani (Ecuador)

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Smoothed partitions of the color space

some more examples: Arabela (Peru)

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Smoothed partitions of the color space

some more examples: Camsa (Colombia)

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Smoothed partitions of the color space

some more examples: Candoshi (Peru)

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Smoothed partitions of the color space

some more examples: Chinanteco (Mexico)

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Smoothed partitions of the color space

some more examples: Guarijio (Mexico)

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Smoothed partitions of the color space

some more examples: Gunu (Cameroon)

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Smoothed partitions of the color space

some more examples: Kalam (Papua New Guinea)

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Smoothed partitions of the color space

some more examples: Menye (Papua New Guinea)

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Smoothed partitions of the color space

some more examples: Tifal (Papua New Guinea)

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Convexity

note: so far, we only used information from the WCS the location of the 330 Munsell chips in L*a*b* space played no role so far still, apparently partition cells always form continuous clusters in L*a*b* space Hypothesis (G¨ ardenfors): extension of color terms always form convex regions of L*a*b* space

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Support Vector Machines

supervised learning technique smart algorithm to classify data in a high-dimensional space by a (for instance) linear boundary minimizes number of mis-classifications if the training data are not linearly separable

green red −3 −2 −1 1 2 3 −3 −2 −1 1 2 3

  • o
  • SVM classification plot

y x

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Convex partitions

a binary linear classifier divides an n-dimensional space into two convex half-spaces intersection of two convex set is itself convex hence: intersection of k binary classifications leads to convex sets procedure: if a language partitions the Munsell space into m categories, train m(m−1)

2

many binary SVMs, one for each pair

  • f categories in L*a*b* space

leads to m convex sets (which need not split the L*a*b* space exhaustively)

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Convex approximation

Waorani (Ecuador)

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Convex approximation

Arabela (Peru)

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Convex approximation

Camsa (Colombia)

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Convex approximation

Candoshi (Peru)

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Convex approximation

Chinanteco (Mexico)

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Convex approximation

Guarijio (Mexico)

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Convex approximation

Gunu (Cameroon)

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Convex approximation

Kalam (Papua New Guinea)

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Convex approximation

Menye (Papua New Guinea)

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Convex approximation

Tifal (Papua New Guinea)

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Convex approximation

  • n average, 93.7% of all Munsell chips are correctly classified

by convex approximation

  • 0.80

0.85 0.90 0.95 proportion of correctly classified Munsell chips

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Convex approximation

compare to the outcome of the same procedure without PCA:

  • without PCA

with PCA 0.0 0.2 0.4 0.6 0.8 1.0 proportion of correctly classified Munsell chips

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Conclusion

empirical support for G¨ ardenfors’ thesis that natural properties are convex sets quantitative data analysis reveals robust universal tendencies techniques from statistical pattern recognition are useful for typological studies R is a great tool

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