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Multidimensional scaling. Research Methods Fall 2010 Tamás Bőhm. Multidimensional scaling (MDS). Earlier methods: measuring the properties of one specific perceptual dimension ( e.g. brightness, pitch ) Simple stimuli with one physical dimension varied S pot of light, pure tones etc.

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multidimensional scaling

Multidimensional scaling

Research Methods

Fall 2010

Tamás Bőhm

multidimensional scaling mds
Multidimensional scaling (MDS)
  • Earlier methods: measuring the properties of one specific perceptual dimension(e.g. brightness, pitch)
    • Simple stimuli with one physical dimension varied

Spot of light, pure tones etc.

  • MDS: exploring what the perceptual dimensions are
    • Complex stimuli with multiple dimensions

Faces, melodies, etc.

  • Perceptual maps are created from similarity judgments
multidimensional scaling1
Multidimensional scaling
  • What does the MDS algorithm do?

From a matrix of distances…

Kruskal & Wish, 1978

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Multidimensional scaling
  • What does the MDS algorithm do?

…it calculates a map…

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Multidimensional scaling
  • What does the MDS algorithm do?

…but it cannot tell the orientation and the meaning of the axes.

multidimensional scaling4
Multidimensional scaling

Experiment setup

  • Present the stimuli pair-wise and ask the observer how similar they are(e.g. on a 0-100 scale)
  • Create the dissimilarity matrix
  • Run MDS to get a perceptual map of the stimuli
  • Interpret the dimensions of the map
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Stimuli: 4 different salt concentrations(A: 0.5%, B: 2%,C: 1%, D: 1.5%)

Dissimilarity judgments (0: perfect similarity;100: no similarity)

A vs B: 90

A vs C: 10

A vs D: 55

B vs C: 80

B vs D: 35

C vs D: 45

Dissimilarity matrix

Multidimensional scaling

Symmetrical(i.e. A vs B = B vs A)

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Multidimensional scaling
  • Perceptual map: each stimuli represents a point, their distances correspond to dissimilarities

A

C

D

B

1D solution

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Multidimensional scaling
  • Interpreting the dimensions: looking for correspondences between physical and perceptual dimensions

B

D

Dimension 1(from MDS)

Dimension 1: intensity of salt taste

C

A

Salt concentration

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Multidimensional scaling

Diet taste

20

Pepsi

Diet Pepsi

10

10

20

Coke

Diet Coke

30

30

Cherry Coke

Diet Cherry Coke

20

Cherry taste

2D solution

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Multidimensional scaling

Shepard, 1963:

  • Morse-codes presented in pairs to naïve observers (each possible combination)
  • Same/different task
  • Confusion matrix (% same responses): can be interpreted as a dissimilarity matrix
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Multidimensional scaling

Jacobowitz (see Young, 1974):

  • Children and adults judged the similarity of all pairs of 15 parts of the human body
  • Task: rank ordering of similarity to a standard  dissimilarity matrix
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Multidimensional scaling

7-year-olds

adults

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Multidimensional scaling
  • Hair (long/short)
  • Jaw(smooth/rugged)
  • Eye (bright/dark)
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Multidimensional scaling

Additional perceptual dimension revealed

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Multidimensional scaling
  • Directly asking about the perceptual dimensions:
    • requires prior knowledge
    • introduces bias
  • MDS:
    • no prior assumptions about the possible dimensions (exploratory)
    • no response bias
  • Reveals the hidden structure of the data
  • MDS is about relationships among stimuli(does not tell us about the perception of individual entities)