Multidimensional scaling

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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

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

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 scaling
• What does the MDS algorithm do?

From a matrix of distances…

Kruskal & Wish, 1978

Multidimensional scaling
• What does the MDS algorithm do?

…it calculates a map…

Multidimensional scaling
• What does the MDS algorithm do?

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

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

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)

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

A

C

D

B

1D solution

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

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

Multidimensional scaling

Shepard, 1963:

• Morse-codes presented in pairs to naïve observers (each possible combination)
• Confusion matrix (% same responses): can be interpreted as a dissimilarity matrix
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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7-year-olds

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