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
1. Present the stimuli pair-wise and ask the
observer how similar they are
(e.g. on a 0-100 scale)
2. Create the dissimilarity matrix
3. Run MDS to get a perceptual map of the
stimuli
4. Interpret the dimensions of the map
Multidimensional scaling
•
Stimuli: 4 different salt
concentrations
(A: 0.5%, B: 2%,
C: 1%, D: 1.5%)
1. 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
2. Dissimilarity matrix
A
A
B
C
D
90 10 55
B
90
80 35
C
10 80
D
55 35 45
45
Symmetrical
(i.e. A vs B = B vs A)
Multidimensional scaling
3.
Perceptual map: each stimuli
represents a point, their
distances correspond to
dissimilarities
A C
D
1D solution
A
A
B
90
C
D
10
55
B
B
90
80
35
C
10
80
D
55
35
45
45
Multidimensional scaling
4.
Interpreting the dimensions: looking for
correspondences between physical and perceptual
dimensions
B
D
Dimension 1
(from MDS)
C
A
Salt concentration
Dimension 1:
intensity of salt taste
Multidimensional scaling
Another example: soft drinks
Coke
Diet
Coke
Pepsi
Diet
Pepsi
Cherry
Diet
Coke Cherry
Coke
Coke
Diet Coke
20
Pepsi
10
22
Diet Pepsi
22
10
20
Cherry Coke
30
36
40
45
Diet Cherry Coke
36
30
45
40
20
Multidimensional scaling
Diet taste
Pepsi
20
10
Coke
10
20
30
Cherry
Coke
Cherry taste
Diet Pepsi
Diet Coke
30
20
Diet Cherry
Coke
2D solution
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
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
Multidimensional scaling
7-year-olds
adults
Multidimensional scaling
• Hair (long/short)
• Jaw
(smooth/rugged)
• Eye (bright/dark)
Multidimensional scaling
Additional
perceptual
dimension
revealed
Multidimensional scaling
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)