FAST, a novel “Factorial Approach” for Sorting

Transcription

FAST, a novel “Factorial Approach”
for Sorting Task data
Marine Cadoret, Sébastien Lê, Jérôme Pagès
AGROCAMPUS OUEST, France
9th Sensometrics conference
July 20-23 2008, Canada
Introduction
Sorting task (or categorization) consists in
grouping objects in function of their
resemblances.
Following this task, a verbalization task can
also be asked to describe the groups
(“qualified” categorization).

2
Data
98 consumers carried out a “qualified” categorization
on 12 luxury perfumes:
Angel
Shalimar
Lolita
Lempicka
L'instant
Cinéma
Aromatics
Coco
Chanel n°5
Elixir Mademoiselle
J'adore J'adore
(ET)
(EP)
Pure
Poison
Pleasures
3
« gourmand,
vanilla, wooded »
« spicy, aldehyde »
« white flower,
vanilla, orange »
« oriental,
showy,
wooded,
Patchouli oil »
« flower,
floral,
green »
4
Data
produit
Angel
Aromatic Elixir
Chanel n°5
Cinéma
Coco Mademoiselle
J'adore (EP)
J'adore (ET)
L'instant
Lolita Lempicka
Pleasures
Pure Poison
Shalimar
juge 12
1
3
4
2
1
1
2
1
1
3
1
2
juge 13
4
3
3
5
5
6
6
4
5
4
1
2
juge 14
1
5
4
6
2
2
2
6
1
6
2
3
juge 15
5
2
1
4
4
3
3
2
5
3
4
2
juge 16
2
1
3
2
3
3
3
4
2
4
4
1
For example, Consumer 12 put in the group 1 Angel, Coco Mademoiselle,
J'adore (EP), L'instant, Lolita Lempicka and Pure Poison
5
Data
produit
Angel
Aromatic Elixir
Chanel n°5
Cinéma
Coco Mademoiselle
J'adore (EP)
J'adore (ET)
L'instant
Lolita Lempicka
Pleasures
Pure Poison
Shalimar
juge 12
fleuri doux
fort homme
Gr 4
fleuri artificiel herbe
fleuri doux
fleuri doux
fleuri doux
fleuri doux
fort homme
fleuri doux
juge 13
fruité fort
capiteux grand-mère
capiteux grand-mère
fruité moyen
fruité moyen
sucré faible
sucré faible
fruité fort
fruité moyen
fruité fort
acidulé désodorisant
fort lavande eau de cologne
juge 14
vanillé épicé esprit des îles
rude fort
toilettes
sucré
douceur fleuri
douceur fleuri
douceur fleuri
sucré
vanillé épicé esprit des îles
sucré
douceur fleuri
renfermé agressif
juge 15
à manger sucré
le vieux
savon
doux
doux
fleuri
fleuri
le vieux
à manger sucré
fleuri
doux
le vieux
juge 16
nourriture épice
ménager cire
connu classique
nourriture épice
connu classique
connu classique
connu classique
fleuri
nourriture épice
fleuri
fleuri
ménager cire
Each consumer can be considered as a categorical variable
Let’s run MCA on this data table!
6
The approach
Why does it work?
7
Disjunctive table
variable 1
1
variable j
k
variable J
x ik
001000
K
1
i
010000
I
I1
Ik
I
K
xik is equal to 1 if perfume i belongs to group k; Ik is the
number of perfumes in the group k
8
Distance between individuals

The distance between two products is null if they were put
systematically together.
Two products are all the more close (resp. distant) that they
were put together by a great (resp. few) number of
consumers.
9
Objects categorized by two assessors
Assessor 1
A
Assessor 2
B
B
A, D, C
C, D, E, F,
G, H, I
B, E, F
G, H, I

They have made three groups each (a disc represents a
group).

The two assessors distinguished between products A and B,
but in a more remarkable way for assessor 1
10
Distance between categories

Two categories/descriptions are all the more distant that
they have few common individuals. In other words, that the
number of individuals that were put either in k, either in k’ is
big.
11
The approach
In how can it be specific to sensory
analysis?
12
i products
j consumers
Data table
i×j
P4
P1
P3
P2
F4
F1
F2
F3
Representation of the products
13
i products
j consumers
Data table
i×j
P4
P1
P3
P2
F4
F1
F2
F3
Superimposed representation of the products and their descriptions
14
P4 is at the barycentre of the words used to
describe the groups
P4
P1
P3
P2
F4
F1
F2
F3
15
Panelist’s words
(resampled)‫‏‬
Data table
i×j
P4
product P4
16
Data table
i×j
product P4
P4
17
Confidence ellipses around products
P4
18
Representation of the consumers
0.6
0.8
1.0
Using Multiple Factor Analysis
2 consumers are all the more close as they carried out
similar categorizations
Consumers representation linked to the ones of products
and words
j
0.0
0.2
0.4
j’
0.0
0.2
0.4
0.6
0.8
1.0
19
Results
« FAST » function implemented
in
20
Co-occurrences among the perfumes
Coco
Mademoiselle
J'adore
(ET)
Alone
6
7
24
12
7
6
12
14
17
11
11
12
13
18
18
18
7
Shalimar
Aromatics
Elixir
Chanel
n°5
Angel
Lolita
Lempicka
Cinéma
L'instant
Pure
Poison
Shalimar
98
42
30
21
9
10
13
11
9
6
Aromatics Elixir
42
98
51
27
6
8
13
12
12
11
Chanel n°5
30
51
98
15
8
9
10
21
11
14
Angel
21
27
15
98
36
18
14
10
10
Lolita Lempicka
9
6
8
36
98
42
22
18
21
Pleasures
J'adore
(EP)
Cinéma
10
8
9
18
42
98
26
28
30
22
23
24
5
L'instant
13
13
10
14
22
26
98
25
20
23
28
22
9
Pure Poison
11
12
21
10
18
28
25
98
33
30
29
28
7
Coco Mademoiselle
9
12
11
10
21
30
20
33
98
28
28
38
8
Pleasures
6
11
14
11
18
22
23
30
28
98
38
48
8
J'adore (EP)
6
12
12
11
18
23
28
29
28
38
98
56
2
J'adore (ET)
7
7
14
12
18
24
22
28
38
48
56
98
2
21
Some textual analysis
Description of the products Angel and Shalimar sorted
by descending order of significativity
Angel
vanillé
épicé
sucré
fort
intern %
2,58%
3,23%
9,03%
10,32%
global %
0,55%
0,94%
5,18%
6,45%
p-value
0,007
0,011
0,025
0,036
Shalimar
fort
agressif
mentholé
oriental
vieux
médicament
poivré
masculin
intern %
12,42%
3,92%
1,31%
1,31%
2,61%
1,31%
1,96%
1,96%
global %
6,45%
1,05%
0,11%
0,17%
0,77%
0,22%
0,55%
0,55%
p-value
0,003
0,004
0,007
0,020
0,025
0,038
0,045
0,045
22
0
50
100
150
Number of words per group
0
1
2
3
4
5
7
9
23
Representation of the perfumes
MCA factor map
1.5
Angel
1.0
0.5
Cinéma
Shalimar
L'instant
0.0
Dim 2 (13.64%)‫‏‬
Lolita Lempicka
Aromatics Elixir
-0.5
Coco Mademoiselle
Pure Poison
J'adore (ET)‫‏‬
Pleasures
J'adore (EP)‫‏‬
-1.0
Chanel n°5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Dim 1 (17.8%)‫‏‬

Plan defined by dimensions 1 and 2 of MCA
24
Representation of the words

25
Old
Strong
Aggressive
Heady

26
Old
Strong
Aggressive
Heady
Flowery
Exotic
Gentle

27
Sweet
Spicy
Cotton candy
Chocolate
Young
Old
Strong
Aggressive
Heady
Flowery
Exotic
Gentle

28
1.5
2.0
Representation of the perfumes and
their respective confidence ellipses
Angel
1.0
0.5
Dim 2 (13.64%)‫‏‬
Lolita Lempicka
Cinéma
Shalimar
Aromatics Elixir
Chanel n°5
-1.0
-0.5
0.0
L'instant
Coco Mademoiselle
Pure Poison
J'adore (ET)‫‏‬
J'adore (EP)‫‏‬
Pleasures
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Dim 1 (17.8%)‫‏‬

29
1.0
Representation of the consumers
31
40
0.2
Dim 2 (13.64%)
0.4
0.6
0.8
Shalimar
Aromatics Elixir
Chanel n°5
Coco Mademoiselle
J'adore (EP)
J'adore (ET)
L'instant
Pleasures
Pure Poison
Angel
Cinéma
Lolita Lempicka
93
juge 18
2
2
3
3
1
3
2
3
1
3
3
1
juge 31
1
2
4
1
1
1
1
1
2
5
3
3
juge 40
4
5
5
2
1
1
2
1
2
6
3
3
juge 93
4
3
3
2
1
2
1
1
2
1
2
2
0.0
18
0.0
0.2
0.4
0.6
0.8
1.0
Dim 1 (17.8%)

Plan defined by dimensions 1 and 2 of MFA
30
http://sensominer.free.fr
Journal of sensory studies SensoMineR a package for sensory data analysis
http://factominer.free.fr
Journal of statistical software FactoMineR: an R package for multivariate analysis
31