Combining the best of two worlds, the “sorted

Combining the best of two worlds, the “sorted

Combining the best of two
worlds, the “sorted napping”
Marine Cadoret, Sébastien Lê, Jérôme Pagès
Applied mathematics department
Agrocampus Ouest, France
SPISE 2009
Ho Chi Minh 1City
7 August 2009
Products
• 8 smoothies
• 4 flavors:
– Strawberry-RaspberryBlueberry (SRB)
– Pineapple-Banana-Coco
(PBC)
– Strawberry-Banana (SB)
– Mango-Passion fruits
(MP)
• 2 types of brands:
– Distributor brand name:
Casino, Carrefour
– Great brand name:
Immedia, Innocent 2
Holistic approaches
•
•
•
•
•
Categorization, napping
Global approaches
Require no special competences
Can be used by experts or consumers
Each judge uses his own criteria
3
Categorization
• The judges are asked to group the products
according to their resemblances
Banana
Sweet
Strawberry
Bitter
Thickly
Simplicity
4
Napping
• The judges are asked to provide a tablecloth
with the products
Banana
Banana
Sweet
Thickly
Strawberry
Strawberry
More nuanced
5
Sorted napping
• The judges are asked to provide a tablecloth
with the products that have been possibly
gathered
Banana
Sweet
Thickly
Strawberry
Bitter
6
Method
7
The dataset: Napping
X Y
5 24
Y
31
29 21
24
13 31
20 10
57 20
29 6
5
13
X
38 20
50 33
8
The dataset: Categorization
C
1
2
1
2
3
2
2
3
9
The dataset: Categorization
Banana
Sweet
Thickly
C
thickly
strawberry-bitter
thickly
strawberry-bitter
banana-sweet
Strawberry
Bitter
strawberry-bitter
strawberry-bitter
banana-sweet10
The dataset: Sorted napping
Y
C
5 24
1
29 21
2
13 31
1
20 10
2
57 20
3
29 6
2
38 20
2
50 33
3 11
X
The dataset: Sorted napping
X
Banana
Thickly
Strawberry
Y
C
5 24
thickly
29 21
strawberry
13 31
thickly
20 10
strawberry
57 20
banana
29 6
strawberry
38 20
strawberry
50 33
banana
12
The dataset
• For each judge, we have:
– 2 columns for the coordinates of the products on the tablecloth
– 1 column for the partition
X Y C
X Y C
X Y C
5 24 1
12 14 1
45 23 3
29 21 2
2 33 1
12 17 1
13 31 1
23 7 1
37 12 3
20 10 2
45 20 3
23 34 1
57 20 3
34 33 3
18 5 1
29 6 2
55 15 2
58 25 3
38 20 2
23 28 2
6 18 2
50 33 3
5 7 2
43 20 2
13
The dataset
Judge 1
Judge j
Judge J
X1 Y1 C1
Xj Yj Cj
XJ YJ CJ
1
i
Xj (i)Yj (i)Cj (i)
I
14
Nested partitions
Judge 1
X1 Y1
C1
Judge j
Xj Yj
Judge J
Cj
XJ YJ
CJ
Let’s run Hierarchical Multiple Factor Analysis (HMFA)
15
HMFA
• Takes into account the hierarchy
• Balances:
– The role of each judge
– The role of each appoach
• Classical outputs: representation of the
products, etc
• Specific ouputs: representation of each
node, partial representation for each node
16
Results
17
6
Representation of the smoothies
Carrefour_SB
2
0
Casino_SRB
-2
Immedia_MP
Carrefour_MP
Immedia_SRB
Innocent_PBC
Casino_PBC
-4
Dim 2 (19.4 %)
4
Innocent_SB
-6
-4
-2
0
2
Dim 1 (33.17 %)
4
6
18
Representation of the words
Dim 2 (19.4 %)
0
2
4
6
indeterminate_taste
doughy-a_little_tasteless-slightly_sweet
thick_in_the_mouth-slightly_sweet
bitter
unknown_taste-heavy
tastelessly-neutral
undefinable
strong_taste_of_strawberry_raspberry
strawberry-thick
strawberry-acid
more_soft-less_sweet
mixture
too_much_bitter
strawberry-raspberry
Carrefour_SB
very_creamy-light_fruity_taste
marked_taste Innocent_SB
tasteless
not_sweet-liquid-tasteless
more_or_less_tasteless
liquid-fruit_juice-unknown_taste
bitterness
soft_fruits-soft-sweet
-4
-2
pineapple banana-strawberry-thick
strawberry
banana-spicy-citrus fruit
Casino_SRB
peach-apricot
soft-tasteless-disagreeablet
pulp-fruity
acid
soft
sweet banana-coconut-soft-sweet
sweet
orange
Carrefour_MP soft_fruits
exotic
exotic pulp-sweet
taste_of_fruits-cold
Immedia_MP
soft-smooth_in_the_mouth-not_soft_fruits
orange_juice
strawberry-thick-sweet
Immedia_SRB
acid-sweet-citrus_fruit
Innocent_PBCbanana-sweet-doughy
very_sweet
banana
without_pulp-exotic I_hate
creamy-soft
acid-thick
Casino_PBC more_or_less_sweet
banana_aroma-heavy
sweet-fluid
coconut
strawberry-good-thick
banana
soft_fruits-liquid-acid
-6
-4
-2
0
2
4
6
banana-very_sweet-thick-soft 19
spicy
thick-pure-banana-vanilla
Dim 1 (33.17 %)
tasteless
Representation of the words
Dim 2 (19.4 %)
0
2
4
6
indeterminate_taste
doughy-a_little_tasteless-slightly_sweet
thick_in_the_mouth-slightly_sweet
bitter
unknown_taste-heavy
tastelessly-neutral
undefinable
strong_taste_of_strawberry_raspberry
strawberry-thick
strawberry-acid
more_soft-less_sweet
mixture
too_much_bitter
strawberry-raspberry
Carrefour_SB
very_creamy-light_fruity_taste
marked_taste Innocent_SB
tasteless
not_sweet-liquid-tasteless
more_or_less_tasteless
liquid-fruit_juice-unknown_taste
bitterness
soft_fruits-soft-sweet
-4
-2
pineapple banana-strawberry-thick
strawberry
banana-spicy-citrus fruit
Casino_SRB
peach-apricot
soft-tasteless-disagreeablet
pulp-fruity
acid
soft
sweet banana-coconut-soft-sweet
sweet
orange
Carrefour_MP soft_fruits
exotic
exotic pulp-sweet
taste_of_fruits-cold
Immedia_MP
soft-smooth_in_the_mouth-not_soft_fruits
orange_juice
strawberry-thick-sweet
Immedia_SRB
acid-sweet-citrus_fruit
Innocent_PBCbanana-sweet-doughy
very_sweet
banana
without_pulp-exotic I_hate
creamy-soft
acid-thick
Casino_PBC more_or_less_sweet
banana_aroma-heavy
sweet-fluid
coconut
strawberry-good-thick
banana
soft_fruits-liquid-acid
-6
-4
-2
0
2
4
6
banana-very_sweet-thick-soft 20
spicy
thick-pure-banana-vanilla
Dim 1 (33.17 %)
tasteless
6
Representation of the smoothies
and their confidence ellipses
2
0
Casino_SRB
-2
Immedia_MP
Carrefour_MP
Immedia_SRB
Innocent_PBC
Casino_PBC
-4
Dim 2 (19.4 %)
4
Carrefour_SB
Innocent_SB
-6
-4
-2
0
2
Dim 1 (33.17 %)
4
6
21
1.0
Representation of the judges
5
4
0.6
14
0.4
12
2
21 9
8
0.2
7
6
16
22
23
20
13
3
18
24
11
1
15 19
10
0.0
Dim 2 (19.4 %)
0.8
17
0.0
0.2
0.4
0.6
Dim 1 (33.17 %)
0.8
1.0
22
Innocent_SB
10
Carrefour_SB
Immedia_MP
Casino_SRB
Innocent_PBC
Carrefour_SB
Innocent_SB
Casino_SRB
Immedia_MP
Carrefour_MP
Immedia_SRB
-4
0
Casino_PBC
Dim 2 (19.4 %)
-2
0
6
2
4
Immedia_SRB
Carrefour_MP
20
30
40
Categorized tablecloth of judge 5
0
10 20 30 40 50 60
-6
-4
-2
Innocent_PBC
Casino_PBC
0
2
4
Dim 1 (33.17 %)
6
23
1.0
Representation of the judges
5
4
0.6
14
0.4
12
2
21 9
8
0.2
7
6
16
22
23
20
13
3
18
24
11
1
15 19
10
0.0
Dim 2 (19.4 %)
0.8
17
0.0
0.2
0.4
0.6
Dim 1 (33.17 %)
0.8
1.0
24
Partial representations of Carrefour_SB
5
12
8
14
4 17
23
21
6
16 20 7
2 Carrefour_SB
Innocent_SB
18
11
9 223
24
19
13
0
Casino_SRB
Carrefour_MP
Immedia_MP
Immedia_SRB
10
15
1
Innocent_PBC
Casino_PBC
-5
Dim 2 (19.4 %)
10
5
-5
0
5
Dim 1 (33.17 %)
10
25
Sorted tablecloths of judges 8 & 22
Judge 22
40
40
Judge 8
Carrefour_SB
Carrefour_MP
Immedia_MP
Carrefour_SB
Immedia_SRB
Innocent_PBC
Carrefour_MP
10
Immedia_SRB
Casino_SRB
10
20
Casino_PBC
30
Innocent_SB
Innocent_SB
20
30
Casino_SRB
Immedia_MP
Innocent_PBC
0
0
Casino_PBC
0
10
20
30
40
50
60
0
10
20
30
40
50
60
26
Partial representations of Carrefour_SB
5
12
8
14
4 17
23
21
6
16 20 7
2 Carrefour_SB
Innocent_SB
18
11
9 223
24
19
13
0
Casino_SRB
Carrefour_MP
Immedia_MP
Immedia_SRB
10
15
1
Innocent_PBC
Casino_PBC
-5
Dim 2 (19.4 %)
10
5
-5
0
5
Dim 1 (33.17 %)
10
27
Conclusion
28
Conclusion
• Sorted napping: combines the simplicity of
categorization and the nuance of napping
• Can be used by experts or consumers
• Realizable in practice
• Data analyzed by HMFA
• HMFA provides useful and easily
interpretable results
29
SensoMineR a package for sensory data analysis
Journal of sensory studies (2008)
FactoMineR: an R package for multivariate analysis
Journal of statistical software (2008)
http://www.agrocampus-rennes.fr/math/
30