Construction of an Ideal Map - OP&P Product Research

Food Quality and Preference 26 (2012) 93–104
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Food Quality and Preference
journal homepage: www.elsevier.com/locate/foodqual
Construction of an Ideal Map (IdMap) based on the ideal profiles obtained
directly from consumers
Thierry Worch a,b,⇑ , Sébastien Lê b , Pieter Punter a , Jérôme Pagès b
a OP&P Product Research, Utrecht, The Netherlands
b Laboratoire de Mathématiques Appliquées, Agrocampus Ouest, Rennes, France
article
info
abstract
Article history:
Received 20 January 2012
Received in revised form 13 March 2012
Accepted 1 April 2012
Available online 10 April 2012
Keywords:
Ideal Profile Method
Preference mapping
Confidence ellipses
Consumers
Optimization
In this paper, the Ideal Mapping technique is presented. It is similar to the preference mapping technique
using the quadratic model proposed by Danzart. Indeed, both methods start from the sensory product
space (i.e. they are both called ‘‘external’’ maps) and aim at defining areas within the product space that
would satisfy a maximum number of consumers.
However many differences are observed between the maps. Among them, there is (1) the nature of the
maps (based on hedonic ratings vs. ideal profiles), (2) the way they are constructed (individual models vs.
variability of the ideal profiles), (3) their meanings (liking zones vs. ideal zones) and (4) the proportion of
consumers they would satisfy (high vs. low).
The application of both methodologies on the two examples shows that the IdMap is rather a complement
to the PrefMap than a substitute. When the final ideal product (i.e. satisfying a maximum number of
consumers) belongs to the product space (e.g. perfume dataset), the IdMap confirms the PrefMap solution.
When the final ideal product is located outside the product space (e.g. croissant dataset), the IdMap can be
seen as an extension of the PrefMap.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
In sensory analysis, a common practice is to ask a panel of experts
or trained panelists to rate the products tested on a set of
pre-defined attributes (Quantitative Descriptive Analysis or QDA Ò ,
Stone, Sidel, Oliver, Woosley, & Singleton, 1974). Meanwhile, consumers
evaluate the same products and rate them according to
their liking (Central Location Test or CLT). From these two tests,
two different types of information concerning the products are collected:
the sensory profile on one hand and the hedonic scores on
the other hand.
In order to better understand the consumers’ hedonic judgments,
and more especially which sensory attributes influence positively
or negatively their liking, an analysis joining these two types
of information – sensory description and hedonic judgments – is
performed. For instance, the two tables can be combined and analyzed
simultaneously. This is the principle of the preference mapping
techniques (Greenhoff & MacFie, 1994) which became important in
the process of product development as it guides for products’
improvement.
⇑ Corresponding author at: OP&P Product Research, Burgemeester Reigerstraat
89, NL-3581KP Utrecht, The Netherlands.
E-mail address: thierry@opp.nl (T. Worch).
In practice, two types of preference mapping technique exist
(Carroll, 1972). These two techniques differ according to the point
of view adopted:
– if the focus is on the hedonic data – the sensory information being
projected as supplementary within the preference space – an
internal preference mapping (or MDPref) is performed;
– if the focus is on the sensory profiles of the products, the hedonic
scores being then regressed on the sensory dimensions, an
external preference mapping (or PrefMap) is performed.
In both cases, several derivatives exist. For the internal preference
mapping, there are the Consumers’ Preference Analysis (CPA:
Lê, Husson, & Pagès, 2006) or the Landscape Segmentation Analysis
(LSA, Ennis, 2005). For the external preference mapping, the diversity
mainly lies in the choice of the model explaining the individual
liking scores in function of the sensory dimensions (Schlich & McEwan,
1992). It can be more or less complex, going from the linear
model to the quadratic model proposed by Danzart (1998).
At the present time, the model proposed by Danzart (noted here
as PrefMapD) is the standard model used in external preference
mapping. It allows constructing a surface plot at the panel level
(as an addition of individual surface plots obtained from each consumer)
in which the profiles of an ideal product which belongs to
the area where a maximum proportion of consumers would like
0950-3293/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.foodqual.2012.04.003

94 T. Worch et al. / Food Quality and Preference 26 (2012) 93–104
the product can be estimated (Danzart, 2009; Mao & Danzart,
2008).
Although many external preference mapping studies involving
all types of products have been published in the recent years (for
a short review, see Van Kleef, Van Trijp, and Luning (2006)), it is
subject to many criticisms. Among them can be mentioned (Faber,
Mojet, & Poelman, 2003):
- only the two first sensory dimensions are used to explain the
liking scores. Hence, some relevant information is discarded,
which can lead to ‘‘irrelevant’’ models for a non-negligible number
of consumers;
- adding extra dimensions in the circular, elliptic or quadratic
models can over-fit the liking scores. In this case, the optimization
of the products can be due to a small proportion of consumers
only, as only a low number of degrees of freedom are
available for the estimation of the parameters.
Therefore, other multi-table analyses such as Multiple Factor
Analysis (MFA, Couronne, 1996; Escofier & Pagès, 2008), PLS
regression (Husson & Pagès, 2003) or the L-PLS regression – when
extra information concerning the consumers is available –
(Lengard & Kermit, 2006) have been proposed.
In this paper, we propose a variation of PrefMap when sensory
data is collected according to the Ideal Profile Method (IPM, Worch,
2011; Worch, Lê, Punter, & Pagès, 2011). In this case, the consumers
provide three types of information: the sensory profiles (i.e.
how consumers perceive the products), the hedonic scores (i.e. how
they like the products) as well as their ideal profiles (i.e. what are
the consumers’ expectations). This technique takes into consideration
the sensory profiles of the products and the ideal profiles directly
provided by consumers for the construction of the map.
2. Materials and methods
2.1. Notation
The same notation as the one used in the paper from Worch, Lê,
Punter, and Pagès (2012) checking for the consistency of the ideal
data obtained from the IPM are used here. Hence, we denote in the
rest of the article (the vectors are in bold):
P: number of products tested;
A: number of attributes used to describe the products tested as
well as the ideal products;
J: number of consumers.
y jpa : intensity perceived by the consumer j for the product p and
the attribute a;
y j,a ={y jpa ; p =1:P}: vector or intensities perceived by the
consumer j for the P products and the attribute a;
Y j;a : average over the index p; average intensity perceived by
the consumer j on attribute a over the P products. (Table 1)
Z jpa : ideal intensity of the attribute a provided by the consumer
j after testing the product p;
Z j,a ={Z jpa ; p =1;P}: vector of ideal intensities of the attribute a
provided by the consumer j for the P products;
z j;a : average over the index p; average ideal intensity of the
attribute a provided by the consumer j over the P products.
h jp : hedonic judgment provided by the consumer j for the product
p;
H j ={h jp ; p =1:P}: vector of hedonic judgments provided by the
consumer j for the P products.
The difference between consumers related to a different use of
the scale is not of great interest here. The averaged ideal profile
from each consumer is hence corrected by subtracting, for each
attribute, the averaged intensity that the consumer perceived for
the entire set of products (Eq. 1). The corrected averaged ideal profile
is denoted ~z j .
~z j;a ¼ z j;a
y j;a ð1Þ
Note: The term corrected refers to a geometric translation of the
ideal ratings according to the consumer’s use of the scale. It is performed
in order to readjust all the consumers’ scales together. In
other words, corrected refers to corrected for the scale use. In the rest
of the document, we denote as corrected ideal profile the ideal profile
from a consumer which has been corrected from the use of the
scale using Eq. (1).
2.2. Materials
To illustrate the methodology presented below, two datasets
obtained from the IPM are used: the perfume (Worch, Lê, & Punter,
2010) and the croissant datasets.
Perfume: It concerns 12 luxurious women perfumes among
which two were duplicated (Table 2). Each product has been rated
on 21 attributes (listed in Table 2) by 103 Dutch consumers. For
each perfume and each attribute, both the perceived and ideal
intensities have been rated on a line scale. After rating each product
on perceived and ideal intensity, overall liking was rated on a
structured 9-point category scale. The 14 samples were presented
in monadic sequence, taking care of order and carry-over effects
(MacFie, Bratchell, Greenhoff, & Vallis, 1989) in two 1-h sessions.
Croissant: Following the same procedure, nine croissants have
been tested by 151 Dutch consumers (Table 3). Each product has
been rated on 26 attributes (Table 3). For confidentiality reasons,
the product names and their differences in the recipes will not
be mentioned here.
Table 1
Organization and illustration of the notation for the sensory data.
Table 2
List of products and attributes in the perfume study. Note: the products Pure Poison
and Shalimar have been duplicated.
Products Type Attributes
Angel Eau de Parfum Intensity Spicy
Cinema Eau de Parfum Freshness Woody
Pleasures Eau de Parfum Jasmine Leather
Aromatics Elixir Eau de Parfum Rose Nutty
Lolita Lempicka Eau de Parfum Chamomile Musk
Chanel No. 5 Eau de Parfum Fresh lemon Animal
L’Instant Eau de Parfum Vanilla Earthy
J’Adore (EP) Eau de Parfum Citrus Incense
J’Adore (ET) Eau de Toilette Anis Green
Pure Poison Eau de Parfum Sweet fruit
Shalimar Eau de Toilette Honey
Coco Mademoiselle Eau de Parfum Caramel

T. Worch et al. / Food Quality and Preference 26 (2012) 93–104 95
Table 3
List of products and attributes in the croissant study.
Products Attributes
Croissant 1 Length External color Butter taste
Croissant 2 Height Internal color Overall taste
Croissant 3 Bending Aroma of butter Sweetness
Croissant 4 Shape Aroma overall Saltiness
Croissant 5 Twist Crispiness Fatty taste
Croissant 6 Consistency of shape Lamination Musty taste
Croissant 7 Consistency of size Firmness Aftertaste intensity
Croissant 8 Layers Moistness of crumb Aftertaste length
Croissant 9 Gloss Chewiness
2.3. Methods
The construction of the Ideal Map is based on the methodology
of the PrefMapD. Therefore, a comparison of results obtained from
both methodologies is also presented.
2.3.1. IdMap
2.3.1.1. Definition of the product space. Like for PrefMapD, the IdMap
takes as starting point the sensory product space. Thus, the IdMap
is defined as an external map which is directly comparable to
PrefMapD.
The product space is created from the averaged sensory profiles
y p;a (Table 4a). It is obtained by multivariate analysis (Principal
Component Analysis, MFA, Generalized Procrustes Analysis, etc.). In
this case, PCA is used.
2.3.1.2. Projection of the corrected ideal products from each consumer
and of the liking scores on that space. In this product space, the corrected
ideal products ~z jpa obtained from each consumer are projected
as supplementary entities (Table 4b). The distribution of
the projection of these ideal products provides a first idea on the
direction to take to develop an eventual ideal product satisfying
a maximum of consumers (Fig. 1).
2.3.1.3. Creation of the IdMap as a density map. To create the IdMap,
a first solution consists in measuring the density of points (i.e. ideal
products) projected in each zone of the space (Fig. 2).
However, the low density of points projected (PxJ for full designs)
does not allow the creation of a map which would be as
precise as the one obtained with PrefMapD. Indeed, a high resolution
(i.e. square the space in a high number of small zones) only
Table 4
Organization of the data used for the definition of the sensory space (a) with projection of the corrected ideal profiles as supplementary entities (b), and of the liking scores as
supplementary variables (c).
Dim 2 (26.14%)
-20 -10 0 10 20 30
-40
-20
0
20
40
Dim 1 (45.41%)
Fig. 1. Projection of the corrected ideal products provided from the consumers on the sensory product space.

96 T. Worch et al. / Food Quality and Preference 26 (2012) 93–104
Fig. 2. Ideal Map obtained based on the density of ideal products projected in each zone of the space.
associates each individual zone with a very small number of projections
while a low resolution (i.e. squaring the space in a lower
number but wider zones) creates a ‘‘gross’’ map.
Moreover, this procedure does not take into account important
information concerning the variability of the ideal profiles provided
by the same consumer. Indeed, the IdMap created based on
the density does not consider the origin of the projections: in this
case, no difference is made whether the ideal products in a same
zone are provided by one or many consumers.
Let’s consider 100 consumers providing 10 ideal profiles each.
One thousand points are hence projected on this map. An ideal
product belonging to a zone of the space regrouping 10% of the
projections can either be linked to a large number of consumers
(one point per consumer), or to a small number of consumers
(the 10 ideal profiles of 10 consumers). In these cases, the impact
is not the same since the creation of such ideal product will not affect
the same population (100 vs. 10 consumers).
2.3.1.4. Smoothing procedure: use of confidence ellipses around the
averaged ideal products. In order to take into account the variability
within consumers of their ideal ratings, a confidence ellipse is constructed
around the averaged ideal profile provided by each consumer
(Husson, Lê, & Pagès, 2005). These confidence ellipses are
obtained by partial bootstrap on the products tested.
In practice, a random sampling with replacement of P 0 among
the P tested products is performed (usually, P 0 is equal to P). For
each consumer, the corrected ideal profile averaged over the P 0
products is computed and projected as illustrative on the sensory
space. This corresponds to answering the following question:
‘‘where the corrected averaged ideal product of a consumer would
be projected if, instead of rating it according to the P products, he
would rate it according to the P 0 products?’’
This simulation step is iterated many times (500 times in practice)
and the confidence ellipses containing 95% of the projections
are constructed around each consumer (Fig. 3).
Note: In this situation, the consumers are associated to one unique
ideal profile that they described P times with a certain variability
highlighted by the confidence ellipses. When the products
tested are from different categories (e.g. milk and dark chocolate),
consumers might provide multiple ideals. In such situation, the Id-
Map should be performed on the larger subset of products corresponding
to one unique ideal.
Dim 2 (26.14%)
-15 -10 -5 0 5 10 15
-10 -5 0 5 10 15 20
Dim 1 (45.41%)
Fig. 3. Confidence ellipses constructed around the corrected averaged ideal
products from each consumer.
For each point of the sensory space, the amount (in percentage)
of ellipses covering that area is computed. In other words, for each
point of the space, the proportion of consumers having an ideal in
each area of the space is measured (Fig. 4).
In order to facilitate the interpretation of the results, a color
code is associated to each zone of the space: the larger the proportion
of consumers in an area of the space, the lighter the color.
2.3.1.5. Creation of the IdMap. Finally, the external Ideal Map
including contour lines associated with the proportion of consumers
is constructed (Fig. 5).
2.3.1.6. Notion of weight for the consumers. In theory, a large confidence
ellipse means that the product is associated with a large variability.
In our case, a large variability can be interpreted in two
ways:

T. Worch et al. / Food Quality and Preference 26 (2012) 93–104 97
Dim 2 (26.1%)
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-10 -5 0 5 10 15 20
Dim 1 (45.4%)
Fig. 4. Proportion of consumers sharing a common ideal for each point of the
sensory space.
Dim 2
-6 -4 -2 0 2 4 6 8
3
1
7
20
2
15
6
-5 0 5 10 15
Dim 1
Fig. 5. Ideal Map including contour lines indicating the proportion of consumers.
- the consumer considered is associated with a large ideal area;
- the consumer considered has difficulties rating stable ideals.
In practice, it is impossible defining a threshold above which a
confidence ellipse would be considered as large as well as determining
the reason of this variability. However, a consumer associated
with a large (vs. small) confidence ellipse has a stronger
influence (resp. lower) in the construction of the IdMap. Indeed, a
larger (resp. smaller) area of the sensory space is covered.
For that reason, it might be worthwhile homogenizing consumers.
To do so, each consumer is associated with a weight which is
inversely proportional to the size of its corresponding ellipse. Each
weighted consumer is thus associated with an ellipse of area equal
to one unit which is spread on the sensory space:
5
30
10
25
4
15
15
10
- a consumer rating stable ideal intensities (hence associated
with a small ellipse) has a strong weight on each point of the
small surface it covers;
- a consumer rating large ideal intensities (hence associated with
a large ellipse) has a small weight on each point of the wide surface
it covers.
The map thus obtained is noted weighted Ideal Map or wIdMap.
In this case, the contour lines do not correspond to the raw proportion
of consumers, but to a corrected proportion according to
the different consumers’ weights.
If one assumes that large confidence ellipses correspond to consumers
with wide ideal area, the use of the IdMap is recommended.
However, if one assumes that wide ellipses correspond to instability
of the ideal ratings, the wIdMap is preferred.
2.3.1.7. Definition of the ideal product. For the PrefMapD, the coordinates
corresponding to the maximum proportion of consumers
overlapping can be extracted. By using the inverse formula from
the PCA – which aims at estimating the sensory profile of a product
based on the coordinates on the map – a potential profile of the
ideal product can be estimated based on these coordinates.
This procedure can also be applied to the IdMap technique. As
the individual ideal profiles are known, one could also use as ideal
product the averaged ideal profile calculated directly from the consumers
sharing an ideal product in this area of the map.
2.3.2. Comparison of the IdMap and the PrefMapD
Although both methodologies (IdMap and the PrefMapD) are
similar, the nature of the data involved differs. And it is especially
according to this difference that both techniques are compared.
2.3.2.1. Link between the maps (a priori). According to Worch et al.
(2012), a consumer is consistent if the ideal product provided
shares similar characteristics with the preferred product.
Thus, in the sensory space, the projection as illustrative of the
ideal profiles provided by a consumer must be close to the preferred
product. To check that, the corrected ideal profiles of the
consumers (Table 4b) on one hand and the hedonic scores on the
other hand (Table 4c) are, respectively, projected as supplementary
entities and supplementary variables on the sensory space (Table
4a). For a panel composed of consistent consumers, the distribution
of the consumers within the correlation circle (hedonic) is
coherent (i.e. going in the same direction) with the distribution
of the projections of their ideal profiles within the sensory space.
This double projection provides a first visual impression about
the relationship between IdMap and PrefMapD. However, it is only
approximate as the one to one relationship is not further studied
here.
2.3.2.2. Liking threshold and definition of the PrefMapD and IdMap
maps. In this study a product is defined as liked by a consumer if
the consumer considered would like it more than a certain threshold
value. Similarly, each consumer is associated to an area of liking
corresponding to the area of the sensory space which contains
products he/she would like.
The construction of the PrefMapD depends on the threshold value
(also called liking threshold), as it determines whether a product
belonging to the sensory space would be liked or not by each
consumer.
In practice, for a given consumer, each point of the space is
associated with a product whose liking score is estimated based
on a model defined for that consumer. This estimation of the liking
score is compared to the liking threshold: if the estimation is larger
(resp. smaller) than the threshold, the product corresponding to
this point of the space is liked (resp. rejected) by the consumer.

98 T. Worch et al. / Food Quality and Preference 26 (2012) 93–104
The larger the threshold, the smaller the surface of liking for
each consumer. Thus, increasing the threshold reduces the chances
of overlap between individual areas of liking, hence reducing the
proportion of consumers sharing a common ideal.
In this paper, the standard threshold is considered for PrefMapD.
It corresponds to the averaged hedonic rating h j each consumer
provided to the products. In practice, this threshold means liking
on average half of the product space for each consumer. Thus,
the liking area defined for each consumer is wide and is not defining
a maximum-liking area for the standard PrefMapD.
The use of such a threshold does not occur with the IdMap.
However, it is possible to influence (to a lesser extent) the proportion
of consumers sharing a common ideal by adjusting the size of
the individual confidence ellipses: the larger the individual ellipses,
the higher the chances of overlap. The size of the ellipses depends
on several parameters:
- the variability of the ideal profiles provided by a consumer;
- the p-value used to create the ellipses (by default, the ellipses
contain 95% of the projections, and reducing this proportion
reduces the size of the ellipse);
- the number of products used for the resampling: increasing the
number of products in the resampling procedure reduce the
size of the ellipses;
- at some extent, the application of weight to the ellipses as in the
wIdMap.
In practice, the confidence ellipses cover only a small area of the
product space. By definition, this liking area corresponds to
(a)
maximum liking (i.e. ideal product) for each consumer. Thus, we
are talking about ideal area with the IdMap.
The theoretical difference in the meanings of the individual liking
and ideal areas in PrefMapD and IdMap is related to the threshold
used. This threshold as well as the surface of the area in each
map are schematized Fig. 6.
2.3.2.3. Comparison of the results through the estimated ideal profiles
obtained. Besides the visual comparison of the maps obtained with
the two techniques, one can also compare the sensory profiles of
the ideal products both methods would generate.
However, a one-to-one comparison of the ideal profiles might
not be sufficient, as references are needed. To enrich the comparison,
the sensory profiles of the tested products are added to the
comparison. These sensory profiles are standardized on each attribute
(Eq. 2a), and the same transformation is applied to the sensory
profiles of the estimated ideal products (Eq. 2b).
Standardization of the sensory profiles of the tested products
: ðy pa
y a Þ=ry;a
Standardization of the sensory profiles of the ideal products
: E pa
y a =ry;a
The P + 2 standardized products are represented graphically.
(b)
ð2aÞ
ð2bÞ
Density
acceptance threshold
for PrefMapD
Density
acceptance threshold
for IdMap
Liking scores
Liking scores
Fig. 6. Theoretical difference in the ‘‘threshold’’ used to define the individual acceptance area for PrefMapD (left, a) and IdMap (right, b). Note: the arrow shows that for the
PrefMapD, the acceptance threshold can be adjusted.
Table 5
Properties and definition of the maps obtained with PrefMapD et IdMap.
Ideal Profiles
PrefMapD
Indirect
Globally estimated from an aggregation of individual data
No possible validation
IdMap
Direct
Directly measured at the consumer level, and then aggregated
Direct validation through the study of the consistency of the individual
data
Extended product space (the individual ideal data can be outside the
product space)
Space considered
Product space only (the individual estimations belong to the
product space)
Interpretation issues Models: Ellipses:
-Strong dependence to the individual models
-Size: large ideal area or unstable ratings?
-Low number of degrees of freedom
-Homogenization of the ellipses? (use of individual weights)
Proportion of consumers Mechanic dependence to the threshold considered
Mechanic dependence to the size of the ellipses
(contour lines)
High when the threshold is low: there is a risk of finding Generally low by construction as it corresponds to a common ideal for
Meanings of the map
unstable maxima
Area of non-rejection (rather than area of preference) when
the threshold is low
a group of consumers
Ideal area for each consumer

T. Worch et al. / Food Quality and Preference 26 (2012) 93–104 99
2.3.2.4. Properties of the different maps. The properties of the different
maps obtained according to PrefMapD and IdMap are summarized
Table 5.
3. Results
The methodology presented above is applied to the perfume and
to the croissant datasets.
3.1. Measure a priori of the link between the maps
The consistency of the ideal and hedonic data is measured visually
in the sensory space by projecting simultaneous the corrected
ideal products from each consumer as supplementary entities and
the hedonic ratings as supplementary variables.
In the perfume example, the projection of the hedonic ratings as
supplementary variables highlights homogeneity of the panel, the
majority of consumers preferring the products located on the negative
part of the first dimension (Fig. 7). Meanwhile, the projection
of the corrected ideal products also suggests homogeneity of the
panel, the majority of the points being located along the negative
part of the first dimension.
In the croissant example, the projection of the hedonic ratings as
supplementary variables highlights more heterogeneity than in the
perfume example (Fig. 8). However, most of them point to the lower
right corner of the space (positive side on the first dimension
Dim 2 (17.06%)
-20 -10 0 10 20 30
Dim 2 (17.06%)
-1.0 -0.5 0.0 0.5 1.0
-30 -20 -10 0 10 20
Dim 1 (68.12%)
-1.0 -0.5 0.0 0.5 1.0
Dim 1 (68.12%)
Fig. 7. Projections as supplementary entities (left) of the corrected ideal profiles and as supplementary variables (right) of the liking ratings on the sensory space (perfume
example).
Dim 2 (16.31%)
-40 -30 -20 -10 0 10 20
Dim 2 (16.31%)
-1.0 -0.5 0.0 0.5 1.0
-20 -10 0 10 20 30
Dim 1 (38.4%)
-1.0 -0.5 0.0 0.5 1.0
Dim 1 (38.4%)
Fig. 8. Projections as supplementary entities (left) of the corrected ideal profiles and as supplementary variables (right) of the liking ratings on the sensory space (croissant
example).

100 T. Worch et al. / Food Quality and Preference 26 (2012) 93–104
1
Dim 2 (17.06%)
-6 -4 -2 0 2 4 6
JAdore_EP
JAdore_ET
Pleasures CocoMelle
PurePoison2
LolitaLempicka
LInstant
Cinema
Chaneln5
AromaticsElixir
Shalimar
Shalimar2
Angel
Dimension2 (17.06 %)
0
-1
citrus
sweet_fruit
freshness
green
rose
jasmin
fresh_lemon
vanilla
honey
caramel
anis
camomille
intensity
nutty
animal
musk
woody
incense
leather
earthy
spicy
-5
0
Dim 1 (68.12%)
5
-1 0 1
Dimension1 (68.12 %)
Fig. 9. Sensory space obtained for the perfume dataset.
As it is often the case in PrefMapD, only the first two dimensions
are considered in this case.
Dim 2
-6 -4 -2 0 2 4
60
and negative side on the second dimension). The projection of the
individual ideal profiles (as supplementary entities) in the same
space shows homogeneity of the consumers in their ideal products,
the majority of them being projected into the lower right corner of
the sensory space.
As the repartition of both projections is consistent in both
examples, one can a priori expect some similarities in the results
of the IdMap and the PrefMapD.
3.2. Comparison of the maps
70
70
70
90
JAdore_EP
50
80
LInstant
Cinema
JAdore_ET
PleasuresCocoMelle
PurePoison PurePoison2
-4 -2 0 2 4 6
Dim 1
In order to construct the different maps, the sensory space has
to be defined. This space is obtained by PCA performed on the sensory
profiles of the products (Table 4a).
40
LolitaLempicka
Chaneln5
Fig. 10. PrefMapD for the perfume dataset.
AromaticsElixir
30
30
20
Ang
Shalimar
Shalimar2
3.2.1. Perfume example
In the perfume example, the first plane of the PCA (Fig. 9) summarizes
85% of the information. The first dimension opposes
J’Adore and Pleasures described as fresh and fruity to Shalimar
and Angel described with stronger oriental notes. The second
dimension opposes Angel and Lolita Lempicka described with sweet
notes to Aromatic Elixir.
The PrefMapD (Fig. 10) highlights a stronger liking area along
the negative part of dimension 1. Thus, the most liked products
are J’Adore and Coco M elle . The homogeneity of consumers mentioned
previously is highlighted here by the large proportion of
consumers liking these products. Indeed, 80% of the consumers
would like J’Adore and Coco M elle more than average.
However, one can find an ‘‘empty’’ area in which the corresponding
product would be liked by more than 90% of the consumers.
This corresponds to a local ideal product.
The IdMap (Fig. 11a) provides similar results, the ideal area
shared by a maximum of consumers being also located on the negative
part of first dimension. However, this local ideal product
seems a little bit less ‘‘extreme’’ along this dimension than the
one obtained with the PrefMapD. It is shared by 38% of the
consumers.
In this example, the ratio in size between the smallest and the
largest ellipse is about 1–50. In other words, consumers do not rate
their ideal with the same variability, which means that they do not
have the same weight in the construction of the map. To adjust the
map according to those differences, consumers are homogenized
before constructing the map.
The wIdMap is shown in Fig. 11b. In this case, the ideal product
shared by a maximum of consumers (35%) is located in a similar
area as for the IdMap. Here, the consensus areas are globally
smaller than for the IdMap, although they correspond to similar
proportions of consumers.
By using the inverse formula in the PCA, the potential sensory
profiles of the ideal products obtained with the PrefMapD and Id-
Map are estimated. In the PrefMapD, this ideal product is located

T. Worch et al. / Food Quality and Preference 26 (2012) 93–104 101
Dim 2
-4 -2 0 2 4 6 8
10
10
10
20
JAdore_EP
JAdore_ET
20
30
LInstant
Cinema
35
Pleasures
CocoMelle
PurePoison
PurePoison2
15
25
20
10
LolitaLempicka
Chaneln5
AromaticsElixir
Angel
Shalimar
Shalimar2
Dim 2
-4 -2 0 2 4 6 8
JAdore_EP
JAdore_ET
20
10
20
25
LInstant
Cinema
30
20
Pleasures
CocoMelle
PurePoison
PurePoison2
15
LolitaLempicka
15
Chaneln5
AromaticsElixir
Angel
Shalimar
Shalimar2
-5 0 5
Dim 1
-5 0 5
Dim 1
Fig. 11. IdMap (left, a) and wIdMap (right, b) obtained for the perfume dataset.
Table 6
Estimation of the sensory profiles of the ideal products obtained with PrefMapD and
IdMap (perfume example).
IdMap PrefMapD IdMap PrefMapD
Intensity 59,0 56,4 Caramel 25,1 24,6
Freshness 52,2 56,0 Spicy 36,7 34,0
Jasmine 39,6 40,7 Woody 27,0 24,2
Rose 38,1 39,7 Leather 21,1 18,6
Camomile 29,1 28,7 Nutty 28,0 26,5
Fresh_lemon 35,5 37,2 Musk 32,5 29,9
Vanilla 33,1 33,3 Animal 20,2 18,5
Citrus 30,2 31,5 Earthy 20,0 17,6
Anis 24,9 24,6 Incense 26,5 23,9
Sweet_fruit 32,0 34,0 Green 27,1 28,7
Honey 26,6 26,6
at coordinates ( 3, 1), while in the IdMap, it is located at ( 0.9,
0.6). The sensory profiles thus obtained are given Table 6.
In order to better evaluate the differences between these two
profiles, they are standardized on each attribute according to the
profiles of the tested products and represented in Fig. 12. The differences
between these two products being mainly observed on
the first dimension, the attributes are ordered according to their
coordinates on this dimension (in decreasing order). For a better
comparison, the standardized profiles of the products tested are
also shown.
The two estimated ideal profiles belong to the product space.
The ideal intensity ratings are in the same order of magnitude as
the products tested. A more systematic comparison per attribute
of the difference between the perceived and ideal intensities allows
product’s improvement. However, this is not done here.
Fig. 12. Sensory profiles of the ideal products obtained with PrefMapD and IdMap standardized according to the profiles of the products tested in the perfume example.

102 T. Worch et al. / Food Quality and Preference 26 (2012) 93–104
Dim 2 (16.31%)
-4 -2 0 2 4 6
7
6
8
1
9
5
3
2
4
Dimension2 (16.30 %)
1
0
overall_taste
eat
musty_taste
lamination
overall_aroma
internal_color
saltiness
crispiness
aftertaste_intensity
aftertaste_length
fatty_taste
external_color
height
gloss
consistency_shape
moistness_crumb
layers
firmness
butter_taste
sweetness
twist
shape
consistency_size
butter_aroma
bending
-1
-4 -2 0 2 4 6
Dim 1 (38.4%)
-1 0 1
Dimension1 (38.40%)
Fig. 13. Sensory space obtained for the croissant dataset.
Dim 2
-4 -2 0 2 4
40
7
40
40
6
50
40
8
40
50
50
1
50
9
40
-4 -2 0 2 4
Dim 1
Fig. 14. PrefMapD for the croissant dataset.
Although both sensory profiles are very similar, the ideal product
obtained from the PrefMapD is a little bit more ‘‘extreme’’ for
some attributes than the one obtained from the IdMap.
3.2.2. Croissant example
In the croissant example, the first plane of the PCA (Fig. 13) summarizes
55% of the information. The first dimension opposes the
products 7, 6 and 8 described as eat, overall taste, musty taste and
lamination to the products 4, 2 and 3 described as firm, moist of
crumb and butter and fatty taste. The second dimension opposes
the products 3 and 6 defined by shape, bending and consistency of
size to the product 9 defined by saltiness, overall aroma and internal
color.
The PrefMapD (Fig. 14) highlights an area of maximum liking in
the lower right corner of the plane (positive side of the dimension
50
5
3
2
50
60
60
70
70
4
50
1 and negative side of the dimension 2). This corresponds to the results
shown in Fig. 8. Sixty to seventy percent of consumers would
be satisfied with a product belonging to that area. In comparison to
the perfume example, this proportion is relatively low. This can be
explained by the greater heterogeneity of the consumers in this
example.
Although there is a potential ideal product in the lower right
corner of the plane, the map seems to highlight that the maximum
proportion of consumers liking a product has not been reached, a
higher proportion being eventually defined for a product falling
outside the sensory space.
In the IdMap (Fig. 15a), the area containing the ideal product
satisfying a maximum of consumers is also located in the lower
right corner of the space. However, this ideal area is defined outside
the product space as it is more extreme along the 2nd
dimension.
Here again, the ratio in size between the smallest and the largest
ellipse is about 1–50. The solution obtained after balancing
consumer together is also shown here.
The results of the wIdMap (Fig. 15b) are similar to the one of the
IdMap. The ideal product satisfying a maximum of consumers is
also located in the lower right corner of the sensory space. However,
in this case, areas of consensus are less well defined and
the proportions of consumers are slightly decreasing.
By using the inverse formula in the PCA, the potential sensory
profiles of the ideal products obtained with the PrefMapD and Id-
Map are estimated. In the PrefMapD, this ideal product is located
at coordinates (4.3; 1) while in the IdMap, it is located at (4.3;
4.5). The sensory profiles thus obtained are given Table 7.
The standardized ideal profiles are shown Fig. 16. The difference
being mainly along the second dimension, the attributes are ordered
in decreasing order along this dimension.
It shows which attributes (and how) should be changed to improve
the products tested. It appears here that the intensities overall
taste and musty taste should be reduced while sweetness, butter
taste and butter aroma should be intensified. And the ideal profiles
obtained with PrefMapD and IdMap differ mainly for the attributes
musty taste, overall aroma and saltiness for which IdMap requires
less intensity while for lamination, shape, consistency of size and
bending it requires more intensity to get closer to the ideal.

T. Worch et al. / Food Quality and Preference 26 (2012) 93–104 103
Dim 2
-8 -6 -4 -2 0 2 4
7
6
8
1
9
10
5
1010
10
15
3
2
15
10
4
15
10
Dim 2
-8 -6 -4 -2 0 2 4
7
6
8
1
9
5
10
10
3
2
10
10
4
10
-4 -2 0 2 4 6 8
Dim 1
-4 -2 0 2 4 6 8
Dim 1
Fig. 15. IdMap (left, a) and wIdMap (right, b) obtained for the croissant dataset.
Table 7
Estimation of the sensory profiles of the ideal products obtained with PrefMapD and IdMap (croissant example).
IdMap PrefMapD IdMap PrefMapD
Length 63,3 61,7 Crispiness 46,7 51,7
Height 59,8 60,5 Lamination 48,0 38,9
Bending 67,2 47,0 Firmness 65,9 64,5
Shape 62,2 50,9 Moistness_crumb 61,5 60,8
Twist 60,9 42,9 Eat 33,1 35,1
Consistency_shape 40,7 40,9 Butter_taste 54,4 51,7
Consistency_size 56,0 54,1 Overall_taste 25,5 28,4
Layers 58,1 56,9 Sweetness 39,3 37,1
Gloss 49,0 49,6 Saltiness 25,5 27,8
External_color 53,4 55,1 Fatty_taste 42,8 45,0
Internal_color 37,7 43,6 Musty_taste 21,3 23,6
Butter_aroma 54,0 50,5 After taste_intensity 43,3 45,0
Overall_aroma 28,0 30,7 After taste_length 41,9 43,7
Fig. 16. Sensory profiles of the ideal products obtained with PrefMapD and IdMap standardized according to the profiles of the products tested in the croissant example.

104 T. Worch et al. / Food Quality and Preference 26 (2012) 93–104
4. Conclusions
The Ideal Mapping technique is similar to the external preference
mapping technique. However, the nature of the data used is
different: for PrefMapD the sensory profiles of the products are
combined to the hedonic scores while in the IdMap, the sensory
profiles of the products are associated to ideal ratings. For that
matter, the objectives of the techniques are different: the PrefMapD
is used to define zones of maximum liking, and eventually market
opportunities while the IdMap aims at defining (estimated or directly)
the profile of an ideal product that could be used to guide
product developers for the improvement of their products. Moreover,
the IdMap can also be used to find clusters of consumers
based on their ideals.
In the construction of the maps, the major difference between
both techniques is related to the meaning of the liking area defined
for each consumer.
In the PrefMapD, the individual surfaces are obtained by comparing
the estimations to a threshold. As the standard value of this
threshold corresponds to the average hedonic rating provided by
each consumer for all products, the individual surfaces are large.
Hence, they cannot be considered strictly as ideal area. In the Id-
Map, the individual surfaces are smaller as they correspond to
the ideal surface for each consumer. A consequence is that the proportion
of consumers overlapping is decreased in this case.
In order to get more similar maps (especially in terms of proportions
of consumers), one could raise the threshold in the Pref-
MapD. The liking areas thus defined correspond to areas where
only potentially highly liked products are considered for each consumer,
which corresponds more to an ideal area for each consumer.
And by raising the threshold, the individual surfaces of
liking are reduced, which also reduces the likelihood of overlap between
consumers.
As opposed to PrefMapD, the IdMap does not require to model
the hedonic ratings in function of the sensory descriptions. The
variability of the ideal ratings provided by each consumer is used
to define individual ideal surfaces from which the map is constructed.
The confidence ellipses thus obtained can eventually be
balanced together depending on the point of view adopted
(wIdMap).
Thus, the IdMap is rather a complement than a substitute for the
PrefMapD. It is therefore recommended to combine both techniques,
PrefMapD being thus used to validate IdMap. Meanwhile,
IdMap can enrich PrefMapD.
Indeed, one can expect here that the two maps are:
close and consistent if the ideal product obtained with Pref-
MapD belongs to the product space;
consistent and going in the same direction when it is defined
outside the product space.
In the two examples considered, the results from IdMap and
PrefMapD are consistent. The information provided by the two
maps is complementary (especially in the croissant example). Specifically,
when the ideal product is defined outside the product
space, the sensory profile provided directly from the IPM is more
stable than the ideal profile estimated from PrefMapD.
In practice, with the PrefMapD, ideal profiles can also be estimated
outside the product space. However, this procedure is not
advised as the validity of the estimation is questionable for
products outside the range of values (models being calibrated to
a certain range). More precisely, there is a risk that the quadratic
effects become predominant and the more the product is extreme
(and hence far from the product space), the more the products is
liked by the consumers.
For that reason, the estimation of an ideal product outside the
product space seems more valid with IdMap. In this case, the interpretation
still should be done cautiously as consumers have not
been confronted with such product. A validation step which consists
in creating a product closer to this part of the space and to test
it again with the same consumers to ensure a higher liking is
obtained.
In these two examples, the consumers are homogeneous in
their ideal and hedonic ratings. No clusters were found here. However,
in a situation where the panel of consumers is heterogeneous,
one may consider to segment the panel in homogeneous group of
consumers first before applying the methodology proposed here on
each cluster separately. This corresponds to the standard methodology
for analyzing consumer data when the panel is
heterogeneous.
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