Segmentation of consumers taking account of external data. A clustering of variables approach

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1 Food Quality and Preference 13 (2002) Segmentation of consumers taking account of external data. A clustering of variables approach E. Vigneau*, E.M. Qannari ENITIAA/INRA, Unité de Sensométrie et de Chimiométrie, la Géraudière, BP 82225, Nantes Cedex, France Received 6July 2001; received in revised form 11 April 2002; accepted 11 April 2002 Abstract A procedure for clustering of variables is proposed for segmenting a panel of consumers when it is desirable to relate preference of consumers to external data such as sensory data. The underlying principle of the method is to find K groups of variables, associated with the scores of consumers, and K latent components such that the variables in each group are as highly correlated as possible to the corresponding latent component. In addition, the latent components are constrained to be linear combinations of the external data. This approach is complementary to External Preference Mapping. However, it allows a direct segmentation of the panel and involves a smaller number of models than External Preference Mapping. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Consumer segmentation; Acceptance/preference data; Sensory data; Clustering of variables; PrefMap 1. Introduction In a previous paper (Vigneau, Qannari, Punter, & Knoops, 2001), segmentation of a panel of consumers based on a method of clustering of variables around latent components was investigated. In this paper, the approach is extended to the case where it is desirable to relate preference of consumers to external data such as sensory data. One of the most common methods used to relate the preferences of a panel of consumers to external data is External Preference Mapping analysis (PrefMap). Its principle mainly consists of regressing the scores of acceptability of each consumer on the coordinates of the products obtained from the multivariate analysis of the external data (Greenhoff & MacFie, 1994). In practice, linear or quadratic models which include the two (or three) first principal components of the external data are considered. By comparison, the clustering approach suggested herein: (a) directly provides a segmentation of the panel of consumers, (b) gives, in each segment, a single model which relates preference scores to external data, whereas Pref- Map derives a separate model for each consumer, * Corresponding author. Tel.: ; fax: (c) captures the most relevant information for explaining preference data even if this information is not contained in the first principal components of external data. (d) leads to the determination of latent components which, although not orthogonal, are respectively associated with homogeneous groups of consumers, whereas PrefMap analysis is based on orthogonal components which are not necessarily linked to segments of consumers. This reminds us of oblique transformation used in Principal Components Analysis which derive non orthogonal, but more easily interpretable, components. The underlying principle of the method of clustering of variables (i.e. consumers in our context) discussed in Vigneau et al. (2001) is to find K groups of variables and K latent components, each being associated with a group, such that the variables in each group are as highly correlated as possible to the corresponding latent component. When external data are available, the principle of the clustering remains the same, except that the latent components are expressed in terms of these external data. By imposing the constraint that the latent components are linear combinations of the external variables, the aim is to explain the hedonic ratings of consumers in each segment using the information contained in these variables. It is worth noting that the external data may include not only chemical or sensory measurements but also quadratic or /02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S (02)

2 516 E. Vigneau, E.M. Qannari / Food Quality and Preference 13 (2002) cross-product terms. This allows the investigation of vector or ideal point models as well. The groups and the associated latent variables are determined by means of a partitioning algorithm. Furthermore, this partitioning algorithm is complemented by a hierarchical clustering technique that helps the practitioner to establish the appropriate number of clusters and gives an initial solution to be used as a starting point in the partitioning algorithm. 2. Methodology Consider a panel of p consumers and the hedonic scores, x 1, x 2,..., x p they have attributed to n products. These variables are assumed to be centered, but not necessarily standardized. If the data are not standardized, the range of scoring is taken into account. This makes it possible to distinguish between those consumers who express marked differences of liking among products (large variance) from those who prefer the products more or less similarly (small variance). Should this aspect be considered as irrelevant, the scores of each consumer might be standardized. In addition to these liking data, we also consider a data set, Z, which contains the characterization of the products according to q external variables. Usually these external data consist of the sensory description of the products provided by a trained sensory panel. However, the external data can also be chemical, physical variables, process parameters... We seek to find simultaneously K groups of consumers, G 1, G 2,...G K and K latent components c 1, c 2,...,c K, respectively associated with the K groups, such that: S ¼ XK X p kj covðx j ; c k Þ ð1þ k¼1 j¼1 is maximized, under the constraints that: c k ¼ Za k and a 0 k a k ¼ 1 where kj =1 if the jth consumer belongs to the group G k, kj =0 otherwise. Criterion S (Eq. 1) involves the covariance between x j and c k [cov(x j,c k )] as a measure of the relationship between the vector of hedonic scores given by consumer j and the latent component in group k. The constraint in Eq. (2) imposes to the latent components to be linear combinations of the external data, whereas the normalizing constraint in Eq. (3) is as usual introduced in order to avoid a scaling indetermination problem. In a matrix form, criterion S can be expressed as: S ¼ XK X p kj a 0 k Z0 x j ð4þ k¼1 j¼1 ð2þ ð3þ In order to maximize this criterion a partitioning algorithm is implemented. This algorithm runs as follows: Step 1: Start with an initial solution consisting of K groups of consumers, obtained by random allocation or, preferably, from the hierarchical clustering method which will be discussed below. Then, iteratively, until the stabilization of the partition is achieved, the following steps are run: Step 2: In each cluster G k, for k=1, 2,.., K, the vector of loadings a k which defines the latent component c k is set to: Z 0 x k a k ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 0 k ZZ0 x k where x k is the centroid of cluster k, defined as the average of the scores associated with consumers in cluster k. Step 3: New clusters are formed by moving each consumer to a new group if the covariance of his (or her) scores with the latent component of this group is higher than the covariance with the latent components associated with any other group. In practice, it is recommended that one performs a hierarchical algorithm beforehand. This algorithm helps in choosing the number K of clusters and defining an initial partition to be used in Step 1 of the previous algorithm. The hierarchical procedure is an agglomerative technique based on the same criterion S (Eq. 1) that is used for the partitioning algorithm. Initially, each consumer forms a cluster and in the final step, all the consumers are merged in a unique group. At each stage i of the agglomeration, it can be shown that the merging of two groups leads to a decrease of criterion S. Therefore, the rule used is to merge the two groups of consumers which result in the smallest decrease of S in order to preserve S as large as possible after each stage. The plot of the evolution of the aggregation criterion =S i 1 S i in the course of the hierarchical algorithm is a very helpful tool in order to decide how many segments are present in the panel. If jumps when passing from a solution with K segments to a solution with (K 1) segments by merging two clusters, then this should be considered as an indication that unnatural clusters are being merged. Therefore, a partition with K segments should be retained. 3. First case study The data considered herein were collected by students at ENITIAA (Nantes, France) during a practical training phase. The objective was to manufacture jams by varying the percentages of apple and pear and adding flavour aroma (vanilla or cinnamon). Hedonic ratings were given by a panel of consumers. We focus on the ð5þ

3 E. Vigneau, E.M. Qannari / Food Quality and Preference 13 (2002) Table 1 Composition of the jams Jam % Apple 50% 50% 50% 25% 75% 75% 25% % Pear 50% 50% 50% 75% 25% 25% 75% Flavour Cinnamon - Vanilla Vanilla Vanilla Cinnamon Cinnamon analysis of the hedonic data and its relation with the experimental parameters of production. Seven jams were manufactured according to the experimental design given in Table 1. Three varieties of jams were obtained with equal proportions of apple and pear but were differently flavoured (no flavour, cinnamon or vanilla flavour). The four other jams were produced with a higher proportion of apple or a higher proportion of pear, with cinnamon or vanilla aroma. Fifty-six consumers were selected among the students. The seven jams were rated by each consumer on a 7-point hedonic scale. The mean vector of preferences over the whole panel was: {5.27; 6.21; 4.72; 4.53; 5.39; 4.68; 5.08}. This indicates that the jam without flavour seems to be on average the most appreciated by the panel. Nevertheless, an internal preference mapping (MDPREF) performed on the centred hedonic data suggested that the panel was not homogeneous. Fig. 1a displays the products according to the two first principal components that explained 35 and 22% of the total variance, respectively. It can be seen that the products are clearly discriminated according to their aroma. Along the first principal component, the vanilla flavoured jams, on the one hand, and the cinnamon flavoured jams, on the other hand, are further apart. The second principal component singles out the jam with no flavour. Fig. 1b was obtained by projection of the hedonic scores of each consumer onto the two first axes. This figure makes it clear that a majority of consumers have a direction of preference oriented towards the jam with no flavour aroma, but some consumers are also oriented towards the left side of the figure in the direction of the vanilla flavoured jam. Few consumers have their vector of preference oriented towards the right side of the figure in the direction of the cinnamon flavoured jam. In order to perform the segmentation of the panel and attempt to interpret the partition in terms of experimental parameters, a clustering of variables (consumers) under constraints, as described in Section 2, was performed. The matrix of the external data is formed by the variables of the experimental design (Table 2). It could be noticed that this matrix does not take into account the quadratic effect of the variable percentage of apple, the quadratic effect of the variable percentage of pear nor the interaction between these two variables. The introduction of the quadratic or interaction Table 2 Coding of the experimental variables (matrix Z) Jam % Appl % Pear w (no flavour) c (cinnamon) v (vanilla) Fig. 1. Internal Preference Mapping of the seven varieties of jam. (a) Configuration of the products on the two first principal axes. (b) Configuration of the consumers on the two first principal axes.

4 518 E. Vigneau, E.M. Qannari / Food Quality and Preference 13 (2002) Fig. 2. Evolution of the aggregation criterion in the course of the hierarchical algorithm (jam data). effects did not substantially change the outcomes of the analysis. In a first step, the hierarchical algorithm was performed. The evolution of the aggregation criterion =S i 1 S i in the course of the hierarchy is given in Fig. 2. It turns out that when passing from four to three clusters the criterion S did not change significantly, but the loss in the quality of the partition is important when passing from three to two clusters. This loss is even greater when the two last clusters are merged into one cluster. Therefore, a partition into three segments was retained. The partition obtained by cutting the hierarchical tree in three clusters is used as the initial solution for the partitioning algorithm. For this initial partition, the segments contained respectively, 16, 21 and 19 consumers and the criterion S was equal to The partitioning algorithm converges after only two iterations to a solution in three segments of size 17, 20 and 19, respectively, with an optimal value for criterion S equal to Thus the partitioning algorithm led to a slight improvement, which is generally the case as the initial partition obtained by means of the hierarchical algorithm is sub-optimal. The characterization of the three segments thus obtained is achieved using, on the one hand, the latent component in each group (Fig. 3a) and, on the other hand, the vector of loadings associated with each latent component (Fig. 3b). From Fig. 3a, it appears that the consumers in the first segment like cinnamon flavoured jams (especially P1 and P7) whereas the consumers in the second segment appreciate the vanilla flavoured jams and the jam without aroma (P2, P3, P4, P5). The third segment is formed by consumers who prefer products with higher proportion of apple. These remarks are corroborated by the inspection of the loadings shown in Fig. 3b. Opposite loadings are given to cinnamon and vanilla in groups 1 and 2. In the first group, the presence of cinnamon aroma and a high percentage Fig. 3. (a) Latent components: c 1 in group G 1 (17 consumers), c 2 in group G 2 (20 consumers) and c 3 in group G 3 (19 consumers). (b) Vectors of loadings associated with the latent component in each group: a 1 in group G 1, a 2 in group G 2 and a 3 in group G 3.

5 E. Vigneau, E.M. Qannari / Food Quality and Preference 13 (2002) of pear are associated with positive loadings whereas the presence of vanilla is negatively scored. The presence of vanilla aroma or the absence of aroma have a positive effect on the consumers in the second group, whereas the presence of cinnamon aroma is negatively scored. The most important factors for the consumers in the third group are the percentages of apple and pear, with a positive loading for the proportion of apple and a negative loading for the proportion of pear. 4. Second case-study This second example deals with sensory and preference data from a study on 12 Southern Hemi-sphere eating apples (Dalliant-Spinnler, MacFie, Beyts, & Hedderley, 1996). Peeled apple quarters of each variety were evaluated on a hedonic unstructured scale, 10 cm long, by a panel of 60 consumers (matrix X). Independently, the same 12 variety of apples, peeled and quartered, were assessed by 12 sensory trained assessors using 43 attributes: nine attributes for internal odour of the samples (io), seven attributes for internal appearance (ia), two for the first bite texture appreciation (fb), four attributes for the texture during chewing appreciation (tx), 15 attributes for the flavour during chewing (fl) and six attributes of flavour evaluated after swallowing (as). The average scores over the twelve assessors were considered as the external data set (matrix Z). Further details about the experimental procedures and results are given in Dalliant-Spinnler et al. (1996). In order to compare our results with those reported by Dalliant-Spinnler et al. (1996), we chose to standardize the consumers scores and the sensory attributes as these authors did. Nevertheless, the outcomes of the analysis whether the variables were standardized or not were to a large extent similar. The hedonic data were in a first step analysed by means of External Preference Analysis (PrefMap) with vector model. The first two principal components of the sensory data (which explained 69.7% of the total variance) were retained and the hedonic scores of each consumer were fitted onto the space spanned by these two components. The results given in Fig. 4a and b (ignoring so far the label associated with each consumer) gives useful information about the directions of preference of the consumers according to the sensory characteristics of the apples. However, this approach does not provide a direct segmentation of the panel. It can be observed that there are two main and opposite directions of preference. A majority of consumers seems to prefer Braeburn, Granny Smith or Aurora apples which are described as having juicy/crisp texture and acid/green flavour. On the opposite side, consumers react favourably to Compact Golden Delicious (C.golden), Royal Gala or GS330 apples which have more sweet flavour, flavour associated with fresh plums or cherries (flplumc), flavour associated with fresh pears (flpearl) or characteristics associated with red apples (ioredap, flredap, asredap). Independently from the PrefMap analysis, the clustering of the consumers was performed. According to the clustering approach (Section 2), a latent component is definedineachclusterandexpressedasalinearcombination of the sensory attributes. From the graph of the evolution of the aggregation criterion (Fig. 5), it is obvious that the panel of consumers is structured in two groups. The partitioning algorithm is thereafter run in order to improve the partition in two groups obtained by the hierarchical approach. The two groups which were eventually formed contained 40 and 20 consumers, respectively. The scores of the apples given by the latent components associated with the two groups are given in Table 3. In addition, the loadings (a k ) of the sensory Fig. 4. External Preference Mapping (vector model) for peeled apples. (a) Biplot display of products and attributes on the two first principal axes. (b) Consumers vectors fitted onto the sensory space spanned by the first two principal components.

6 520 E. Vigneau, E.M. Qannari / Food Quality and Preference 13 (2002) Table 3 Scores of the apples on the two latent components associated respectively with the first and the second groups of consumers Apples t 1 (in G 1 ) t 2 (in G 2 ) Top Red Splendour Roy.Gala GS Granny Sm Golden Fuji Fiesta Celeste C.Golden Braeburn Aurora Fig. 5. Evolution of the aggregation criterion in the course of the hierarchical algorithm (peeled apple data). attributes associated with these latent components are graphed in Fig. 6a and b. From these results, it can be seen that the 40 consumers in the first segment prefer the Braeburn, Granny Smith and Aurora apples and reject the Compact Golden Delicious (C.golden), Royal Gala and GS330 apples. These preferences may be explained by the fact that consumers in group G 1 appreciate products which have an internal appearance, a texture and a flavour associated with juicy and green perceptions. Moreover, consumers in G 1 reject apples which are described by a pear-like or soapy flavour and a spongy texture. Consumers in the second group have almost opposite directions of preference than those in the first group. They appreciate apples of the varieties Compact Golden Delicious (C.golden), Royal Gala, GS330 and also Fuji apples. They reject green apples (especially Braeburn and Granny Smith) and to a certain extent dislike Aurora apples which are more sweet and juicier. The attributes which are the most related to the directions of preference of consumers in group G 2 belong to the categories internal odour, flavour and after swallow. Texture attributes seem to have less importance for the second group than for the first group of consumers. Consumers in group G 2 seem to appreciate sweetness of apples and characteristics associated with red apples. The identification of the group membership of consumers was reported on Fig. 4b. It is clear that the interpretation of the results based on PrefMap displays or derived from the clustering approach are in this case study very similar. In fact, both approaches are complementary: while the PrefMap analysis produce very useful graphical displays, the clustering approach exhibits segments of consumers and a model within each segment which links the acceptability of the consumers to the sensory data. Fig. 6. (a) Loadings of the latent component associated with, the first group of consumers. (b) the second group of consumers.

7 E. Vigneau, E.M. Qannari / Food Quality and Preference 13 (2002) Conclusion The clustering approach of variables around latent components whether by imposing constraints on these latent components as discussed in this paper, or without imposing such constraints (Vigneau et al., 2001) is very useful to analyse preference data or to relate these data to external variables. This approach is complementary to the most common methods used within the framework of consumer data analysis. We have particularly stressed this complementarity in the second case-study by showing the extent to which the outcomes of our approach tally with and complement those of PrefMap. It should be emphasized that PrefMap is efficient when the most relevant information in the external data for explaining the acceptability of the consumers is contained in the first principal components. Our approach does not suppose such an assumption as it automatically captures the most relevant information in the external variables to explain the preferences in each segment of consumers. It should be stressed that other methods of analysis, which tackle the problem of segmenting a panel of consumers, are discussed by several authors (Courcoux & Chavanne, 2001; De Soete & Winsberg, 1993; Poulsen, Brockhoff, & Ericksen, 1997). These approaches are based on latent class models and, as a result, involve normality assumptions and relatively heavy computations (EM algorithm). From this standpoint, it appears that our approach is based on simple and intuitive idea and involves simple computations. As illustrated in the two case studies, the hierarchical algorithm is very useful in order to determine the appropriate number of segments. More investigation is needed in order to set up a hypothesis testing framework regarding the actual number of segments. Monte- Carlo simulation may be very useful in this endeavour. References Courcoux, Ph., & Chavanne, P. C. (2001). Preference mapping using latent class vector model. Food Quality and Preference, 12, Dalliant-Spinnler, B., MacFie, H. J. H., Beyts, P. K., & Hedderley, D. (1996). Relationships between perceived sensory properties and major preference directions of 12 varieties of apples from the southern hemisphere. Food Quality and Preference, 7(2), De, Soete, G., & Winsberg, S. (1993). A latent class vector model for preference ratings. Journal of Classification, 10, Greenhoff, K., & MacFie, H. J. H. (1994). Preference mapping in practice. In H. J. H. MacFie, & D. M. H. Thomson (Eds.), Measurement of food preferences (pp ). London: Blackie Academic & Professional. Poulsen, C. S., Brockhoff, P. M. B., & Erichsen, L. (1997). Heterogeneity in consumer preference data a combined approach. Food Quality and Preference, 8(5/6), Vigneau, E., Qannari, E. M., Punter, P. H., & Knoops, S. (2001). Segmentation of a panel of consumers using clustering of variables around latent directions of preference. Food Quality and Preference, 12(5 7),