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Figure 1: Relationships that could be modelled with
Bayesian networks |
Case study
The value and practical feasibility
of using Bayesian network technology for the purpose described
above were investigated by means of a case study. This case study
was about meat replacers. First it was tried to model
relationships between product properties as perceived by the
consumer and overall liking by the consumer. This was done in
order to investigate what are the important product properties in
the eyes of the consumer. Only consumer data were used. Six
different meat replacers were prepared and offered to consumers
for evaluation. The products were evaluated only after
preparation.
The model describing the problem was built
together with experts, one expert in the field of meat replacers
and one expert in the field of consumer research. This model
(figure 2) shows that someones attitude towards meat replacers;
the appearance and the smell of the product determine expected
liking, or Liking before tasting. This expected liking, the taste
and the texture of the product determine the overall liking, or
Liking after tasting.
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Figure 2: Bayesian network showing how appreciation of meat
replacers is affected by other variables |
The questions
related to the attitude were answered on a 7-point scale. The
answers on all the other questions were given on a continuous
scale from 0 to 100. To make it possible to learn the parameters
effectively, the data had to be rescaled. Attitude, Liking before
tasting and Liking after tasting got three different values, -1,
0 and 1. The other variables got four different values, 1, 2, 3
and 4. Parameter learning went successfully.
The purpose in consumer oriented food product
design is to maximize Liking after tasting. A high appreciation
after tasting is a prerequisite for the consumer to buy the
product again. Therefore, the evidence Liking after tasting is 1
(maximum) was entered in the model. The posterior probabilities
were calculated and together with the prior probabilities they
are shown in figure 3.
From these figure it is clear that the
probability that taste is good (3 or 4), strongly increases due
to the evidence Liking after tasting is 1. It can be concluded
that taste has a high influence on the overall appreciation of
the product. This is an example of useful information extracted
by means of Bayesian network technology.
By means of the Maximum Posterior Explanation
function it was possible to find the typical meat replacer
belonging to maximum Liking after tasting. The configuration of
the variables for this MPE is shown in figure 4. This feature of
the software makes it possible to get insight in non-linear
relationships between variables. As relationships in sensory
science are mostly non-linear [Kvaal & McEwan, 1996], this is
an important feature of Bayesian network technology.
The next question is: given that taste
strongly influences Liking after tasting, how can the taste be
improved. Therefore it was tried to extend the model to the left
by including real sensory product attributes. The factors
influencing the taste appreciation by the consumer are shown in
figure 5.
Learning the parameters for this model was
not possible. Given that the five parent variables of taste have
ten possible values, the conditional probability table of taste
contains 4 * 105 cells. With such a table, the data (250 cases)
become too sparse. To solve this problem, it is possible to use
parameterised models, for instance the Noisy max models. This
will be done in future research.
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Figure 3: Marginal probability distributions (blue) and
posterior probability distributions based on maximizing
Liking after tasting (red) |
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Figure 4: Configuration of the variables for the typical
meat replacer of maximum Liking after tasting |
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Figure 5: Bayesian Belief Network showing sensory
attributes influencing the taste as perceived by the
consumer |
Conclusion
Although research on this topic has
just started, it is already clear that Bayesian technology can
help in determining what are the most important product
properties in the eyes of the consumer. The next step is to
include sensory attributes and physical product properties to
find out how important properties (in the eyes of the consumer)
can be optimised. This was not possible yet, but use of
parameterised models could help in solving this problem. Future
research will start with investigating this.
References
- Corney D. 2000. Designing Food with
Bayesian Belief Networks. In Parmee, I. (Ed.), Evolutionary
Design and Manufacture ACDM2000, Springer-Verlag, 83-94.
- Jongenburger H.J. 2005. Bayesian
Belief Networks as a tool for Consumer Oriented Food Product
Design. MSc-thesis. Wageningen University, Wageningen, The
Netherlands.
- Kvaal K., McEwan J.A. 1996. Analysing
complex sensory data by non-linear artificial neural networks.
In Naes T., Risvik E. (Eds.) Multivariate Analysis of Data in
Sensory Science, Amsterdam, Elsevier Science.
