Food tasting is crucial for companies to adapt their products to consumer tastes. The main instrument for measuring this sensory analysis is not a machine but a group of people, trained for years. This, together with the need to buy adequate equipment and hire specialized personnel, means that few food companies can afford the process. To alleviate this situation, new geometry-based tasting methods have appeared in recent years, sacrificing precision in exchange for saving time and money.
One of them is the SensoGraph method, which uses geometry to evaluate, with the help of untrained consumers rather than experts, quickly and easily different foods, deciding which samples resemble each other and which do not. For example, suppose that a winery wants to launch a new wine and they want to know how consumers are going to position it with respect to other wines that are already on the market.
Even if you have ever said that “I don't understand about wines, I only know if I like it or not ”you can participate in this tasting; You just have to place nearby the wines that are similar to you and those that you find different far away. SensoGraph then averages all the opinions of the participants to see which wines on the market the new proposal from the winery resembles. If, for example, we have groups 1-2-3-4 and 5-6-7 and the new wine is 7, we will know that for consumers this new wine is similar to wines 5 and 6. If these are selling well, it is to be hoped that the new one will also be well received in the market.
Although averaging some positions on the plane does not seem as easy as averaging some numbers, with the SensoGraph method it is. Let's imagine that four tasters have given us their answers. The first thing SensoGraph does is detect patterns in each response, connecting dots in a way similar to how ancient astronomers linked stars to form constellations; Two points are joined when they form the diameter of a circle that does not contain any other point.
If, for example, constellations similar to the Ursa Major Chariot are formed in two answers, we will know that these two tasters have similar opinions. Therefore, to know how similar wines 1 and 2 are, it will be enough to count in how many responses the constellation obtained contains the segment that connects 1 and 2. The unions that appear in more responses will have more weight in the global opinion and will tell us that those wines are more similar to each other and, therefore, should be closer in the final result.
To obtain the final graph, a graph drawing method based on these weights is used. Let's imagine that we place some pucks on an air hockey table like those at arcades or fairs. If we join the pairs of discs with springs of different strengths and let them slide until they reach an equilibrium position, in the end the stronger springs will bring their discs closer than those that were joined by weaker springs. program allows anyone to use it, from small to large companies. As a taster, it is enough to be able to place the similar close and the different far away, without the need for long training. As a producer, you just have to look at what products ours looks like, without having to be an expert in statistics or have specialized training. In this way, those companies that could not afford to do sensory analysis can now quickly and easily know the opinion of consumers.
David Orden Martín is a tenured professor of Applied Mathematics at the University of Alcalá and is one of the speakers at the event outreach March, mathematics month and member of the H2020-CONNECT and AEI-TOPPING projects
Café y Teoremas is a section dedicated to mathematics and the environment in which they are created, coordinated by the Institute of Mathematical Sciences (ICMAT) , in which the researchers and members of the center describe the latest advances in this discipline, share meeting points between mathematics and other social and cultural expressions and remember those who marked its development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: "A mathematician is a machine that transforms coffee into theorems."
Editing and coordination: Ágata A. Timón García-Longoria (ICMAT)
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