Sensory evaluation of foods is as important as chemical, physical or microbiological examinations, being specially relevant in food industries. Classical methods can be long and costly, making them less suitable for certain industries like the wine industry. Some alternatives have arisen recently, including Napping®, where the tasters represent the sensory distances between products by positioning them on a tablecloth; the more similar they perceive the products, the closer they position them on the tablecloth. This method uses multiple factor analysis (MFA) to process the data collected. The present paper introduces the software SensoGraph, which makes use of proximity graphs to analyze those data. The application is described and experimental results are presented in order to compare the performances of SensoGraph and Napping®, using eight wines from the Toro region and two groups of twelve tasters with different expertise.Ministerio de Ciencia e InnovaciónEuropean Science FoundationJunta de Castilla y Leó

Díaz Báñez, José Miguel (Coordinador)

Fernández Fernández, Encarnación

Garijo Royo, Delia (Coordinador)

Miguel, David N. de

Márquez Pérez, Alberto (Coordinador)

Orden Martín, David

Rodríguez Nogales, José Manuel

Urrutia Galicia, Jorge (Coordinador)

Vila Crespo, Josefina

English

idUS. Depósito de Investigación Universidad de Sevilla

XV Spanish Meeting on Computational Geometry, June 26-28, 2013SensoGraph: Using proximity graphs for sensory analysisDavid N. de Miguel∗1, David Orden†2, Encarnación Fernández-Fernández‡3, José M. Rodríguez-Nogales §3, andJosena Vila-Crespo ¶41Universidad de Alcalá, Spain.2Departamento de Física y Matemáticas, Universidad de Alcalá, Spain.3Departamento de Ingeniería Agrícola y Forestal, Universidad de Valladolid, Spain.4Departamento de Anatomía Patológica, Medicina Preventiva y Salud Pública, Medicina Legal y Forense,Universidad de Valladolid, Spain.AbstractSensory evaluation of foods is as important as chem-ical, physical or microbiological examinations, beingspecially relevant in food industries. Classical meth-ods can be long and costly, making them less suitablefor certain industries like the wine industry. Some al-ternatives have arisen recently, including Nappingr,where the tasters represent the sensory distances be-tween products by positioning them on a tablecloth;the more similar they perceive the products, the closerthey position them on the tablecloth. This methoduses multiple factor analysis (MFA) to process thedata collected. The present paper introduces thesoftware SensoGraph, which makes use of proximitygraphs to analyze those data. The application is de-scribed and experimental results are presented in or-der to compare the performances of SensoGraph andNappingr, using eight wines from the Toro region andtwo groups of twelve tasters with dierent expertise.1 Sensory analysisThe goal of sensory evaluation of foods is the studyof the sensations they produce. When consuming afood, stimulus of several classes are perceived; vi-sual (color, shape, brightness), tactile (at ngertipsor mouth epithelium), odorous (at nose epithelium),gustatory (at taste buds), and even auditory (e.g., forcrunchy food). The norm ISO 5492:2008 denes sen-sory analysis as the science related to the evaluationof organoleptic attributes of a product by the senses,and other ISO norms unify the tools and methods∗Email: david.n.demiguel@gmail.com.†Email: david.orden@uah.es. Research partially supportedby MICINN Project MTM2011-22792, ESF EUROCORESprogramme EuroGIGA - ComPoSe IP04 - MICINN ProjectEUI-EURC-2011-4306 and Junta de Castilla y León ProjectVA172A12-2.‡Email: eernan@iaf.uva.es.§Email: rjosem@iaf.uva.es.¶Email: jvila@pat.uva.es.used for that evaluation. The sensory examinationturns out to be as important as chemical, physical ormicrobiological examinations, being specially relevantin food industries.The main tool in sensory analysis is a panel oftasters, either experts or consumers, who evaluatethe products from an analytic and/or hedonic pointof view. As any other instrument depends on itscalibration, such a panel depends on human be-ings. Their perceptions are translated into quanti-able data, which is then treated by means of dierentmethods.The classical method is descriptive analysis, whichaims to describe the sensory characteristics of a prod-uct and use them to quantify the sensory dierencesbetween products [11]. Dierent implementations ofthis method provide a quantitative description of thesensory attributes perceived by a group of experttasters, chosen because of their sensory abilities, whoare trained to describe and evaluate sensory dier-ences among products. Such a training is a criticalstep in the creation of an expert panel of tasters, whentasters agree on the denitions of descriptors and theuse of scales, in order to provide reliable and consis-tent results.However, this training can be long and costly, mak-ing it less suitable for certain industries like the wineindustry. There, sensory characterization is usuallyperformed by the oenologist in charge of the winery,for whom it is dicult to enrol in a panel requiring aregular activity during a long time. Thus, in the lastyears several alternative methods have been proposed,aiming to provide a fast sensory positioning of a set ofproducts, in order to avoid the most time-consumingsteps in classical methods. A prominent one amongthese alternatives is Nappingr [12]. In a single ses-sion, all the products are provided simultaneously tothe tasters, who represent the sensory distances be-tween products by positioning them on a tablecloth.Products which are perceived as similar should be po-sitioned close to each other, while products perceivedas dierent should be positioned far enough. Each69SensoGraph: Using proximity graphs for sensory analysistaster chooses the criteria and the relative importancegiven. These data are later processed using multiplefactor analysis (MFA) [4], in order to take into ac-count the criteria and relative importance of all thetasters. Despite having both advantages and disad-vantages, Nappingr has become a useful tool whensome accuracy can be sacriced for the sake of a fasterstudy [13].2 Proximity graphsGiven a set of points in the plane, a (geometric)proximity graph connects two of them according toa chosen proximity criterion. These graphs have beenwidely used in order to analyze the relative positionof points, for instance looking for clusters or span-ning structures. See [1, 7] and the references therein.Thus, it seems natural to use them in order to an-alyze the data collected by a tablecloth method forsensory analysis, like Nappingr. Among the manydierent types of proximity graphs, we have chosenthe following:Nearest Neighbor Graph (NNG): Each point isjoined to the closest among the remaining points [14].k-Nearest Neighbor Graph (k-NNG): In this gen-eralization of the NNG, each point is joined to the kclosest among the remaining points.Minimum Spanning Tree (MST): Among thetrees passing through all the given points, the MST isthe one which minimizes the sum of edge lenghts [10].Relative Neighborhood Graph (RNG): Thisgraph, introduced by Toussaint [15], joins two pointsP,Q if there is no point whose distances to both Pand Q are smaller than the distance d(P,Q).k-Relative Neighborhood Graph (k-RNG): Thegeneralization of the RNG which allows up to k pointswith distances to both P and Q smaller than d(P,Q).Gabriel Graph (GG): In this graph two points P,Qare joined if there is no other point inside the closeddisk which has the segment PQ as diameter [5].k-Gabriel Graph (k-GG): Generalization of the GGallowing up to k points to lie inside the closed disk.Delaunay Triangulation (DT): Three pointsP,Q,R form a triangle precisely if their circumcircledoes not contain any other point [3].k-Delaunay Triangulation (k-DT):Generalizationof the DT allowing up to k points to lie inside theclosed disk.β-skeleton (β-SK): A family of proximity graphs,one for each value of β ≥ 0, see [9] for more details.For β = 1 we get the GG. For β = 2 we get the RNG.Unit Disk Graph (UDG): In this graph two pointsP,Q are joined if the distance d(P,Q) between themis no greater than a xed threshold [2].3 The SensoGraph applicationSensoGraph is an application, still under develop-ment, which aims to use proximity graphs for the anal-ysis of data collected from tablecloth sensory meth-ods like Nappingr. The interface intends to be intu-itive and easy to use, so that no special knowledge isneeded.Tasting data are stored in the form of an m × 2nmatrix, in which there is a row per product and a pairof columns per taster, storing the two coordinates as-signed to the corresponding product. In a rst screen,this matrix can be manually created or inserted froma CSV le, according to the IETF RFC 4180 stan-dard. After insertion, the matrix can be modied byadding or removing rows or columns, as well as byediting an individual entry. See Figure 1.Figure 1: Matrix of tasting data.After accepting the data matrix, a new screen isshown. There, the user can choose a type of proxim-ity graph among the ones specied in Section 2. Forthose proximity graphs depending on a parameter, k-NNG, k-RNG, k-GG, k-DT, β-SK, and UDG, the usercan change the value of the parameter. Furthermore,the application allows to intersect any of the graphsconsidered with the UDG, in case the user wants toavoid too long edges.For the given choice of a type of proximity graph,the application generates the graph for each of thetaster's tablecloths. The user can choose a taster andcheck its tablecloth and the resulting graph. Whenvisualizing a tablecloth, it is also possible to changethe type of proximity graph, in order to check thedierences between them. See Figure 2.Figure 2: Tablecloth for taster number 2 with theUDG for radius 10.70XV Spanish Meeting on Computational Geometry, June 26-28, 2013Furthermore, chosen a type of proximity graph, theuser can also merge all the tablecloths and their corre-sponding graphs into a single, global, picture. There,every edge is shown with a thickness, computed ac-cording to a simple function: The thickness corre-sponds to the number of tasters for which that edgeappears in the proximity graph. This representationencodes the global opinion of the panel of tasters, sothat those products perceived as similar are joined bythicker edges, while products considered dierent arejoined by thinner edges (or even not joined at all).In order to position the vertices of this global pic-ture, SensoGraph considers the edges like springswhich try to approach their endpoints, with a strengthproportional to the edge thickness. Thus, verticesjoined by thicker edges become closer than thosejoined by thinner edges. In this new picture, the prod-ucts considered similar by the panel of tasters can berecognized not only by the thickness of the edge be-tween them, but also by their mutual distance, seeFigures 4, 6, and 8. Such a positioning is performedby a slight adaptation of the algorithm by Kamadaand Kawai [8].Since some types of proximity graphs insist in join-ing vertices which are far apart, SensoGraph oers asecond way of computing the thickness of an edge.The distance function also looks only at the edgesappearing in the proximity graph chosen but, in addi-tion, it takes into account their length, decreasing thecontribution of long edges to the total thickness. Asmentioned above, the user can also choose to discardtoo long edges, by intersecting any of the proximitygraphs with the UDG.Furthermore, the user can also peel the graph in theglobal picture, by removing edges below any chosenthickness, in order to keep only the most relevant ones.4 Experimental resultsEight wines from the Toro region, elaborated us-ing dierent yeasts during the alcoholic fermentation,were considered. Two panels, of twelve non-trainedtasters each, were selected. The experts panel wascomposed by people, mainly young, with some knowl-edge of the techniques for sensory analysis of wines.The non-experts panel was composed by plain con-sumers, with dierent ages and levels of knowledge.Each of the panels performed a session of Nappingr,and the experts panel repeated for a second session, inorder to check for improvements due to such a slighttraining.The data from those three sessions was then pro-cessed both by multiple factor analysis (MFA) [6], asusual in Nappingr, and by SensoGraph. Figures 3to 8 show the results obtained, with SensoGraph us-ing GG and the simple thickness function.Figure 3: Experts panel, Nappingr.Figure 4: Experts panel, SensoGraph.Figure 5: Repetition of experts panel, Nappingr.Figure 6: Repetition of experts panel, SensoGraph.71SensoGraph: Using proximity graphs for sensory analysisFigure 7: Non-experts panel, Nappingr.Figure 8: Non-experts panel, SensoGraph.Among the three sessions performed, the most rep-resentative results of Nappingr were those from therepetition of the experts panel. Figure 5 shows a35.25% of the variation explained by the rst di-mension and a 26.23% of the remaining variation ex-plained by the second dimension, for a total inertia of61.48%. Being this the session for which Nappingris most reliable, it is the one chosen to compare withthe results provided by SensoGraph.For that session, using SensoGraph with the sim-ple thickness function provides the same clusters asNappingr for all the graphs considered except forNNG, which has too few edges, and for k-DT, whichhas too many edges. Using the distance thicknessfunction does not change the elements in the clus-ters, although the whole picture appears expandedand highlights only the strongest connections betweendierent clusters. Furthermore, it improves the re-sults for the extreme cases above, leading to the sameclusters as Nappingr for k-DT and palliating the dif-ferences for NNG.A possible advantage of SensoGraph is giving otherkind of information than Nappingr. Apart from pro-viding several types of proximity graphs and parame-ters to test with, SensoGraph shows how the dierentclusters are connected. For an example, Figures 5and 6 lead to the same three clusters, but only theone from SensoGraph shows that they are actuallyquite connected, reecting the fact that all the winesconsidered were actually quite similar [6].5 AcknowledgementsThe authors want to gratefully thank Ferran Hurtadofor proposing them the use of proximity graphs inorder to analyze data from tablecloth methods.References[1] J. Cardinal, S. Collette, and S. Langerman, Emptyregion graphs, Computational Geometry: Theory andApplications, 42 (2009), 183195.[2] B. N. Clark, C. J. Colbourn, and D. S. Johnson, UnitDisk Graphs, Discrete Mathematics, 86 (1990), 165177.[3] B. N. Delaunay, Sur la sphere vide, Bulletin of theAcademy of Sciences of the USSR, VII (1934), 793800.[4] B. Escoer and J. Pagès, Analyses factorielles simpleset multiples, Dunod, Paris, 1998.[5] K. R. Gabriel and R. R. Sokal, A new statistical ap-proach to geographic variation analysis, SystematicBiology, 18:3 (1969), 259278.[6] L. Gallego-Expósito, Nuevas técnicas de análisis sen-sorial de alimentos: Métodos espaciales, Degree the-sis, 2011.[7] J.W. Jaromczyk and G.T. Toussaint, Relative neigh-borhood graphs and their relatives, Proceedings of theIEEE, 80:9 (1992), 15021517.[8] T. Kamada and S. Kawai, An algorithm for draw-ing general undirected graphs, Information Process-ing Letters, 31 (1989), 715.[9] D. Kirkpatrick and J. Radke, A framework for com-putational morphology, in: Computational Geome-try, Machine Intelligence and Pattern Recognition,2, North-Holland, Amsterdam, 1985, 217248.[10] J. B. Kruskal, On the shortest spanning subtree of agraph and the traveling salesman problem, Problemsof the American Mathematical Society, 7 (1956), 4850.[11] H. T. Lawless and H. Heymann, Principles of SensoryEvaluation, Aspen Publishers, Gaithersburg, 1999.[12] J. Pagès, Collection and analysis of perceived productinter-distances using multiple factor analysis: Appli-cation to the study of 10 white wines from the LoireValley, Food Quality and Preference, 16 (2005), 642649.[13] L. Perrin , R. Symoneaux, I. Maître, C. Asselin, F.Jourjon , and J. Pagès, Comparison of three sensorymethods for use with the Napping procedure: Caseof ten wines from Loire valley, Food Quality and Pref-erence, 19 (2008), 111.[14] M. I. Shamos and D. Hoey, Closest-point problems,in Proceedings of FOCS, 1975, 151162.[15] G. T. Toussaint, The relative neighborhood graph ofa nite planar set, Pattern Recognition, 12 (1980),261268.72

SensoGraph: Using proximity graphs for sensory analysis

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SensoGraph: Using proximity graphs for sensory analysis

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