dataesr/scientific-paragraphs-categorization huggingface dataset:
Conclusion This paper introduced a new temporal sensory method called Free-Comment Attack-Evolution-Finish (FC-AEF). This method is a combination of the Free-Comment and the Attack-Evolution-Finish methods in which for each of the so-called periods (Attack, Evolution, and Finish), subjects are asked to provide a Free-Comment description instead of selecting a descriptor in a predefined list. FC-AEF was used to collect temporal sensory perceptions of dark chocolates with consumers at home. The data collected were analysed product-wise and period-wise. The product-wise analysis identified in each period the descriptors characterizing each product, while the periodwise analysis identifies for each product the descriptors generating a temporal kinetic of its perception. FC-AEF provides sensory analysts with a new tool for investigating the temporal sensory perception of products by consumers with no need of establishing a predefined list of descriptors, which enables shunting this tedious part and removing all possible issues and biases due to the use of a predefined list.
The STATIS method has been successfully applied to the analysis of sensory profiling data and other kinds data in sensometrics. We discuss its use and benefits and compare its outcomes to alternative methods for the analysis of multiblock data arising in situations such as projective mapping and free sorting experiments. More importantly, a method of clustering a collection of datasets measured on the same individuals, called CLUSTATIS, is introduced. It is based on the optimization of a criterion and consists in a hierarchical cluster analysis and a partitioning algorithm akin to the K-means algorithm. The procedure of analysis can be seen as an extension of the cluster analysis of variables around latent components (CLV, Vigneau and Qannari, 2003)  to the case of blocks of variables. Alongside the determination of the clusters, a latent configuration is determined by the STATIS method.
2 Several sensory procedures directly lead to multiblock datasets. For instance, in sensory profiling evaluation, we are presented with a collection of data organized in blocks of variables. Each data block is associated with an assessor and gives the intensity scores of the products (rows) for several sensory attributes, which may be the same from one assessor to another (fixed vocabulary profiling) or different from one assessor to another (free choice profiling). The STATIS method is a method of analysis of multiblock datasets  (Lavit, Escoufier, Sabatier and Traissac, 1994). It was introduced to the sensometrics domain by  Schlich (1996). It is nowadays popular among the practitioners of sensory analysis  (Pizarro, Esteban-Díez, Rodríguez-Tecedor, González-Sáiz, 2013). We show how this method of analysis can be applied to projective mapping and free sorting data.
We also compare the outcomes from this strategy of analysis to those obtained by means of standard procedures of analysis, namely Generalized Procrustes Analysis (GPA) and Multiple Factor Analysis (MFA) for projective mapping/Napping data, and DISTATIS for free sorting data. Another and more important aim of the paper is to introduce a cluster analysis approach of multiblock datasets, called CLUSTATIS. In the applications discussed hereinafter, CLUSTATIS will be used to segment the subjects involved in a free sorting task or a projective mapping/napping experiments. This clustering method is tightly linked to the STATIS method and consists in a hierarchical cluster analysis and a partitioning algorithm. Both these two strategies aim at optimizing the same criterion; either locally for the hierarchical clustering or globally for the partitioning algorithm They can be run independently or in combination in an attempt to achieve an even better solution than that obtained by one of the two strategies alone.
Again, the efficiency of this clustering approach is demonstrated on the basis of data pertaining to projective mapping/Napping and free sorting tasks. CLUSTATIS can be seen as an extension of the cluster analysis of variables around latent components  (CLV, Vigneau and Qannari, 2003)  to the case of blocks of variables. It follows the same pattern of analysis and enjoys the same properties. Cluster analysis of datasets is not a new topic in sensometrics since this approach has been proposed with the aim of identifying sub-groups of assessors or outlying assessors  (Dahl and Naes, 2004). These authors computed the Procrustes distances between pairs of datasets and subjected the distance matrix thus obtained to algorithms of hierarchical cluster analysis by considering various aggregation criteria.
In particular, the clustering strategies are compared for the purpose of detecting outlying assessors. One of the findings was that single and centroid linkages are better suited for this aim than the other strategies of aggregation. In the context of three-way data where the datasets refer to the same individuals (e. g. , products) and the same variables, Wilderjans and  Cariou (2016)  proposed a strategy of clustering the sensory descriptors in conventional profiling, called CLV3W. By adding a nonnegativity constraint, these authors used this method to segment the consumers  (Cariou, Wilderjans, 2018). Interestingly enough, this strategy of analysis is also an extension of the CLV method, which is a feature shared by CLUSTATIS. However, CLV3W is particularly designed for three-way data. Moreover, the configuration of the individuals (e.
g. , products) within each cluster is restricted to be one dimensional. It is worth noting that CLV3W is a special case of the clusterwise Parafac model, which allows us to have higher-dimensional configurations within each cluster  (Wilderjans, Ceulemans, 2013). By comparison, CLUSTATIS operates on multiblock data, which is a larger setting than three-way data since the variables may not be the same for all the datasets at hand. In section 2 devoted to the material and methods, we start by recapitulating the STATIS method (subsection 2. 1). Thereafter, we discuss the general strategy of cluster analysis (subsection 2. 2) and show how it can be applied to projective mapping/Napping (subsection 2. 3) and free sorting data (subsection 2. 4). In section 3, we illustrate the approach on the basis of case studies pertaining to each of these tasks.
The STATIS method We consider the setting where we dispose of blocks of variables denoted by ,… , , which are assumed to be column centred. These datasets are measured on the same individuals (e. g. , products) but the variables may differ in nature as well as in number from one dataset to another. The STATIS method was introduced to the sensometrics domain by  Schlich (1996)  and is nowadays popular among the practitioners of sensory analysis  (Pizarro, Esteban-Díez, Rodríguez-Tecedor, González-Sáiz, 2013). The cornerstone of this strategy of analysis is the scalar product matrices associated with the datasets at hand. These matrices are computed as follows: = ,…, =. These are × symmetric matrices which reflect the spatial configuration of the individuals (e. g. , products) since the entry corresponding to the l th row and j th column gives the scalar product between these two individuals.
It is recommended to scale the matrices so as to have their norm equal to 1. This is achieved by dividing each by its Frobenius norm. We recall that the Frobenius norm of a matrix (say) is given by ‖ ‖ = ∑ ∑ , where is the ( , ) th entry of matrix. Central to the STATIS method is the RV coefficient which is also very popular in sensometrics  (El Ghaziri, Qannari, 2015; Naes, Berget, Liland, Ares, Varela, 2017). This coefficient reflects the similarity between two configurations. Roughly speaking, the RV coefficient between and can be seen as the correlation coefficient between and. It ranges between 0 and 1 and increases as the similarity, in terms of spatial configuration of the individuals, between the two datasets at hand increases. In the following we shall indifferently refer to this coefficient as ( , ) or ( , ).
The various steps to perform the STATIS method are depicted in Figure  1. It can be seen that the STATIS method seeks a weighted average configuration of the matrices. As indicated in Figure  1 , the weights, , are obtained by computing the first eigenvector of the matrix of the RV coefficients between the various datasets. The weight is relatively large if tends to agree with the other datasets. Contrariwise, the weighting coefficients tend to be relatively small for differing. It is worth noting that the first eigenvalue of the matrix of RV coefficients, ! , stands for an overall agreement or homogeneity index between the various datasets. The standardized index " = # $ % reflects the part of variation in the various matrices explained by the group average matrix. It ranges between ! % and 1.
The CLUSTATIS approach We propose a cluster analysis approach for multiblock datasets. This approach consists in an extension of the CLV method  (Vigneau and Qannari, 2003; Vigneau, Chen and Qannari, 2015). As CLV, CLUSTATIS is based on a hierarchical and a partitioning algorithms whose aim is to cluster the objects at hand (i. e. , variables in the case of CLV and datasets in the case of CLUSTATIS) in such a way that the objects in each cluster are as close as possible to a central (or latent) entity (i. e. , latent variable for CLV and a compromise cross product matrix in the case of CLUSTATIS). Moreover, the aggregation criteria used in the hierarchical algorithms for both methods are very similar. CLUSTATIS aims at minimizing a criterion which reflects the fact that we are seeking homogeneous clusters of datasets.
More precisely, the datasets in each cluster are assumed to be highly related to a latent configuration which is determined by means of the STATIS method. Formally, let us denote by ,… , the datasets at hand, which are assumed to be columnwise centered. We compute the scalar products matrices: = , …, = , and we seek to minimize the following criterion: G = ( ( || - ∈I J K L+! (M) ||² where (N ∈ O L ) are scalars to be determined and assumed to be such that ∑ = 1 ∈I J , P is the number of groups of datasets, O L is the k th group and, for Q (Q = 1, … , P) , (M) is the compromise of the group O L. Obviously, when there is only one group of datasets (i. e. , P = 1), we retrieve the same criterion that underlies the STATIS method. The procedure of cluster analysis to solve this problem is called CLUSTATIS and entails two complementary clustering strategies.
The first strategy consists in a hierarchical cluster analysis. The second strategy consists in a partitioning algorithm akin to the K-means algorithm. Both strategies aim at optimizing the same criterion either locally or globally and, in practice, complement each other. More precisely, the hierarchical cluster analysis can help selecting the appropriate number, P, of clusters and provides a starting partition of the datasets that can be improved by means of the partitioning algorithm. The hierarchical algorithm follows an ascending (or merging) strategy. We start with the situation where each dataset forms a group by itself. Obviously, in this case, G = 0. At each step, we merge two datasets or, more generally as the algorithm proceeds, two groups of datasets until all the datasets are merged in a single cluster.
Alternatively, these quantities could be represented as a bar plot showing their evolution as the number of clusters decreases. The clustering problem based on the criterion G given above can also be solved by means of a partitioning algorithm akin to the K-means algorithm  (Lloyd, 1982; Everitt, Landau, Leese, Stahl, 2011). In the course of this algorithm, the datasets are allowed to move in and out of the groups achieving at each step a decrease of the criterion G. This algorithm assumes that the number of clusters, K, is given beforehand and runs as follows: • Step 1 (Initial partition of the datasets): K groups of datasets are given by the practitioner. These groups could be chosen by a random assignment of the datasets. A better initialization can be performed from the outcomes of the hierarchical clustering described above.
This point will be further discussed below. • Step 2 (Determination of the cluster compromise scalar product matrices) : In cluster O L , the compromise scalar products matrix, (M) , and the associated weights are determined by means of the STATIS method as sketched in Figure  1. • Step 3 (changing clusters): New clusters of datasets are formed by moving each dataset, , to the cluster O L for which \]( , (M) ) is the largest. The steps 2 and 3 are iterated until there is no change in cluster memberships. This means that the criterion G stops to decrease. In practice, both the hierarchical and the partitioning algorithms should be performed to reach a better solution. Firstly, the hierarchical strategy can be used to hint at an appropriate number of clusters by examining the evolution of the aggregation criterion in the course of the aggregation process, as discussed above.
Secondly, the datasets are submitted to the partitioning algorithm using as an initial solution, the partition obtained by cutting the hierarchical tree at the indicated level (i. e. , with the selected number of clusters). By allowing the switching of cluster memberships, the solution obtained by the hierarchical clustering may be improved since the criterion G is likely to be further minimized. It is worth noting that since the hierarchical algorithm can be time consuming in situations where the number of datasets at hand is large, one can use only the partitioning algorithm. However, it is advised to perform a multi-start random partition by running this algorithm using several (random) partitions as starting points. Eventually, the final solution which corresponds to the smallest value of criterion G is retained.
Associated with each cluster of subjects O L , CLUSTATIS yields a weighted average matrix (M) , which is the compromise scalar products as obtained by the STATIS applied to the datasets in O L. An eigenanalysis of the matrix (M) makes it possible to write (M) = F (M) F (M). The matrix F (M) stands for the group average configuration in cluster O L. Several indices associated with the final solution are of paramount interest. In the first place, we consider for each cluster O L , (Q = 1, … , P), the index " L = # $ (J) % J , where ! ( L) is the largest eigenvalue of the matrix of the RV coefficients between the datasets in group O L and L is the number of datasets in this group. We know that this index ranges between ! % J and 1 and reflects the homogeneity in O L. It can be interpreted as the percentage of variation in the datasets of group O L which is explained by the group average configuration associated with (M).
Within the group O L , we can compute for each dataset (N ∈ O L ), the RV coefficient between and (M). This index reflects how each dataset is close to its associated group configuration. Alternatively, we could consider the coefficient (N = 1, … , ) which reflects the same idea. An overall index to assess the quality of the partition of the datasets obtained by the clustering approach is given by the weighted average of the indices " L : " = ∑ % J ^J _ J`$ % = ∑ # $ (J) _ J`$ %. This index can be interpreted as the percentage of variation in the original datasets explained by the group average configurations in the various groups. Finally, in order to assess how the various groups of datasets are close to each other, we can compute the RV coefficients between their associated group average configurations.
The case of projective mapping or Napping From a technical point of view, the procedures called Projective mapping  (Risvik, McEwan, Colwill, Rogers and David, 1994)  and Napping (Pages, 2005) are similar. They consist in instructing the subjects who participate in the experiment to position a set of products on a sheet of paper, considering that similar products should be located near one another and differing products should be placed far apart. Thus, the data can be presented as a collection of datasets; each dataset being associated with a subject and consists of the x and y coordinates of the products on the sheet of paper. Two statistical methods pertaining to the wide range of multi-block data analysis are concurrently proposed, namely Generalized Procrustes Analysis (GPA;  Gower, 1975; Risvik et al.
, 1994)  and Multiple Factor Analysis (MFA,  Pagès, 2005). The STATIS method is also appropriate for the analysis of these data. A thorough comparison of the respective merits of these three methods of analysis is beyond the scope of this paper. We will content ourselves by comparing the outcomes of this method of analysis to those of GPA and MFA on the basis of a case study. Methods of cluster analysis of projective mapping/Napping data were proposed  (Vidal et al. , 2016)  and are backed up by the idea that the subjects are likely to use different criteria to assess the products. These authors advocated using the so-called Lg measures derived from Multiple Factor Analysis (MFA,  Lê and Worch, 2014). Roughly speaking, the Lg measure between a dataset associated with a given subject and a component derived from MFA or any other method of analysis can be seen as a quantity that measures the variation in this dataset explained by the component under consideration  (Lê and Worch, 2014).
By selecting four  MFA components, Vidal et al. (2016)  computed for each dataset associated with a subject four Lg measures. Thus, each subject was considered as a four dimensional data point. Thereafter, these data points were subjected to a hierarchical cluster analysis using Ward's criterion. This approach of clustering the subjects is questionable for several reasons. In the first place, it is based on the configuration of the products obtained by means of an analysis performed on the whole panel. In case of a high disagreement among the panellists, which is precisely the reason why we wish to cluster them, this overall configuration is likely to be not very reliable. The second reason is that it appears somehow odd to set up a similarity measure among the datasets on the basis of the variations explained by a set of components when there are direct and easy to interpret measures of similarity among the datasets such as the RV coefficients  (Robert and Escoufier, 1976).
INDSCAL, which can be used for the analysis of multiblock datasets as an alternative method to MFA  (Naes et al, 2017) , yields, for each subject (i. e. , dataset), a set of saliences which reflect the weights that this subject attaches to the various INDSCAL components. Technically speaking, these saliences reflect the variation in the datasets explained by the INDSCAL components and, therefore, can be interpreted in a similar way as the Lg measures. Jackson (2005)  stated that "although one might be tempted to cluster the saliences or carry out other formal analysis on them, these quantities do not lend themselves to that purpose". He gives additional references to support his claim  (MacCallum, 1977; Coxon and Davis, 1982). CLUSTATIS can be applied in a straightforward way to the projective mapping or Napping data.
In a more recent paper,  Cariou and Qannari (2018) , investigated the agreement among the subjects involved in a free sorting task by computing a co-occurrence matrix that gives for each pair of subjects the numbers of pairs of products that these subjects set in the same group. This co-occurrence matrix is subjected to correspondence analysis and hierarchical cluster analysis. The aggregation criterion of this latter strategy of analysis is devised so as to preserve as much as possible the m index associated with the co-occurrence matrix. Therefore, the cluster analysis is aligned with correspondence analysis since both these methods aim at preserving as much as possible the m index. The advantage of CLUSTATIS over this strategy of analysis is that it has a wider scope than the free sorting data and, as discussed in the conclusion, can be extended in various directions.
Projective mapping/Napping data The data which are used to illustrate the application of STATIS and CLUSTATIS to Projective mapping/Napping can be found in the R package SensoMineR  (Lê and Husson, 2008). They concern 8 smoothies which were evaluated by 24 consumers. Thus, the data consist of 24 datasets; each dataset is associated with a consumer and consists of the x-y coordinates of the eight smoothies on the sheet of paper. It is usually advocated performing either GPA or MFA  (Tomic, Berget, Naes, 2015). The STATIS method can also be used to analyze this kind of data. In Figure  2   Figure  3  sheds even more light on the differences and similarities between the three methods of analysis considered herein. In this figure, we plot for each of the three methods the cumulative variation in the original datasets explained by the components derived from STATIS, GPA and MFA, respectively.
Since all the datasets at hand are two dimensional, the group average configuration derived from GPA is also two dimensional and, therefore, only two components can be computed. These two components explain less than 19% of the variation in the original datasets. The first two components derived from STATIS and MFA explain as much variation as those from GPA. However, with these two latter methods of analysis, further components can be computed to account for additional variation in the datasets. From Figure  3 , it is clear that STATIS and MFA show the same pattern in terms of total variance in the original datasets recovered by the successive components. As a matter of fact, only one subject changed cluster membership so much so that the overall homogeneity index improved but only slightly (0.
Free sorting data A panel of 25 subjects from Product Perceptions Ltd. 's pool of sensory panelists participated to the free sorting task. They were instructed to sort 14 brands of chocolate. As a matter of fact, the data considered herein are extracted from a larger experiment the details of which are given in  Courcoux et al. (2012). The subjects created between 5 and 10 groups of products. Before undertaking the segmentation of the panellists by means of CLUSTATIS, we compared the outputs of the STATIS method applied on the standardized data as indicated in section 2. 4 to those of well established methods. A particular emphasis is put on the DISTATIS method  (Abdi et al. , 2007)  since it is tightly linked to STATIS. shows the configuration of the products on the basis of the first two components obtained by means of DISTATIS.
IV. Conclusion The CLUSTATIS method is a clustering approach for multiblock datasets. Not only it leads to the clustering of a set of datasets but, within each cluster, it yields a group average configuration which makes it possible to depict the relationships among the individuals (i. e. , rows of the datasets). This group average configuration, also called compromise, is computed by means of the STATIS method applied to the datasets of the cluster under consideration. This means that weights associated with the various datasets are determined. These weights reflect the extent to which each dataset agrees with the general "point of view" of the datasets and are used to compute the group average configuration. This entails that those datasets which are in less agreement with the others are down-weighted.