Fabien Llobell
email: fllobell@xlstat.com

Evelyne Vigneau

El Mostafa Qannari

CLUSTERING DATASETS BY MEANS OF CLUSTATIS WITH IDENTIFICATION OF ATYPICAL DATASETS. APPLICATION TO SENSOMETRICS

Keywords: Segmentation, Cluster analysis, Atypical subjects, Projective Mapping, Napping, Free Sorting

A method of clustering a collection of datasets measured on the same individuals, called CLUSTATIS, was introduced and applied to the segmentation of the subjects participating in a projective mapping experiment or a free sorting task. A refinement of this method of clustering is proposed. It consists in segmenting the subjects while discarding those subjects who can be considered as atypical because they do not fit to the pattern of any cluster. This strategy of analysis requires the determination of a threshold parameter that delineates the boundary between the main clusters and the noise cluster that contains the atypical subjects. An appropriate selection of this parameter is proposed. The general strategy of analysis is illustrated on the basis of a simulation study and data from projective mapping and free sorting experiments.

Introduction

CLUSTATIS is a method of cluster analysis of datasets that pertain to the same individuals. In all the applications considered hereinafter, the individuals refer to products and we shall henceforth designate them as such. CLUSTATIS can be applied to situations where the datasets do not necessary refer to the same variables [START_REF] Llobell | Analysis and clustering of multiblock datasets by means of the STATIS and CLUSTATIS methods[END_REF]. It was successfully applied to the case of projective mapping, also called Napping, and free sorting data. In these experiments, the data from each subject are recorded in a specific dataset. The aim is to find homogeneous clusters of datasets, which for the two tasks considered herein (i.e., Napping and free sorting) will result in a segmentation of the subjects participating to these tasks. However, it very often occurs that there are atypical datasets which do not fit to any particular pattern. Notwithstanding, these datasets are assigned to one or the other of the clusters and, as a result, the homogeneity of the clusters can be affected and the performance of the clustering algorithm can be deteriorated [START_REF] Dave | Characterization and detection of noise in clustering[END_REF]. A strategy for identifying atypical subjects and discarding them is discussed and applied to three case studies pertaining to projective mapping/Napping and free sorting experiments. As a matter of fact, we follow a strategy of analysis similar to that described by Vigneau, Qannari, Navez and Cottet (2016) for the cluster analysis of variables. We also refer to this paper for a general discussion and a brief review of several strategies to deal with atypical data in cluster analysis. In sensory analysis, the atypical subjects that we seek to identify may correspond to outlying subjects, subjects with no clear assessment, undecided subjects, etc. This kind of behaviour was discussed in the context of preference studies by Westad, Hersleth and Lea (2004).

The strategy for identifying atypical datasets is to include in the optimization criterion associated with CLUSTATIS an additional cluster " + 1" besides the main clusters of datasets. All the datasets that do not seem to fit to the pattern of any of the main clusters will be assigned to the " + 1" cluster. [START_REF] Dave | Characterization and detection of noise in clustering[END_REF] who was the first to formalize the concept of the " + 1" strategy, refers to this additional cluster as a 'noise cluster'. A noteworthy feature of this strategy of analysis is that it is simple and intuitively appealing.

In the framework of projective mapping/Napping task, three segmentation methods were discussed by [START_REF] Berget | Segmentation in projective mapping[END_REF] within the framework of projective mapping.

We outline a comparison of CLUSTATIS with two of these methods on the basis of a case study.

The paper is organised as follows. In the "Material and methods" section, we start by sketching a brief reminder of CLUSTATIS and discuss new properties of this method of analysis. In particular, we outline a new formalization of the optimisation criterion which will turn out to be central to the identification of the atypical datasets. We briefly recall how CLUSTATIS can be applied to data from projective mapping and free sorting experiments.

Thereafter, we introduce the " + 1" strategy for identifying atypical subjects for the CLUSTATIS method. We put a particular emphasis on how to select the threshold parameter that delineates the boundary between the main clusters and the noise cluster. We finish this section by a comparison of methods. In section 3, we outline a simulation study to demonstrate the appropriateness of the selected threshold parameter for the determination of the noise cluster. Thereafter, we illustrate the general strategy of analysis on the basis of data from a projective mapping/Napping (subsection 3.2). A second case study is particularly devoted to the comparison of CLUSTATIS with alternative methods (subsection 3.3). A third case study is dedicated to the application of CLUSTATIS to free sorting data (subsection 3.4).

We end the paper by a general discussion and concluding remarks (section 4).

II. Material and methods

CLUSTATIS

Let us consider datasets denoted by ,… , , which are assumed to be column centred. These datasets are measured on the same products but the variables may differ from one dataset to another. CLUSTATIS revolves around the STATIS method [START_REF] Lavit | The act (statis method)[END_REF]Schlich, 1996). The cornerstone of this strategy of analysis is the scalar product matrices associated with the datasets at hand: = ,…,

=

. These are × symmetric matrices which reflect the spatial configuration of the products since the entry corresponding to the row and column gives the scalar product between the and products. Central to the STATIS method is the RV coefficient which reflects the similarity between two configurations (Robert & Escoufier, 1976;Schlich, 1996;[START_REF] El Ghaziri | Measures of association between two datasets; application to sensory data[END_REF]:

( , ) = , ‖ ‖‖ ‖ = ( ) ( ) ( )
.

We will also assume that ‖ ‖ = 1 (! = 1, … , ) which means that these matrices have been standardized by dividing each original by its norm, ‖ ‖ = #$%&'( ). This standardization is performed to account for differences among the datasets such as different scaling, different number of columns, etc.

CLUSTATIS seeks homogeneous clusters of datasets in such a way that the datasets in each cluster are as close as possible to a group average dataset. Formally, CLUSTATIS aims at minimizing the following criterion:

) = ∑ ∑ || - -∈/ 0 1 234 5 - (6) || 7 (1)
Clearly, this criterion pinpoints the fact that we are seeking clusters of datasets in such a way that, in each cluster, 8 2 , the matrices are clustered around an average matrix, (6) . The weights 5 -in each cluster are given by the STATIS method. Thus, those datasets in a given cluster which have less agreement with the other datasets in this cluster will have small weights. Contrariwise, those datasets which are more in line with the general point of view of the cluster under consideration will be allotted relatively larger weights.

For solving this optimization criterion, hierarchical and partitioning algorithms were proposed [START_REF] Llobell | Analysis and clustering of multiblock datasets by means of the STATIS and CLUSTATIS methods[END_REF]. Although it is advised to perform both algorithms in conjunction, each one of them can stand by itself to provide a solution to the clustering problem. We shall focus herein on the partitioning algorithm and discuss how it can be extended to identify atypical datasets (i.e., subjects). This algorithm is akin to the 9-means algorithm and requires the choice of the number of clusters and a starting partition of the datasets into clusters. The starting partition can be derived from the hierarchical cluster analysis [START_REF] Llobell | Analysis and clustering of multiblock datasets by means of the STATIS and CLUSTATIS methods[END_REF] or can be chosen by the practitioner. Alternatively, one may run a multi-start procedure consisting in performing the partitioning algorithm several times (e.

g., 50 times) with, at each time, a staring partition chosen at random. Eventually, the partition that corresponds to the smallest value of criterion ) is chosen.

An interesting ANOVA-like decomposition is the following: (6) ||² that we seek to minimize. We can also show that the percentage of explained variation given by = = ∑ ; (6) ;

7 1 234 ∑ || : -34 || 7 > is equal to ∑ ? @ (0) A 0B@ :
, where C 4

(2) is the largest eigenvalue of the matrix of pairwise coefficients between the datasets in the 9

cluster. This index reflects the overall within-clusters homogeneity. The homogeneity in the 9 cluster can be assessed by

? @ (0)
: (0) where (2) is the number of datasets in the 9 cluster.

We can also show that at the convergence of the clustering algorithm, we have

∑ ∑ 7 ( -∈/ 0 1 234 , (6) ) = ∑ C 4 (2) 1 234 and ) = -∑ C 4 (2) 1 234
. This means that CLUSTATIS can also be defined as a method that seeks to maximize the quantity

∑ ∑ 7 ( -∈/ 0 1 234
, (6) ), which reflects the within-cluster homogeneity.

The application of CLUSTATIS to projective mapping data is straightforward. To each subject ! (! = 1, … , ), we associate a two dimensional dataset which provides the coordinates of the products under study on the sheet of paper given by this subject.

Although all the datasets have two columns, these columns may convey different meanings from one respondent to another. Thus, CLUSTATIS is indicated to analyse this kind of data and segment the respondents. More details are given in [START_REF] Llobell | Analysis and clustering of multiblock datasets by means of the STATIS and CLUSTATIS methods[END_REF]. An illustration of this strategy of analysis together with the demonstration of the interest of detecting atypical subjects are outlined in section 3.

The application of CLUSTATIS to the case of free sorting task was also discussed in [START_REF] Llobell | Analysis and clustering of multiblock datasets by means of the STATIS and CLUSTATIS methods[END_REF]. The data from the subject ! (! = 1, … , ) who has sorted the products at hand into D -clusters are recorded into a matrix E ( xD -) consisting of dummy variables. Each dummy variable (column) is associated to a group and indicates which products belong to this group. Thereafter, each column is standardized by dividing it by the square root of its sum total. This kind of standardization is mainstream in correspondence analysis and allied methods (Qannari, Cariou, Teillet, Schlich, 2010). CLUSTATIS method operates on the datasets thus standardized.

Discarding atypical datasets with the "G+1" strategy

The guiding principle of this strategy of analysis is to set aside those datasets that are weakly linked to all the group average configurations associated with the various clusters. it was formalized by [START_REF] Dave | Characterization and detection of noise in clustering[END_REF] who introduced the concept of "noise cluster" or " + 1" cluster, which collects the objects (i.e., datasets in our context) that have been discarded.

In a first step, the strategy of analysis requires to select a threshold value, H, between 0 and 1 below which the link between two datasets as measured by the RV coefficient is considered as very weak. Formally, we seek to maximize the following criterion:

I J = ∑ ∑ KL -2 7 K , (6) M + L -(1N4) H 7 M : -34 1 234 (3)
Where L -2 is the Kronecker symbol which is equal to 1 if the dataset ! belongs to cluster 9 and 0 otherwise, with the constraint ∑

L -2 = 1 1N4 234
. This constraint stipulates that a dataset belongs to one and only one cluster, including the noise cluster.

The rationale behind this optimization is very simple. Basically, for each

(! = 1, … , ),
we seek the cluster 9 for which K , (6) M is the largest. Then we assess whether K , (6) M > H. If so, then is assigned to cluster 9, otherwise, it is assigned to the cluster "K+1". This means that we filter out those datasets whose degrees of association, as measured by the coefficient , with the main groups are below a threshold value, H. All in all, the partitioning algorithm runs as follows.

Step 0 (initial partition). Choose a partition into clusters of datasets (i.e., subjects) as a starting point. This can be done by a random assignment of the datasets at hand to clusters or by cutting the hierarchical tree at the level corresponding to clusters.

Step 1 (group average datasets). In each cluster 8 2 , the group average (6) is determined by means of the STATIS method.

Step 2 (changing clusters). New clusters of subjects are formed by moving each dataset, , to the cluster 8 2 for which the quantity ( , (6) ) is the largest providing that this quantity is larger than H otherwise, is assigned to the cluster "K+1".

Steps 1 and 2 are iterated until the datasets stop changing clusters.

Choice of the threshold value P

The problem that yet needs to be solved is how to select an appropriate parameter H.

Since this parameter is akin to a similarity measure between two datasets as assessed by the similarity measure , it is comprised between 0 and 1. For H = 0, the "K+1" cluster is empty, and as H increases, more datasets are likely to join this noise cluster. For H = 1, all the datasets are set in the noise cluster. [START_REF] Dave | Characterization and detection of noise in clustering[END_REF] suggested a strategy for choosing an appropriate value for ρ in a clustering problem based on distances between objects. This consists, in a first step, of computing the average of the squared distances between each object and each center of the various clusters. Thereafter, this average should be multiplied by a constant. However, few details are given regarding this constant except that it should be small.

Since the parameter ρ is akin to an RV coefficient, this tremendously restricts the field of prospection in comparison to a cluster analysis on the basis of distances. As a result, we are in a similar situation to the cluster analysis of variables by the CLV method. In this context, Vigneau et al. (2016) proposed several strategies for the selection of the parameter associated with the noise cluster. Among these strategies, we single out the one consisting in exploring the range between 0 and 1 by considering several values of ρ and examining the evolution of the within-cluster homogeneity, on the one hand, and, on the other hand, the evolution of the number of objects (i.e., variables in the context of CLV and datasets in the context of CLUSTATIS) that are assigned to the noise cluster. This strategy can be easily adapted to the CLUSTATIS context as will be illustrated on the basis of a case study. More importantly, we propose to directly define a value for the parameter ρ consisting in calculating the average of the RV coefficients of each dataset with the center of its own group and the center of the nearest group. Formally, the selected value H that we propose is the following:

H = ∑ RST( , ( 6
) )N ST( , K6 UM V W XB@
7:

(4)

where (6 ) is the average scalar products matrix obtained by means of the STATIS method of the cluster to which the ! dataset belongs, and, likewise, (6 Y) is the average scalar products matrix of the nearest cluster to the ! dataset.

In order to pinpoint the idea behind this choice, we refer to Figure 1 where, for the sake of illustration, the fictitious datasets to be clustered are represented as points in a twodimensional space. In reality, they are embedded in a space of much higher dimension. We aim to circumscribe the points of each cluster in a circle so that the points that are close to their own center are inscribed in this circle whereas, the points that are straddling two or more clusters are assigned to the cluster "K+1". The first circles, with the smallest radius, encompass the datasets whose RV coefficients with their own center is larger than the average of the RV coefficients of all the datasets with their own center. These circles leave many points outside. The largest circles encompass the datasets whose RV coefficients with their own center is larger than the average of the RV coefficients of the datasets with all the centers of all the groups, which would be in line with Dave's idea [START_REF] Dave | Characterization and detection of noise in clustering[END_REF]. These circles are far too large and, as a result, very few points are left outside. The intermediate circles correspond to the solution that we propose, namely in each circle, we find those datasets whose RV coefficients with their own center is larger than the average of the RV coefficients of all the dataset with their own center as well as with the center of the nearest cluster. This choice seems to be more appropriate. It is worth emphasizing that herein the criterion of appropriateness means that we aim at defining clear clusters with improved within homogeneity. The datasets that are left aside are not necessarily outliers but are merely deemed not fitting the pattern of any cluster.

Comparison of methods

In a recent paper, [START_REF] Berget | Segmentation in projective mapping[END_REF] applied three analytical strategies to projective mapping data. In the following, we will focus on two methods called Proclustrees and SCR (sequential partitioning by clusterwise rotations). The Proclustrees and SRC methods consist of a hierarchical cluster analysis and a partitioning algorithm, respectively. However, their only common link is the use of Procrustes distance. By comparison, the hierarchical and the partitioning algorithms in CLUSTATIS are tightly linked since they aim at optimizing the same criterion.

By adopting a consistent analysis all along the CLUSTATIS strategy of analysis, we were able to propose an analytic value for the noise parameter, H. The SCR strategy of analysis proposed by [START_REF] Berget | Segmentation in projective mapping[END_REF] also includes the concept of "noise cluster". For the choice of the threshold parameter, it is suggested to use a trial and error procedure by considering, on the one hand, the within-clusters variation (homogeneity) and, on the other hand, the between-clusters variation.

The various strategies of analysis are compared on the basis of a case study in section 3.3.

III. Illustrations

Projective mapping: a simulation study

The aim of the simulation study is to confirm the efficiency of CLUSTATIS and demonstrate the appropriateness of the proposed parameter H for correctly setting aside the atypical datasets.

We strictly followed a simulation framework proposed by [START_REF] Berget | Segmentation in projective mapping[END_REF]. More precisely, projective mapping data were simulated by considering the case of 100 subjects and 9 products. The subjects were assumed to belong to three clusters A, B and C. More specifically, the data were simulated in such a way that the clusters A and B have different perception of the products and, the cluster C contains subjects who should fall in the noise cluster since they "organise the samples more or less randomly and, hence represent noise" [START_REF] Berget | Segmentation in projective mapping[END_REF]. The typical configurations in clusters A and B are given in Figure 2. For each simulated situation, we run CLUSTATIS with the "K+1" option. The parameter H was computed using equation ( 4). In all the simulated data, we obtained 100% of correct identification. This means that all the clusters, including the noise cluster, were perfectly retrieved.

Projective mapping: the smoothies data.

The data which are used to illustrate CLUSTATIS together with the strategy of identification of atypical datasets pertain to a Projective Mapping/Napping experiment and can be found in the R package SensoMineR [START_REF] Lê | SensoMineR: A package for sensory data analysis[END_REF]. They concern 8 smoothies which were evaluated by 24 consumers. Therefore, we have 24 datasets; each dataset being associated with a consumer and consists of the x-y coordinates of the eight smoothies on the sheet of paper.

The dendrogram associated with the hierarchical cluster analysis and the variation, delta, of the criterion ) of the CLUSTATIS analysis are shown in Figure 3. It turns out that, when moving from a solution with three clusters to a solution with two clusters, the variation of the criterion is relatively large. This should arouse the suspicion that, at this step, the merging of two clusters is yielding a heterogeneous cluster. Therefore, we should retain the solution with three clusters. Besides providing a clustering of the datasets at hand, CLUSTATIS simultaneously performs STATIS within each cluster, yielding weights associated with the various subjects which reflect the agreement with the general point of view of the cluster. These weights are also used in CLUSTATIS to compute a group average configuration associated with each cluster. The weights associated with the various subjects arranged in a decreasing order are given in Table 1. Clearly, it appears that subject S2 stands out from the other subjects in cluster 1. Similarly, subjects S8 and S7 stand out from the other subjects in cluster 3.

Cluster 1: The smoothies data: Weights, arranged in a decreasing order, assigned to the subjects in the three clusters. In bold, subjects with relatively small weights.

For the purpose of identifying atypical subjects, we show in Figure 4 the evolution of the overall homogeneity index and the number of subjects who were assigned to the noise cluster as a function of the noise parameter, H. We can see that a parameter around 0.6 is indicated since it entails discarding only three subjects and the gain in terms of overall homogeneity is around 6%. At H =0.65, yet another subject is removed but the gain in terms of overall homogeneity is negligible. At H =0.7, the overall homogeneity increases by approximately 4% at the cost of removing 7 subjects in total. This may be considered too high a price for the derived benefit. As a matter of fact, the parameter H that we computed using the expression in equation ( 4) is equal to 0.6, which is in line with the finding from Figure 4. The three subjects who were discarded are subject S2 from cluster 1 and subject S7 and S8 from cluster 3. These are the subjects who were highlighted as having the smallest weights in Table 1. By way of illustrating the effect of the removal of the two subjects S7 and S8 from cluster 3, we display in Figure 5 the configuration of the products with and without these two subjects. The most important change concerns the positions of the products Immedia-SRB and Carrefour-SB. This can be explained by the fact that, on the one hand, the subject 8 has set the products Carrefour-SB and Casino-SRB very far away from each other and, since this subject was removed, Carrefour-SB appears as less extreme along the second axis. On the other hand, the subject S7 has set the products Immedia-SRB and Carrefour-SB far removed from each other and when this subject was removed, these two products have come relatively closer to each other.

Projective mapping: the yoghurt data

The aim of this section it to compare CLUSTATIS with the Proclustrees and SCR strategies which were used to analyse projective mapping data [START_REF] Berget | Segmentation in projective mapping[END_REF]. For this purpose, we use the same yoghurt data that were used by these authors and which were kindly made available to us. These data concern a projective mapping experiment involving 100 subjects who were asked to assess 12 commercial blueberry yoghurt packages marketed in Norway. For more details regarding these data, we refer to three articles (Naes, Berget, Liland, Ares & Varela, 2017;Varela et al., 2017;[START_REF] Berget | Segmentation in projective mapping[END_REF]. The dendrogram obtained by means of CLUSTATIS (Figure 6) indicates to choose two clusters of subjects. This finding agrees with that derived from the dendrogram obtained by means of Proclustrees [START_REF] Berget | Segmentation in projective mapping[END_REF]. Table 2 gives the within-clusters homogeneity indices based on the RV coefficients (section 2.1). In this table two situations are considered, namely, the situation where the option regarding the noise cluster is not activated (Proclustrees and CLUSTATIS) and the situation where this option is activated (SCR and CLUSTATIS with the noise cluster). In all the cases, it appears that insofar as the within-clusters homogeneity indices are concerned, CLUSTATIS outperforms the other methods. The only exception to this general finding concerns Cluster 2 where Proclustrees very slightly outperforms CLUSTATIS. Figure 7 shows the representation of the products on the basis of the two first STATIS components performed on the subjects of the two CLUSTATIS clusters with the option "K+1". It turns out that the subjects in the two clusters have a different perception of the products since the two configurations appear to be dissimilar. It is also noteworthy that the configuration associated with cluster 1 bears a good similarity with the cluster 1 obtained by means of Proclustrees (figure not shown, see [START_REF] Berget | Segmentation in projective mapping[END_REF]. The RV coefficient between the two configurations is equal to 0.80. The configuration associated with cluster 2 bears a fair similarity to that associated with cluster 2 obtained by means of Proclustrees (RV=0.76, figure not shown, see [START_REF] Berget | Segmentation in projective mapping[END_REF]. The main difference between these latter two configurations concerns the products P4 and P8 which appear in CLUSTATIS close to products P2 and P6 (Figure 7, right), whereas, in Proclustrees, these products occupy an intermediate position between P9 and P5, on the one hand, and P1, P10 and P11, on the other hand [START_REF] Berget | Segmentation in projective mapping[END_REF].

Figure 7: the yoghurt data: Representation of the products on the basis of the first two STATIS components associated with the two clusters of subjects.

Free sorting: the aromas data

The data which are used to illustrate CLUSTATIS with the "noise cluster" option can be found in the R package FreeSortR [START_REF] Courcoux | FreeSortR: Free Sorting Data Analysis[END_REF]. They concern 16 aromas which were evaluated by 31 subjects who are students in food science but who are not experts in oenology and have not received any training in wine tasting. The sixteen aromas, which are known to be perceptible in white or red wines, were selected from "Le nez du vin" box set (Edition Jean Lenoir, 2006). Examples of such aromas are: Lemon, Grapefruit, Honey, Butter, Grilled bread, Grilled hazelnut, etc. The aromas coded by a three-digit random number were presented simultaneously to the subjects in glass vials in a random order. Each subject formed groups of the 16 aromas according to their perceived similarities and differences.

The data from each subject were encoded into dummy variables and standardized as indicated in section 2.1. The datasets thus obtained were submitted to CLUSTATIS with the noise cluster option.

Five clusters can be considered in this case (dendrogram not shown for the sake of saving space). The selected noise parameter based on equation ( 4) is H = 0.66. This entails that four subjects were set in the noise cluster. Table 3 gives the within-cluster homogeneity before and after the removal of the atypical subjects. In particular, we can see that the removal of the four subjects resulted in an increase of nearly 4% of the overall homogeneity index.

The Figure 8 shows the configuration of the aromas associated with the first cluster of subjects with and without the noise cluster option. The main difference between these two configurations concerns the position of the "Butter" aroma. This change can be explained by the fact that the subject that has been set in the noise cluster was the only subject in the first cluster who formed a group containing only the "Butter" and "Grilledbread" aromas whereas, none of the other subjects in this cluster had placed these two aromas in the same group. Therefore, when this subject was set aside, the two aromas moved away from each other.

IV. Conclusion

We believe that the case studies together with the simulation study discussed in this paper have confirmed the interest and the efficiency of the CLUSTATIS strategy of segmentation of a panel of subjects in a projective mapping and a free sorting experiments.

The range of application of this strategy of analysis is larger than these two experiments and include experiments such as sensory profiling with fixed or free choice vocabulary, preference data which include several liking attributes, etc. This method of analysis is flexible enough to offer the option of discarding respondents who do not fit to any cluster. This yields a better, more stable and easier to interpret segmentation of the subjects.

An advantage of the CLUSTATIS approach over competing strategies of analysis is its consistency since the whole strategy is contained in the optimization criterion that seeks to define homogeneous clusters. This same criterion governs the hierarchical and the partitioning algorithms, the definition of the homogeneity indices, the definition of agreement indices within each cluster and, finally, the computation of the configuration of the products associated with each cluster.

In this paper, we have particularly stressed the interest of the noise cluster. We have been inspired by ideas from [START_REF] Dave | Characterization and detection of noise in clustering[END_REF]Vigneau et al.'s (2016) ideas. However, a significant contribution was to propose a noise parameter that seems to be appropriate for setting up the boundary between the main and the noise clusters. We could go further and propose, instead of a common parameter to all the clusters, a specific noise parameter to each cluster to take account of how each cluster is far removed from the other clusters or to take account of the shape of the clusters. Primary investigations into this direction seem to indicate but a very slight improvement over the strategy based on a common noise parameter. Yet, these investigations also indicated that the idea of specific noise parameters deserve further consideration. Notwithstanding, it is clear that a good choice of a noise parameter depends on an appropriate choice of the number of clusters, which is a thorny issue. Indeed, the choice of the number of groups in cluster analysis has caused a lot of ink to flow (Lord, Willems, Lapointe & Makarenkov, 2017). For our part, we limited ourselves to examining the dendrogram resulting from the hierarchical cluster analysis, but we believe that this problem deserves more attention. Conversely, we also believe that the choice of the noise parameter, H, could help choosing the number of clusters, as these two aspects (i.e., noise parameter and the number of clusters) are so closely linked.

From a practical point of view, an R package called ClustBlock to perform CLUSTATIS has been recently launched.

Figure 1 :

 1 Figure 1: Fictitious data: Representation of three clusters. The three circles correspond to

  Simulated data were generated by imposing different amount of within-cluster variability following a normal distribution and varying the proportions of the subjects in the three clusters. For more details, we refer to the paper by[START_REF] Berget | Segmentation in projective mapping[END_REF].

Figure 2 :

 2 Figure 2: Example of simulated data set for cluster 1 (left) and cluster 2 (right). The digits 1 to

Figure 3 :

 3 Figure 3: The smoothies data: Dendrogram given by the CLUSTATIS hierarchical clustering analysis and variation of the criterion ).

Figure 4 .

 4 Figure 4. The smoothies data: Evolution of the overall homogeneity index (left) and the number of subjects in the "K+1" cluster as a function of the noise parameter, H.

Figure 5 :

 5 Figure 5: The smoothies data: Representation of the products on the first two STATIS

Figure 6 .

 6 Figure 6. the yoghurt data: Dendrogram given by the CLUSTATIS hierarchical clustering analysis and variation of the criterion )

Figure 8 :

 8 Figure 8: the aromas data: Two firsts components of the cluster 3's compromise obtained by

  Table 2. the yoghurt data: Comparison of Proclustrees and CLUSTATIS (without the noise cluster) and SCR and CLUSTATIS (with the noise cluster) on the basis of the within-cluster homogeneity indices.

			Without the noise cluster
		Cluster 1	Cluster 2	Overall (weighted average)
	Method of analysis	Proclustrees	CLUSTATIS	Proclustrees	CLUSTATIS	Proclustrees	CLUSTATIS
	(sample size)	(47)	(43)	(53)	(57)	(100)	(100)
	Homogeneity index (%)	25.7	40.4	24.5	23.3	25.1	30.7
			With the noise cluster
		Cluster 1	Cluster 2	Overall (weighted average)
	Method of analysis	SCR	CLUSTATIS	SCR	CLUSTATIS-	SCR	CLUSTATIS-
	(sample size)	(42)	(37)	(26)	(26)	(68)	(63)
	Homogeneity index (%)	39.0	44.6	27.1	35.5	34.5	40.8

Table 3 :

 3

			CLUSTATIS	CLUSTATIS with noise
					cluster
	Clusters	size	Homogeneity	size	Homogeneity
			index (%)		index (%)
	1	6	54.3	5	58.4
	2	5	48.7	4	55.5
	3	4	58.0	4	58.0
	4	13	56.8	11	60.8
	5	3	75.7	3	75.7
	Overall	-	57.0	-	60.8
	(weighted
	average)
	The whole	31	43.9
	panel

the aromas data: Size, homogeneity and global homogeneity indices using CLUSTATIS without and with the noise cluster strategy.

Acknowledgements

We are deeply grateful to Ingunn Berget for sharing with us the yoghurt data and all the programs for running her methods of analysis.


MD Claire Masson

PharmD Constance Minebois

RN Catherine Braux

MD Isabelle Pelloux

Leïla Marcus

MD Valérie Belin

MD Fabrice Cneude

Béatrice Prillard

MD Thierry Debillon

MD ; Leïla Marcus

RN ; Béatrice Prillard

PharmD Caroline Landelle
email: caroline.landelle@gmail.com

MD Marie Reine Mallaret

Bacteriological screening of breast milk samples destined to direct milk donation: Prospective evaluation between 2007 and 2016

Keywords: Neonatal intensive care unit, preterm neonate, breast milk, Staphylococcus aureus, direct milk donation

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Many studies have shown the benefits of breastfeeding for the development of preterm infants during the first months of life [START_REF] Armstrong | Breastfeeding and lowering the risk of childhood obesity[END_REF][START_REF] Herrmann | An Exclusively Human Milk Diet Reduces Necrotizing[END_REF][START_REF] Howie | Protective effect of breast feeding against infection[END_REF][START_REF] Kull | Breast feeding and allergic diseases in infants-a prospective birth cohort study[END_REF]. [START_REF] Picaud | Review concludes that specific recommendations are needed to harmonise the provision of fresh mother's milk to their preterm infants[END_REF] showed that the precocity of breastfeeding is one of the keys to the success of breastfeeding a premature child. There are different types of breastfeeding: direct milk donation or fresh milk donation (milk directly given from the mother to her child hospitalized without pasteurization), mother's milk (milk given from the mother to her child hospitalized after pasteurization) and human milk (anonymous donor gives milk to a milk bank) (Ministère du Travail et des Affaires Sociales, 1997). [START_REF] Cong | Gut Microbiome Developmental Patterns in Early Life of Preterm Infants: Impacts of Feeding and Gender[END_REF] showed that infants fed by mother's own breast milk had a significantly more diverse gut microbiome and higher abundance of Clostridales and Lactobacillale than those fed with human donor milk and or formula. Even if many bacteria contribute to the gut microbiome, some are pathogenic bacteria and can cause severe pathologies in these preterm children because of their immature immune system. Cases of sepsis were described with Escherichia coli, Klebsiella pneumoniae due to direct donation [START_REF] Jawa | Recurrent late-onset group B Streptococcus sepsis in a preterm infant acquired by expressed breastmilk transmission: a case report[END_REF][START_REF] Widger | Breast milk causing neonatal sepsis and death[END_REF]) and more recently with Cronobacter sakazakii [START_REF] Bowen | Notes from the Field: Cronobacter sakazakii Infection Associated with Feeding Extrinsically Contaminated Expressed Human Milk to a Premature Infant -Pennsylvania, 2016[END_REF]. Therefore, this type of diet requires hygiene recommendations to guarantee the infants' safety.

Since 1997, direct milk donation from a mother to her child is authorized in France in the absence of communicable diseases: Human Immunodeficiency Virus (HIV), hepatitis B and C virus, Human T cell Leukemia Virus (HTLV) 1 and 2 (Ministère du Travail et des Affaires Sociales, 1997). In case of very premature infants, born before 32 weeks of Gestational Age (GA) or/ and very low birth weight infant, the French Agency for Food, Environmental and Occupational Health and Safety (ANSES) advises against direct milk donation if the mother has a positive Cytomegalovirus (CMV) serology. Since 2005, ANSES recommends analyzing at least one breast milk sample but there is no bacteriological threshold to define a non-compliant sample. When the collection has been refrigerated for more than 48 h and was not administered to the newborn, it is frozen and sent to the milk bank to be pasteurized [START_REF] Afssa | Recommandations d'hygiène pour la préparation et la conservation des biberons[END_REF].

The university hospital of this study has implemented breast milk direct donation for preterm children under 34 weeks of GA in 2007. The objective of this study was to analyze the bacteriological quality of breast milk samples destined to direct milk donation for preterm children in our institution between 2007 and 2016.

Methods

Setting

We conducted a prospective observational study in a 2200-bed French University Hospital.

All samples of breast milk destined to direct milk donation collected between April 17, 2007, and December 31, 2016, were included in the study. During this period, the average number of deliveries per year was 2661 ± 411 and the average number of births per year was 2745 ± 422. On average, 26 ± 3.4 % of the children were hospitalized in a 36 -bed neonatology and neonatal intensive care units (NICU).

Study ethics approval was obtained on 30 March 2018 (CECIC Rhône-Alpes-Auvergne, Clermont-Ferrand, IRB 5891).

Breast milk collection

Before breast milk collection, mothers' mandatory serologies were checked to avoid virus transmission (HTLV, Hepatitis B and C, HIV, and CMV for preterms under 32 weeks of GA).

Recommendations about inclusion and exclusion criteria have made available in paper format

since 2007 and have made available by electronic means (inclusion in the documentation management software) in 2011. Before milk collection, NICU nurses gave recommendations about everyday body and hand hygiene, and correct cleaning of breast pumps, equipment and surfaces. Before 2013, mothers could only collect their milk in a collection room with stationary pumps. Since 2013, mothers can collect their milk in this room or in their child's room with a portable pump. A hygiene recommendation sheet is posted in the breast milk collection room and above each portable pump. An information booklet in their language about breast milk collection is given to every mother before the first collection.

Bacteriological analyses of breast milk samples

French regulation recommends to analyze at least one breast milk sample during direct milk donation in the hospitalization even though there is no bacteriological threshold to define a non-compliant sample. As a consequence, we defined our own threshold. We have considered a sample to be compliant if its total flora is under 10 6 CFU/mL and in the absence of Staphylococcus aureus and pathogens (Enterobacteriaceae, Enterococcus…). Milk testing was done only once at birth for every infant, except for infants with a GA < 34 weeks, for whom milk was tested every 4 weeks until they reached 34 weeks of post conceptional age.

If the sample presented total flora was ≥10 6 CFU/mL, or pathogenic bacteria, direct milk donation was halted until the mother's education about milk collection was strengthened. If S. aureus was present, a decolonization treatment was given to the mother (chlorhexidine showers once a day for 5 days and intranasal mupirocin applications for 5 days) [START_REF] Reagan | Elimination of coincident Staphylococcus aureus nasal and hand carriage with intranasal application of mupirocin calcium ointment[END_REF]. Mothers were not allowed to donate milk during the decolonization process. Milk was tested after the process to check if breastfeeding could start again.

If infants had under 34 weeks of GA and their mother wished to give their milk at the time of non-compliant result, sample were controlled as required. Mothers had more than one sample if it was a non compliant sample or when the GA was less than 34 weeks.

Mothers could also decide to stop direct milk donation, so if the initial sample was not compliant, there was no need to have other samples. Samples of milk were seeded: 0.01 mL on blood agar and 0.01 mL on Chapman agar, and inoculated at 36°C for 48 hours with a first verification after 24 hours (Ministère du Travail et des Affaires Sociales, 1997).

For non-compliant breast milk samples, we checked whether the child had a bacteraemia with the bacteriology laboratory data until the hospital 's discharge of the newborn.

Statistical analysis

Qualitative variables were described by their number and their percentage and quantitative variables by their mean and their standard deviation. Comparison of qualitative variables was conducted with a Chi2 test if the conditions for application of this test were verified.

Otherwise a Fisher's exact test was performed.

We analyzed breast milk samples of the mother of a single child (exclusion of samples from a mother of twins). Samples from mothers of twins are not independent. We excluded them to avoid confusion in the results. We decided to analyze periods according to the visual distribution of the non-compliance rate. We chose to exclude the 2007 tests because it was incomplete. The significance threshold was set at 0.05. The statistical analyses were performed with R version 3.3.2.

Results

A total of 808 direct milk donation samples were collected from 641 mothers between April 17, 2007, and December 31, 2016: 777 samples from mothers who gave birth to a single child and 31 from mothers of twins.

Among the 777 samples, 629 were initial samples and 148 were control samples (Figure 1).

Of the 629 initial samples, 495 (78.7%) were compliant. Among the 134 (21.3%) non-compliant samples, 63 (10.0%) had a total flora ≥ 10 6 CFU/mL, 63 (10.0%) were only contaminated by a pathogenic bacteria and 8 (1.3%) were non-compliant because of both (Table 1). On the whole, S. aureus was identified in 58 (9.2%) samples. One was a methicillin-resistant S. aureus, 19 (3.0%) were ≥10 4 CFU/mL. Other pathogens were found in 15 (2.4%) samples: mainly Gram-Negative Bacilli (Klebsiella pneumoniae, Klebsiella oxytoca, Escherichia coli, Enterobacter cloacae...), with one E. coli producing extended-spectrum beta-lactamases (ESBL).

We described in figure 2 the evolution of the number of samples analyzed and the proportion of non-compliant samples between 2007 and 2016. There was an increase in the number of samples analyzed in 2011.

According to figure 3, an increase of the non-compliance rate was observed between 2008 and 2016 (10.2% to 26.1%). The rate of non-compliance was stable until 2009, decreased in 2010, increased in 2011 and reach a peak in 2013 and then decreased. The evolution of the total flora non-compliance rate was similar. The presence of S. aureus in breast milk appeared stable over time. For the pathogenic bacteria presence (without S. aureus), the rate increased in 2014. The overall non-compliance rate was significantly higher between 2011-2013 and between 2014-2016 than between 2008-2010 (23.4% vs. 9.4%; p=0.001 and 29.2% vs.9.4%, p<0.001) (Table 2). This result was also observed for the total flora ≥ 10 6 CFU/mL (15.6% vs. 1.6%, p<0.001 and 14.4% vs. 1.6%; p<0.001). No statistically significant difference of the presence of S. aureus in breast milk was observed between 2008-2010, 2011-2013 and 2014-2016 (7.9%, 9.3% and 10.5% p = 0.7). For the pathogenic bacteria presence, the rate was significantly higher between 2014-2016 than between 2011-2013 (4.7% vs. 0.5%; p=0.008).

Forty-seven samples of breast milk were verified, 27 (57.4%) were not compliant.

Among the 27 samples, 11 (40.7%) had a second verification and 5 were not compliant (Figure 1). Of note, one sample was verified 5 times.

Among 134 children with an initial non-compliant breast milk sample, 21 bacteraemia were recorded and 8 occurred after breast milk donation. Of those eight, four had bacteraemia due to coagulase negative Staphylococcus. The breast milk samples collected before bacteraemia were non-compliant due to an excess of the total flora. The four other children were already colonized by S. aureus and developed a bacteraemia with S. aureus, or had bacteraemia due to a different pathogen from the one of the milk sample.

Discussion

This study highlighted an increase in the overall non-compliance rate of breast milk destined to direct milk donation between 2008 and 2016 in our institution. A peak was observed in 2013. Rates of samples with total flora ≥10 6 CFU/mL increased between 2008 and 2016.

The overall non-compliance rate was 21.3% in accordance with our strict criteria. The noncompliance rate was higher than the 11% non-compliance rate found in French milk banks before pasteurization (Dewitte et al., 2015) but criteria were not the same mainly for S. aureus. [START_REF] Dewitte | Contamination of human milk with aerobic flora: Evaluation of losses for a human milk bank[END_REF] showed that 4.6% of the overall collected breast milk was discarded because of non-compliant total flora (≥10 6 CFU/mL).

In our study, the contamination by pathogenic bacteria (S. aureus and other pathogens) was 11.3%. This result is concordant with [START_REF] Picaud | Review concludes that specific recommendations are needed to harmonise the provision of fresh mother's milk to their preterm infants[END_REF] and it is in the low range. [START_REF] Picaud | Review concludes that specific recommendations are needed to harmonise the provision of fresh mother's milk to their preterm infants[END_REF] reported that approximately 10-40% of human milk samples collected from mothers in neonatal units were contaminated with pathogenic germs. This result is very reassuring.

In this University Hospital study, the evolution of the overall non-compliance rate followed closely the total flora non-compliance rate. Decrease in 2010 of the overall noncompliance rate could be explained by an outbreak of Bacillus cereus with several infections between June and December 2009. No breast milk samples have been identified B. cereus but all hygiene practices were reinforced during and after this outbreak. An increase of the overall non-compliance rate and the total flora non-compliance rate began in 2011 and was observed until 2013. We observed that the number of samples nearly doubled in 2011, probably in link with increasing availability of recommendations. Therefore, nurses could not be as often present as during the past years during milk collection which can be an explanation to the increase of the non-compliance rate. For example, we notice nowadays that mothers without supervision tend to use smartphones during milk collection, which is not the case when there is a staff member. Our hypothesis is that when being observed while pumping milk, mothers are more attentive to correct hygiene practices. The non-compliant total flora decreases from 25.4% in 2013 to 7.7% in 2016. This result could be linked to the implementation of portable breast milk pumps in 2013. Before portable pump implementation, only one breast milk collection room with three stationary pumps was available, where mothers expressed milk without any supervision of the hospital staff. Portable pumps enable to express milk in the child's room under supervision of the hospital staff. In the child's room, the nurse can check the mother's habits and give advice, unlike in the collection room with stationary pumps where advice for a better milk collection is given only once. In the Bowen et al. (2017) note to Centers for Disease Control, Cronobacter sakazakii (Gram Negative Bacillus) infection was recorded in a preterm infant fed with expressed maternal milk. The mother had expressed milk with her proper pump and a hospital bedside breast pump. This pathogen was found in the mother's pump which had been cleaned at home and probably contaminated by inadequate cleaning. Best practices to clean pumps are an important factor to avoid contamination. In China, a screening program for breast milk found a 63% rate of contamination (contamination defined by any growth of pathogens including Gram negative bacteria, enterococci or S. aureus, or total bacterial count >10 5 CFU/mL). Avoiding bathing after birth for one month is a Chinese tradition for mothers [START_REF] Ng | Bacteriological screening of expressed breast milk revealed a high rate of bacterial contamination in Chinese women[END_REF]. [START_REF] Picaud | Review concludes that specific recommendations are needed to harmonise the provision of fresh mother's milk to their preterm infants[END_REF] reported that some studies showed that collecting human milk in neonatal units significantly reduces the risk of microbial contamination in comparison to home collection. These studies highlight the importance of personal hygiene before breast milk collection. Education of the mother by a nurse or a neonatologist is important in avoiding contamination.

Our study reported a significant increase of pathogenic bacteria non-compliance rate in 2014, among which are mainly fecal pathogens. This increase may be linked to the increase of activity of the consultation called permanence of access to health care in 2013 due to an increase of human resources. This consultation is dedicated to people in precarious situations (homeless people, without social protection…). We found only two multidrug resistant bacteria; this result is reassuring in the context of the global emergence of multi-drug resistant bacteria. An epidemic Enterobacteriaceae-ESBL breast milk contamination was described in Japan [START_REF] Nakamura | Outbreak of extended-spectrum βlactamase-producing Escherichia coli transmitted through breast milk sharing in a neonatal intensive care unit[END_REF].

The level of S. aureus in mother's milk was 9.2% and seems to be stable in our institution, ranging from 7.9% in 2008-2010, 9.3% in 2011-2013 to 10.5% in 2014-2016. Furthermore, 3.0% was ≥10 4 CFU/mL. In the lactarium study of [START_REF] Dewitte | Contamination of human milk with aerobic flora: Evaluation of losses for a human milk bank[END_REF], 5.9% of the overall breast milk was discarded because of a non-compliance rate due to the presence of S. aureus ≥10 4 CFU/mL. Nowadays, recommendations are not precise for the bacteriological quality evaluation of breast milk destined to direct milk donation. We did not find bacteraemia linked to direct milk donation. This result is reassuring. A recent review [START_REF] Picaud | Review concludes that specific recommendations are needed to harmonise the provision of fresh mother's milk to their preterm infants[END_REF] reported that infants who received direct milk donation were exposed to pathogenic bacteria without systematically developing an infection, whereas there is a documented risk of severe infections in preterm infants with several bacteria (Streptococcus B, S. aureus and enterobacteria). The incidence of bacterial infections transmitted by direct milk donation is difficult to quantify. [START_REF] Picaud | Review concludes that specific recommendations are needed to harmonise the provision of fresh mother's milk to their preterm infants[END_REF] indicated that premature infants fed with direct milk donation or pasteurized donor human milk had fewer infections than those fed with preterm formula. They proposed a strategy to reduce the risk of transmission of pathogenic bacteria to preterm infants born before 28 weeks of GA or with a birthweight below 1000g. They proposed for these preterm infants to perform a microbiological follow-up once a week until corrected GA ≥28 weeks, and to wait for the results before breastfeeding. For infants born after 28 weeks of GA, breastfeeding was performed without waiting for microbiological results, but mothers were monitored.

Contrary to the fact that some countries (South Africa, Sweden, and Switzerland) do not quantify total flora, we will pursue our policy of having no pathogenic bacteria and total flora quantification <10 6 CFU/mL [START_REF] Dewitte | Contamination of human milk with aerobic flora: Evaluation of losses for a human milk bank[END_REF] and we will include the strategy proposed by [START_REF] Picaud | Review concludes that specific recommendations are needed to harmonise the provision of fresh mother's milk to their preterm infants[END_REF] for the Gestational Age of the preterm infants. These criteria guarantee the bacteriological quality of breast milk destined to direct milk donation.

Our study has several limitations. Firstly, milk collection practices were not audited during this period. Secondly, only one sample of the first milk collection was analyzed for compliance rate evaluation, and this sample did not necessarily reflect the bacteriological quality during all the breast feeding period. Thirdly, we cannot exclude that some unknown events could have affect the rate of non-compliance sample. Finally, this is a single center study.

Conclusions

The increase in the overall non-compliance rate of direct milk donation since 2007 should indicate the need to strengthen best practices for mothers, particularly hand hygiene with smartphone use. We are considering setting up direct milk donation only with portable breast pumps in the child's room. Hygiene recommendations by pediatric nurses could lead to better practices.

TABLE 1 :

 1 Description of the type of the non-compliance for the first breast milk samples : Colony Forming Units; MRSA: Methicillin-resistant Staphylococcus aureus; ESBL: Extended-Spectrum Beta-Lactamases. Results are expressed by number and percentage. 17

TABLE 2 :

 2 Comparison of the overall non-compliance, total flora, Staphylococcus aureus and other pathogens presence according to the 3 periods NOTE. n : number of samples, % : percents of samples a: Significant P value between the 2008-2010 period versus 2011-2013 period b: Significant P value between the 2008-2010 period versus 2014-2016 period c: Significant P value between 2011-2013 period versus 2014-2016 period d: Significant P value between the

  Compliance of breast milk samples destined to direct milk donation for a single child FIGURE 2: Evolution of the number of samples analyzed and the proportion of noncompliant samples destined to direct milk donation between 2007 and 2016 FIGURE 3: Evolution of breast milk samples percentage with total flora ≥10 6 CFU/mL, with presence of S. aureus, with presence of pathogenic bacteria and the evolution of the overall non-compliance between 2007 and 2016

	FIGURE 1:
		2008-2010		2011-2013	2014-2016
		n	%	n	%	n	%
	Breast milk samples non compliance
	Overall non compliance	12	9.4	48	23.4 a	75	29.2 b,d
	Total flora≥ 10^6	2	1.6	32	15,6 a	37	14.4 b,d
	Staphylococcus aureus presence	10	7.9	19	9.3	27	10.5
	Pathogenic bacteria presence (without Staphylococcus aureus)	1	0.8	1	0.5	12	4.7 c,d
	Total of samples	127	100	205	100	257	100
	3 periods
		18

Acknowledgments

We thank pediatric nurses who explained breast milk collection to the mothers, the laboratory technicians for the microbiological analysis, Dr Elodie Sellier and Marianne Jeannin for the delivery and birth data in the study hospital, Dr Jacqueline Shum and Dr Philippe Saviuc for their explanation and memory of events, and Alison and William Terreaux for their help to the English translation.

Conflict of Interest:

All authors report no conflicts of interest relevant to this article.


Fabien Pottier

Anne Michelin

Laurianne Robinet

Recovering illegible writings in fire-damaged medieval manuscripts through data treatment of UV-fluorescence photography

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

As time passes, historical documents are exposed to multiple potential sources of alteration (natural ageing, conservation issues, natural disasters, vandalism, reutilization,…) that can have a strong impact on the legibility of their original content. Recovering access to these invaluable accounts of the past is an important aspect of current research in cultural heritage. The use of stateof-the-art technologies offer new access to thought-to-be irremediably lost writings. Spectral reflection imaging (also referred to as multi-or hyperspectral imaging) [START_REF] Easton | Spectral image processing and analysis of the Archimedes Palimpsest[END_REF][START_REF] Snijders | Using hyperspectral imaging to reveal a hidden precolonial Mesoamerican codex[END_REF][START_REF] Pouyet | Revealing the biography of a hidden medieval manuscript using synchrotron and conventional imaging techniques[END_REF], X-ray tomography [START_REF] Bukreeva | Virtual unrolling and deciphering of Herculaneum papyri by X-ray phase-contrast tomography[END_REF][START_REF] Mills | Apocalypto: revealing the unreadable[END_REF][START_REF] Baum | Revealing hidden text in rolled and folded papyri[END_REF][START_REF] Mocella | Revealing letters in rolled Herculaneum papyri by X-ray phase-contrast imaging[END_REF] or XRF mapping [START_REF] Pouyet | Revealing the biography of a hidden medieval manuscript using synchrotron and conventional imaging techniques[END_REF][START_REF] Duivenvoorden | Hidden library: Visualizing fragments of medieval manuscripts in early-modern bookbindings with mobile macro-XRF scanner[END_REF][START_REF] Albertin | X-ray spectrometry and imaging for ancient administrative handwritten documents[END_REF] can provide a contrast between the writings and their support based on the imaging of chemical or physical properties (Visible to NIR reflection, X-ray absorption and X-ray fluorescence, respectively). Despite the great technological performances added to meaningful historical (re-)discoveries, these imaging techniques require substantial acquisition and processing time, high technical skills and expensive instrumentation. As a result, they are generally applied to a limited number of rare and/or precious documents, amongst the large number of historical records that could benefit from such recovery tool in library and archive collections.

Hence, there is a need for a fast, low-cost and simple methodology that could be applied on a large scale, in the same way libraries and archival documents are currently being digitized [START_REF] Watteeuw | What do we lose when we lose a library ?[END_REF]. The primary objective of digitization is to give access to rare, fragile or endangered historical documents, via the accurate recording of the documents appearance, in particular colors. Unfortunately, if altered, the document being recorded as such, will not be exploitable for philology and art history studies.

The prestigious medieval manuscripts collection of the Chartres library in France is a good illustration of this situation [START_REF] Poirel | Rediscovering the Manuscripts from Chartres[END_REF]. Chartres was well known for its famous cathedral school, among the most important occidental intellectual center during the 11 th and 12 th centuries. On the 26 th of May 1944, during an allied bombing of the city, a fire irremediably destroys almost half of the collection. Of the 518 original medieval manuscripts, at least 215 survived the fire but remained in very variable states, from almost intact to entirely calcined. The cumulated actions of fire, water (to extinguish the fire) and the subsequent biological infestation (worms) resulted in different types and levels of alteration. During restoration campaigns, the distorted and agglomerated parchment leaves were separated and flattened. Considering the fragility of the fragments, a digitization campaign was started in 2006 by the Image department of the Institut de Recherche et Histoire des Textes (IRHT-CNRS) so the documents could be available again for research [12]. However, in some manuscripts the alteration caused the writings to become partly or totally unreadable (Figure 1), preventing their study. For that reason, historians working on these documents raised the need for a simple imaging solution that would improve the readability of the manuscripts and could be implemented in the digitization process.

Figure 1. Examples of degraded manuscript fragments from Chartres; from left to right, fragments identification numbers L306-3, L76-2, L28-13 (top), L326-3, MS1032-2, MS1027-68 and L182-1 (bottom).

RESEARCH AIM

The great sensitivity of modern camera sensors added to the development of simple image post-treatments open a new range of possibilities to recover degraded writings. In standard digital photographs, color contrast results from the diverging reflection properties of the surface of the document in the visible spectral range. When using UV radiation as a light source on the other hand, the camera sensor does not detect the UV reflected light but instead the visible light resulting from the fluorescence emitted by the parchment. UV-fluorescence photography has been used over a century for the examination of historical documents or works of art to reveal additional information, and the fluorescence colors have sometimes provided clues regarding the chemical nature of the emitting materials [START_REF] Baldia | Photographic methods to detect colourants in archaeological textiles[END_REF][START_REF] Montani | Enhancement of writings on a damaged medieval manuscript using ultraviolet imaging[END_REF][START_REF] Cosentino | Practical notes on ultraviolet technical photography for art examination[END_REF][START_REF] Rorimer | Ultra-violet rays and their use in the examination of works of art, The Metropolitan Museum of Art[END_REF]. However, although accurate color restitution is a key aspect to digital archiving, it is only one way of visualizing photographic data, and other contrast information can be revealed with specific post-treatment tools. As for multispectral images data treatments, color photographs datasets can be explored to enhance contrast and reveal unexpected contents [START_REF] Easton | Spectral image processing and analysis of the Archimedes Palimpsest[END_REF][START_REF] Harman | Using decorrelation stretch to enhance rock art images[END_REF][START_REF] Boussellaa | A Concept for the Separation of Foreground / Background in Arabic Historical Manuscripts using Hybrid Methods[END_REF].

In the present paper, a simple methodology using two complementary sources of contrast enhancement was implemented to recover the writings in most of the Chartres manuscript fragments examined. The different approaches developed are illustrated based on examples displaying different alteration types and level of complexity.

EXPERIMENTAL

Photographs were taken with a Nikon D800 digital camera equipped with a Nikon 60 mm f/2.8G ED AF-S Micro Nikkor lens, mounted on a copy stand. Two RB-200 flash lights were used to record the reflection properties of the parchments (standard photography), while a Vilber Lourmat UV-A VL-215L lamp (365 nm) was used to record their UV fluorescence. Because the intensity of the fluorescence emission is weak, all photographs were shot in a dark room, on a black fabric, paying attention to get rid of any stray light (daylight, computer screen, LED indicators) or any fluorescent materials (e.g. optical brighteners emitting a strong blue light in modern papers). The aperture was set at f/11. Since all parchments present different emission properties, the exposure time was automatically adjusted according to the fluorescence intensities (generally several seconds). The data were recorded as raw files (.neff) in order to avoid any data compression (and loss of useful information) before image treatment. Photographs were color-calibrated with the AIC-PhD target (see the center of Figure 1). Open-source software ImageJ was used for all the data treatments, updated with different plugins: Color Inspector 3D (3D visualization of the chromatic distribution in a color space of interest), MSA_514 (Principal Component Analysis (PCA) of a color image), Color Transformer (L*a*b* to HSL color space conversion) and DStretch (decorrelation stretch contrast enhancement).

A corpus of manuscript fragments was selected in order to cover the diversity of alteration encountered in the collection. Four main types of alterations were identified, sometimes present simultaneously on certain fragments: darkened (calcined) substrate, transparent (gelatinized) substrate, faded (washed-out) writings and superimposition of matter on the writings. In total, 132 manuscripts fragments were photographed (back and front) under standard (visible) and UV-A illumination. Representative examples are shown and discussed in the results.

RESULTS AND DISCUSSION

The efficiency of UV fluorescence photography was rapidly evidenced for a large number of Chartres manuscript fragments. In the example shown in Figure 2 (top), the action of fire considerably darkened the parchment substrate, preventing any clear reading of the contents under normal lighting conditions. Additionally, the writing from the front and the back of the fragment are both seen in the photographs (see the word written in red), due to transparency of the substrate. The two problems are solved simultaneously by the UV-fluorescence (bottom of Figure 2). Ultraviolet radiations provide a better contrast between the ink and the substrate and the weak penetration of the radiation allows a clear separation of the writing between the two sides of the page.

Figure 2. Visible reflection and UV fluorescence photographs of the two sides of fragment MS1032-1

This simple and direct approach to recover the text works well when the parchment support is altered (calcined and/or transparent), however it is not sufficient when the writings have been washed-out. In fragment L326-1, for example (Figure 3, R), the ink was erased to such an extent that it is difficult to know if a text was originally present. The UV-fluorescence photograph reveals lines of text, but contrast is so subtle that reading remains impossible (Figure 3, UV-F). In this type of alteration, several digital enhancement techniques can be applied to increase the reading contrast of the photograph.

The images shown in Figure 1 to Figure 3 were color calibrated so that the fragments appear as a human eye would perceive them when looking at them under visible or UV light. However, more information can be extracted from these images if this color rendering is abandoned. The color described in each pixel of a digital image is coded with the three color channels Red, Green and Blue (RGB), mixed in different proportions to create all visible colors. Hence, a color photograph can be considered as a stack of three photographs (left of Figure 4). Temporarily putting aside the spatial repartition of the colors in a photograph, one can study the distribution of its chromatic cloud (total hue variation) in a three dimensional space, where each RGB channel is associated with a dimension (right of Figure 4). Each color present in the photograph is plotted in this volume, and the chromatic variations are displayed as clouds with progressive tones of colors rather than discrete color values.

Figure 3. Visible reflection and UV fluorescence photographs (actual colors) of fragment L326-1 Figure 4. Schematic representation of a digital photograph content as a superimposition of R, G and B color channels (left), and color distribution in the RGB chromatic space (Color Inspector 3D plugin)(right)

In order to solve the lack of writing legibility in a manuscript, the study of the photograph chromatic dispersion in the RGB space helps to visualize which color dimension is the most relevant to maximize the text contrast. For the UV-fluorescence photograph of fragment L326-1, three clouds are observed in the RGB chromatic space (right of Figure 4), corresponding to the dark colors of the background, and the light blues and dark blues of the fluorescence. The blue (B) channel is the dimension along which the colors associated with the text are the most contrasted, i.e. the axis along which there is the largest text/substrate value gap. Therefore, it is relevant to visualize this channel by itself and ignore the two others. A grey level representation of the B values of the fragment is then obtained. After contrast optimization, by adjusting the maximum and minimum values of the histogram, writings are revealed (Figure 5).

Figure 5. Blue channel (B) after contrast optimization of the UV fluorescence photograph of fragment L326-1

Although great improvement was obtained, this result can still be perfected since the text in the entire fragment is not yet readable. In order to ensure that all the potential contrast information contained in the photograph has been explored, a statistical analysis (Principal Component Analysis (PCA)) can be applied. This data treatment relies on the study of the 3D distribution of the chromatic cloud and calculates three composite dimensions (orthogonal to each other). Each new dimension is composed of a combination of the former R, G and B dimensions (in different proportions) and represents the color information in a re-organized fashion. The aim of this manipulation is to project the chromatic data along new axes that offer different contrast modes (Figure 6). Three new images of the fragment (one for each component) are obtained providing three new views of the document. In fragment L326-1, the third principal component concentrates the text/substrate contrast information giving the best reading conditions (Figure 7).

Figure 6. Color data manipulations involved in photograph contrast maximization Figure 7. Third principal component (PC3) of the UV fluorescence photograph of fragment L326-1

Principal Component Analysis is a very powerful tool to explore the contrast potentialities hidden in a color digital photograph, and ensures that all relevant information contained in an image has been considered [START_REF] Easton | Spectral image processing and analysis of the Archimedes Palimpsest[END_REF]. Calculations take few seconds per image (of 36 MPx) to evaluate and apply the RGB to PC1,PC2,PC3 transformation matrix. This calculation must be performed for each photograph (or detail of interest) since the PC1,PC2,PC3 system is specific for each chromatic distribution. Although this calculation time appears negligible, it may become substantial if the treatment has to be applied to a large number of photographs (as for the thousands of fragments from Chartres).

An alternative to get a similar rendering with a shorter calculation time (avoiding statistical analysis) is to convert the data to a different standard color space. In this operation the conversion matrix is always the same and therefore independent of the image content. Good results are obtained using the HSL color space relying on three different contrast modes Hue, Saturation, Lightness (see the right bottom of Figure 6), and the best reading conditions are obtained by mapping the hue (H) values in grey levels. As another demonstration, the methodology was applied to fragment L306-1, where almost no text appeared visible in the realistic color renderings (top of Figure 8). The third principal component from the PCA treatment of the UV photograph reveals lines of writings, and a similar contrast is obtained with the (faster) conversion to the HSL (H) color space. This similarity in the results of the two treatments was observed for all fragments studied.

Figure 8. Visible reflection and UV fluorescence photographs (actual colors, PC3 and H values) of fragment L306-1

This observation helps understand the exact origin of the text/support contrast, not explicitly given by the PCA. The contrast in hue (H) implies that the area where the writings used to be generate a fluorescence with a slightly different shade than the fluorescence emitted by the unwritten parchment substrate. These different emission properties may indicate a structural modification or the presence of different fluorophores. Lightness (L), on the other hand does not provide any contrast (image not shown), because text and parchment emit at exactly the same intensity level. The human brain cannot perceive low hue contrast, this is the reason why the text is so hard to read in the color photograph.

Despite the improvement offered by these contrast treatments, in some cases the image quality does not allow a proper reading of the text. In the example Figure 9, the large size of the fragment L451-1 necessitated to enlarge the field of view, which considerably lowered the spatial resolution of the images. Small details (specifically the writings of interest) are consequently very hard to discern, even after UV-fluorescence data treatments (see UV-F (PC3) (detail), Figure 9). To overcome this problem, macrophotography should be used to focus on details and improve the image spatial resolution. The image treatment is then applied to the macrophotograph and a much better readability is obtained (compare the results of the PCAs, Figure 9).

Figure 9. Full scale and macro visible reflection and UV fluorescence photographs (actual colors and Third principal component) of fragment L451-1 (details are extracted from the photographs of the complete fragment)

Another enhancement treatment worth mentioning, is implemented in the very handy DStretch plugin developed by John Harman [START_REF] Harman | Using decorrelation stretch to enhance rock art images[END_REF] and based on a decorrelation stretch algorithm [START_REF] Gillespie | Color enhancement of highly correlated images. I. Decorrelation and HSI contrast stretches[END_REF][START_REF] Alley | Algorithm Theoretical Basis Document for Decorrelation Stretch[END_REF]. This plugin was designed for rock art color enhancement of standard (reflection) photographs (see [START_REF] Le Quellec | Digital image enhancement with DStretch : Is complexity always necessary for efficiency?[END_REF][START_REF] Caldwell | An historic sign, possible Mesolithic menhir, DStretch, and problems in dating rock art to the Sauveterrian in the Massif de Fontainebleau[END_REF][START_REF] Defrasne | Digital image enhancement for recording rupestrian engravings: Applications to an alpine rockshelter[END_REF][START_REF] Fernández-Lozano | 3D digital documentation and image enhancement integration into schematic rock art analysis and preservation: The Castrocontrigo Neolithic rock art (NW Spain)[END_REF] for example), but has occasionally been applied to other materials, such as an Egyptian wall painting [START_REF] Evans | DStretch and Egyptian tomb paintings : A case study from Beni Hassan[END_REF] and a Mesoamerican manuscript [START_REF] Brownstone | The Lienzo of Tlapiltepec : a painted history from the Northern Mixteca[END_REF]. We show that it can be equally useful for the enhancement of medieval writings (or any other graphical contents) in UV fluorescence color photographs (Figure 10). Though the DStretch plugin does not seem to offer better results than the PCA or HSL conversion (compare Figure 10 to Figure 9, Figure 8 and Figure 7), its user-friendly interface greatly facilitates the color data exploration for non-specialists.

Figure 10. Contrast enhancement of UV fluorescence photographs of fragments L326-1 (left), L306-1 (top right) and L45-1 (bottom right) with the DStretch plugin in ImageJ.

From a practical point of view, the presented methodology only requires a digital camera, a UV-A light source and rely on open source software and plugins for the image treatments, therefore the cost investment is limited. To assess the possibility of using the methodology on a large scale, a test was carried as part of the digitization process with the image team of the IRHT at the library in Chartres. This experiment showed that it only takes half a day and two persons to digitize 64 fragments (back and front), in standard and UV-fluorescence photography (so about 2 minutes per fragment, which roughly doubles the time necessary for a standard digitization). The methodology could probably be further optimized using an automated system to collect photographs with both illuminations with only one person. Lastly, the ease of use of the different contrast enhancement tools was tested, validated by historians, and the deteriorated fragments already revealed relevant new historical data [START_REF] Fronska | Rescapé du feu et de l'eau. L'histoire partiellement révélée du Volumen parvum chartrain, ms. 273[END_REF][START_REF] Chastang | Lectures d'un obituaire Chartrain du 14ème siècle[END_REF][START_REF] Bretthauer | Les registres capitulaires de Chartres, XIIIe-XIVe siècle : essai de reconstitution[END_REF].

CONCLUSION

UV fluorescence photography proved to be a powerful tool to (at least partially) reveal initially illegible content in most of the manuscripts fragments from Chartres that were studied. In the cases of darkened and/or transparent substrate, the accurate color restitution of the UV fluorescence was generally sufficient to reveal the text, whilst an extra step of color contrast optimization was necessary when the inks were washed out. Unfortunately, some fragments are in such an advanced degradation state that the presented methodology did not provide much legibility improvement (for example fragment L326-3, at the bottom left of Figure 1). Neither would it help when matter is superimposed on top of the writings (eg. fibers from blotting papers used during the emergency conservation treatments (not shown)). In these cases, it seems that more sophisticated imaging instrumentations, such as X-Ray based techniques, will have to be explored.

The ever improving capabilities of imaging sensors in modern digital cameras offer new possibilities for the study of historical documents. UV-fluorescence generates useful complementary visualization mode to standard visible reflection photographs. The additional color contrast optimization through PCA, color space conversion or decorrelation stretch helps to reveal hidden contents and ensures that all relevant information contained in a photograph is explored. Not only does digital photography give great results in terms of contrast enhancement, but its implementation is fast, simple, inexpensive and realistically applicable on a large scale for collections. Moreover, none of the acquisition or image treatment steps require specific scientific or technical skills, so this approach can be used by non-specialists.

Regarding future research, one should note that the presented contrast optimization procedure through color space transformation is applicable to any other types of digital color photography (reflection, transmission, IRFC [START_REF] Cosentino | Infrared Technical Photography for Art[END_REF],..) of any degraded/faded polychromatic surfaces (rock art, manuscripts, but also drawings, paintings, ceramics, textiles, analog photographs…). Therefore, this methodology could potentially be of interest in these various fields.

AKNOWLEDGEMENT

The authors wish to thank Catherine Merlin and Michèle Neveu of the Médiathèque l'Apostrophe in Chartres, who permitted access to the collection and greatly facilitated the work. We are also grateful to Claudia Rabel and Dominique Poirel from the Institut de Rercherche et d'Histoire des Textes (IRHT-CNRS) for their expertise as medieval philologists, and to Gilles Kagan from the IRHT-CNRS for sharing his experience in medieval manuscript digitization. This project was funded with a post-doctoral fellowship of the Fondation des Sciences du Patrimoine/LabEx PATRIMA (ANR-10-LABX-0094-01).