D R Ajoy

Kumar Biswas

Bethune

Arnab Biswas

The Choice of Bins of a Histogram: A Kolmogorov Distance-based Approach

Keywords: Histogram, Empirical distribution function, Empirical probability, Kolmogorov distance

The histogram is widely used for visualizing continuous data and calculating empirical probabilities, but it is usually not clear how to choose the number and size of the bins. We propose a new histogram method that optimally deals with the two main tasks of the histogram: detecting features such as mode, increase, spike, gap, outlier and discrete component embedded in the empirical distribution and providing empirical probabilities. We follow Kolmogorov's approach for measuring distance between a histogram distribution function (hdf) and the empirical distribution function (edf), and select a histogram to minimize the distance subject to an upper bound for the number of bins. The idea is that the edf tightly holds all the information in the data and a histogram will serve the main tasks well if the distance between hdf and edf is small. Our comparison study with real-life data demonstrates that the proposed method performs uniformly well in detecting data-features and approximating empirical probabilities. Moreover, the proposed method is appropriate for continuous data with or without discrete component. We provide Rcodes for computing the proposed histogram in the Appendix.

Introduction

The histogram is a classical, simple, widely used diagram for exploring the distribution of univariate, continuous data. In practice, histograms with equal-width bins are common; histograms with equal-area bins are also used. Recently, histograms with bins of variable width and count are proposed in the literature. An equal-width histogram consists of bins each of equal width, and an equal-area histogram consists of bins each containing (as nearly as possible) the same number of data-values. In the case of equal bin-width, popular examples of rules for the number of bins are that proposed by [START_REF] Sturges | The choice of a class interval[END_REF], which is still the default rule in R, [START_REF] Scott | On optimal and data-based histograms[END_REF] and [START_REF] Taylor | Akaike's information criterion and the histogram[END_REF]. Most of these rules are derived by considering the histogram as an estimator of a smooth density underlying the data and choosing the number of bins to minimize an asymptotic risk in estimating the density. In applications, however, these rules are more often used to construct histograms for inspecting data for distribution features. Although, relying on asymptotic risk may lead to inappropriate recommendations for the number of bins when the histogram is used as a dataexploratory device [START_REF] Denby | Variations on the histogram[END_REF]. [START_REF] Denby | Variations on the histogram[END_REF] pointed out the complementary strengths and weaknesses of the equal-width and equal-area histogram approaches, when the histogram is used as a dataexploratory tool. They advocated a compromise of these two approaches and proposed to cut the edf diagonally by parallel lines and select bins corresponding to the cuts. This approach gives bins of variable width and count. They coined the term diagonally-cut histogram. Authors such as Fushing and [START_REF] Roy | Complexity of possibly gapped histogram and analysis of histogram[END_REF] and [START_REF] Li | The essential histogram[END_REF] also focused on the edf and proposed histograms with bins of variable width and count. Fushing and [START_REF] Roy | Complexity of possibly gapped histogram and analysis of histogram[END_REF] aimed to select a serial composition of linear-segments and gaps well approximating the edf with a balance between number-of-bins and error-in-approximation and choosing the bins corresponding to the linear-segments. They assumed that a set of data-values in a bin [a,b] will be from Uniform(a,b) distribution if its decoding error sum of squares is about (ab) 2 /3, but they did not mentioned how to test the assumption in practice. [START_REF] Li | The essential histogram[END_REF] tried to derive a confidence set of hdf such that each hdf in the confidence set estimates the true probabilities of different intervals via areas in an asymptotically optimal way and then selecting one from the confidence set so that the corresponding histogram has the fewest bins. They called it essential histogram. They adopted certain likelihood ratio tests on a judiciously chosen set of intervals and then inverted the family of tests to have the confidence set. Their histogram method ignores the gap (if any) embedded in the edf, while some authors (e.g., Mosteller et al.,1983, p. 4;[START_REF] Roy | Complexity of possibly gapped histogram and analysis of histogram[END_REF] demonstrated that a gap is an important piece of information in exploring the data.

The present paper proposes a new method for constructing a histogram that is motivated by the two main tasks of the histogram (see [START_REF] Li | The essential histogram[END_REF]Freedman et al., Ch. 3, 2007): to give a display of the data that is simple but informative, i.e., having a few bins, but still showing important features of the data such as mode and discrete component, and to provide empirical probabilities of different subintervals with high precision. And the idea: the edf holds all the information in the data but so tightly that it needs to be extracted, and a histogram extracts more information and better serves its main tasks as the distance between hdf and edf becomes smaller. We follow Kolmogorov's approach for measuring the distance, and select bins to reduce the distance subject to an upper bound for the number of bins. To display the discrete component and the gap, if present in the data, we are to operationalize them a priori based on the data.

We temporarily remove the discrete component (if present) of the data and thus get the continuous part of the data. We judiciously choose some real numbers for capturing gaps. We consider the real numbers and the smallest and the largest values in the continuous data-part as the initial set of breakpoints. To obtain the final set of breakpoints, we extend the initial set by adding a few breakpoints one-by-one so as to reduce the Kolmogorov distance between hdf and edf smaller than a preset value subject to a specified upper bound for the number of bins. We construct histogram-bars using the final set of breakpoints and the continuous part of the dataset. Finally, we put vertical arrows to represent relative frequencies of the values constituting the discrete component. As the proposed histogram is largely based on Kolmogorov metric, we call it Kolmogorov histogram, in short KHist. The proposed method is fairly general, as we make no assumption regarding the underlying data generating mechanism. In particular, it is applicable to data from a mixed-type distribution having both continuous and discrete components, and mixedtype distributions are common in real life [START_REF] Unwin | Graphical data analysis with R[END_REF][START_REF] Weld | Mixed-type distribution plot[END_REF]. To note that the proposed method approximates the edf of the continuous part of the data by linear segments and does not put any breakpoint in zones where the edf is close to being linear. With data examples, we show that the proposed histogram serves the two main tasks well as compered to some other methods.

This article is distinct from the earlier attempts in constructing the histogram with bins of variable width and count such as [START_REF] Denby | Variations on the histogram[END_REF]Mallows (2009), Fushing &[START_REF] Roy | Complexity of possibly gapped histogram and analysis of histogram[END_REF] and [START_REF] Li | The essential histogram[END_REF]. [START_REF] Denby | Variations on the histogram[END_REF] diagonally cut the edf into linear segments by parallel lines. Fushing & [START_REF] Roy | Complexity of possibly gapped histogram and analysis of histogram[END_REF] partitioned the edf into linear-parts and gaps based on a criterion of decoding error sum of squares from the perspective of data compression via uniformity. [START_REF] Li | The essential histogram[END_REF] divided the edf into linear segments by inverting a family of multi-scale likelihood ratio tests. While the proposed method partitions the edf into linear segments based on Kolmogorov metric. Moreover, only the proposed method regards mixed-type data having continuous and discrete components. Thus the proposed approach is largely distinct from the above three approaches.

The Kolmogorov Distance in Data Environment

Let x be a univariate dataset of size n and xc and xd be the continuous and the discrete parts of x, respectively. The size of xc is at most n. Here we describe the empirical distribution function (edf), a histogram distribution function (hdf), and the Kolmogorov distance (dK) between these distribution functions.

The edf of x is defined as edf(x)=n( x)/n, n( x) being the number data-values in x that are less than or equal to x. For the dataset {1, 2.4, 5.1, 8.4}, edf( 5

The Proposed Histogram Method

For the given dataset x={xi,i=1,2,…,n}, let x(1)  x(2)  x(m) be the unique data-values. The edf of x represents all the information in the data and can be converted easily into a histogram with m breakpoints x(1), x(2),…, x(m). The resulting histogram with m breakpoints provides empirical probabilities via areas without any error and thus serves the second task totally, but it is bad for identifying the key features of the data such as mode and gap, as it is much too rough, and thus fails to serve the first task. So the problem is: determine a histogram that approximates the empirical probabilities adequately well and is simple for visualizing the key features of the data. The premise in this paper is that it is generally possible to wisely select a small proportion of the m breakpoints, but still have a histogram that approximates the empirical probabilities with small errors and detects the key features of the data well. This motivates us to propose a new histogram method based on Kolmogorov distance between the edf and a hdf with an upper bound for the number of bins.

The algorithm for the new histogram method consists of the following steps:

Step 1: Identify the discrete component xd (if any) of the dataset x. Consider a data value with frequency dcdpn or more as a member of the set xd, dcdp being the discrete component defining percentage of n. We set dcdp=7.5 as the default value, which considers a data-value x with frequency 0.075n or more as a member of xd.

Step We set dubKd = 0.5/n and dubnbins = 1.25nbinsSturges as the default values, nbinsSturges being the number of bins given by the Sturges rule [START_REF] Sturges | The choice of a class interval[END_REF]. The default value 0.5/n of dubKd is chosen from the fact that for n36, the critical points of Kolmogorov-Smirnov test for goodness of fit is of the form z/n with z decreases as the level of significance  increases [START_REF] Massey | The Kolmogorov-Smirnov Test for goodness of fit[END_REF].

Step 6: Repeat the Step 5 until a set of breakpoints b is obtained satisfying dK(b)  dubKd or length(b)dubnbins+1.

It is the final set of breakpoints for xc.

Step 7: With the final set of breakpoints, construct a (relative frequency) density-based histogram of xc; it is a histogram of total area unity. Add vertical arrows at the values in xd mentioning their relative frequencies (in percentage). It is the final histogram for the whole dataset x. This histogram is optimal with a trade-off between visual-simplicity and error-in-approximating empirical probabilities.

The parameter dubKd of the proposed histogram ranges from 0 to 1. One is set dubKd to 0.1/n or even smaller if the aim is to capture the empirical probabilities with high accuracy; a smaller value of dubKd results more bins waning visual simplicity.

Comparison Study with Data Examples

We consider four datasets that reflect a range of variations on the histogram. For comparison, we include equal bin-width histogram (ewHist), equal bin-area histogram (eaHist), diagonally cut histogram (dHist) proposed by [START_REF] Denby | Variations on the histogram[END_REF] and essential histogram (essHist) proposed by [START_REF] Li | The essential histogram[END_REF]. We compute the ewHist using the built-in R function hist and the dHist using the function dhist collected from the supplementary material of the article of [START_REF] Denby | Variations on the histogram[END_REF]. We compute the essHist using the function essHistogram in the R package essHist, available on CRAN. To note that we adjust the tuning parameters of KHist (the proposed histogram), dHist and essHist so that all the histograms have the same number of bins as that of ewHist given by the R function hist. We believe that it is better to consider the same number of bins (as far as possible) in comparing different histogram approaches.

To compare the histogram methods in approximating empirical probabilities of subintervals (,x], we partition the range (x(1),x(m)) of the dataset x into (n1001) equal-width subintervals by n100 points ui=x(1)+iw, i=0,1,2,…, (n1001), w (x(m)x(1))/(n1001) and summarize the errors ei=hdf(ui,b)edf(ui) using mean and standard deviation of the absolute errors |ei|. Dataset 1: pH data. All the histograms in Figure 1 indicate that the data-distribution is J-shaped and negatively skew. The KHist shows that there is a gap and a pit in the distribution. The ewHist captures only a part of the gap but fails to capture the pit. The eaHist captures the pit but fails to identify the gap. The dHist captures the gap but fails to detect the pit. In sharp contrast, the essHist fails to identify both the gap and the pit. Thus the KHist is the best and the essHist is the worse in detecting important features of the data-distribution. Further, from Table 1 we may conclude that KHist is the best and eaHist is the worse in providing empirical probabilities of subintervals (¸x], x being real numbers. In sum we may conclude that the KHist is the best for pH data. To note that for this dataset, the essHist allows at the most five bins (taking alpha=1). 2016), Data from: River banks and channels as hotspots of soil pollution after large-scale remediation of a river basin, Dryad Repository, (https://doi.org/10.5061/dryad.f74fs) Dataset 2. Duration data. Duration time in minutes for the Geyser dataset of size 299 (Azzalini & Broman, 1990;R package MASS). This dataset is used by [START_REF] Li | The essential histogram[END_REF]. Figure 2 indicates that only the KHist captures the discrete component consisting of the values 2 and 4 with 8% and 18% data values, two modes, a gap and an outlying observation in the data, and thus is the best in identifying the key features in the data-distribution. To explain the discrete points 2 and 4 in the dataset, it is to be noted that some nocturnal duration-times were considered as 2 or 4 minutes, having originally been recorded as 'short' or 'long'. Further, from Table 2 we see that KHist is the best and eaHist is the worst in approximating empirical probabilities for subintervals (¸x], the differences being substantial. For this data, we may conclude that the KHist is the overall best. Dataset 3. Unemployment-rate-2020 data. This is a dataset of size 3192. All the histograms in Figure 3 indicate that the data distribution is bell shaped and unimodal. The KHist shows the mode more precisely as compared to the essHist. From Table 3, we see that essHist is the best, KHist is the second best and ewHist is the third best in approximating empirical probabilities. For this dataset, in sum, we may conclude that KHist and essHist are jointly best. To note that for this dataset, the essHist allows at the most eleven bins (taking alpha=1).

Discussion

In this article, the aim has been to construct a new histogram that have a few bins, but still showing mode, gap and other key features of the data distribution, and providing empirical probabilities with high accuracy. The search has met with some success. This study proposed a histogram method that selects bins to minimize Kolmogorov distance between histogram and empirical distribution functions with a check on the number of bins. Our comparison study illustrated that only the proposed method is capable in displaying discrete component, spike, mode, gap, pit, increase and outlier embedded in the empirical distribution. And, in providing empirical probabilities, the proposed method is far better than the traditional equal bin-width method and almost equal to the recent essential-histogram method. In summary, the proposed method performs uniformly well, relative to the other methods, in doing both the tasks: detecting data features and providing empirical probabilities. So, the proposed method should be considered worthy on its own merits and not as an alternative to the other methods.

We leave as a research project the extension the proposed histogram method to estimate probability density and probability mass components of a mixed-type population distribution.

  )= 2/4. Let a total-area-unity histogram of xc, with (relative frequency) densities as the height of the bars, has been constructed using a given ordered-set of breakpoints b. Then the histogram distribution function hdfc(x,b) of xc is defined as the area under the bars in the interval ( ,x]. And the histogram distribution function hdf(x,b) of x is defined as hdfc(x,b) plus total of the relative frequencies of values in ( ,x] xd. To elaborate, let edfc(x,b) be the edf of xc, edfc(2.1,b) be 0.3 and the height of the bar on the bin (2.1,3.2] be 0.1. Then hdfc(2.4,b) is equal to {0.3+0.1(2.42.1)}; it is the value of the relative cumulative frequency at x= 2.4 given by the total-area-unity histogram of xc. To note that hdfc(2.4,b) is equal to the y-value at x=2.4 given by the straight line passing through the points (2.1,edfc(2.1,b)) and (3.2,edfc(3.2,b)). An hdfc(x,b) approximates edfc(x) by piecewise linear segments. Further, let there be two discrete values 1.5 and 2.0 lying in ( ,2.4] ] xd with relative frequencies 0.08 and 0.1, respectively. Then hdf(2.4,b)=hdfc(2.4,b)+0.08+0.1. The Kolmogorov distance dK(F,G) between two theoretical distribution functions F(x) and G(x) is defined as dK(F,G)=sup{|F(x) G(x)|, xR}, R being the set of real numbers. We extend this definition to data environment. For a given histogram distribution function hdf(x,b) of the given dataset x, we consider dK(b)=max{|hdf(x,b) edf(x)|, xx} as the Kolmogorov distance between edf(x) and hdf(x,b).

  2: For the time being, remove xd from x and obtain the continuous component xc= x xd. Step 3: Identify gaps in xc (if any). Consider an interval between two adjacent values x1, x2 in the ordered xc as a gap if |x1x2 |gdmh, h being the common width of the bins given by Sturges (1926) rule for xc and gdm being the gap defining multiplier of h. To capture the gaps, add real numbers y to xc. For example, to capture the gap between x1 and x2, x1< x2, add real numbers x1+gcmh and x2gcmhto xc, gcm being the gap capturing multiplier of h. We set gcm=0.25 as the default value. Step 4: Consider b = {min(xc), max(xc), y} as the initial set of breakpoints. Step 5: Construct a passing histogram of xc using the breakpoints b and obtain the corresponding histogram distribution function hdfc(x,b). Also obtain the empirical distribution function edfc(x) of xc. Calculate the Kolmogorov distance between hdfc(x,b) andedfc(x), dK(b) =max{|hdfc(x,b)edfc(x)|: xxc}. If dK(b)  dubKd or length(b) dubnbins+1, stop and consider the b as the final set of breakpoints; dubKd being the desirable upper bound of the Kolmogorov distance and dubnbins being the desirable upper bound for the number of bins. Else, identify a single data value xxc at which |hdfc(x,b)edfc(x)| attains its maximum. Consider this x as a new breakpoint and thus obtain an improved set of breakpoints b={b,x}.

Figure 1 .

 1 Figure 1. The empirical distribution function (edf) and the five histograms for the pH dataset of size 60; KHist, ewHist, eaHist, dHist and essHist are Kolmogorov histogram, equal width histogram, equal area histogram, diagonally cut histogram and essential histogram, respectively.

Figure 2 .

 2 Figure 2. The empirical distribution function (edf) and the five histograms of the duration dataset of size 299; KHist, ewHist, eaHist, dHist and essHist are as in Figure 1

Figure 3 .

 3 Figure3. Unemployment-rate-2020 dataset. The empirical distribution function (edf) and the five histograms; KHist, ewHist, eaHist, dHist and essHist are as in Figure1

  M[,3] <-cumsum(M[,2]) dcinxv <-which(M[,2]>= n*dcdp/100) ndcs <-length(dcinxv) dcvv <-M[,1][dcinxv] dcfv <-M[,2][dcinxv] dat_ndc <-dat[! dat %in% dcvv] n1=length(dat_ndc) t1 <-nclass.Sturges(dat_ndc) tv1 <-range(udat) h <-(tv1[2]-tv1[1])/t1 diff <-abs(udat[-ludat]-udat[-1]) tv21 <-which(diff >= gdm*h) tv22 <-tv21+1 tv31 <-udat[tv21]+gcm*h; tv32 <-udat[tv22]-gcm*h breaks.gaps <-unique(c(tv31,tv32)) bks <-unique(sort(c(breaks.gaps,range(dat_ndc)))) udat.ext <-unique(sort(c(udat,breaks.gaps))) #ext=extendex unique data values ludat.ext <-length(udat.ext) A=matrix(0,nrow=ludat.ext,ncol=8) A[,1]=udat.ext A[,2] <-sapply(A[,1], f,dat_ndc) A[,3] <-cumsum(A[,2]) t=length(bks)-1 for(i in 1:t){#i=1;j=1 t1 <-which(A[,1]==bks[i]) t2 <-which(A[,1]==bks[i+1]) slope <-(A[t2,3]-A[t1,3])/(bks[i+1]-bks[i]) for(j in 1:ludat.ext){ if(bks[i]<=A[j,1] & A[j,1]<=bks[i+1]){ A[j,4] <-A[t1,3]+slope*(A[j,1]-bks[i]) } } } tv <-which(A[,1] %in% bks) bks.idx =sort(tv) repeat{ A[,5] = abs(A[,4]-A[,3]) MaxAbsError_cf <-max(A[,5]) t <-max(which(A[,5]==MaxAbsError_cf)) bksNew = udat.ext[t] bks = unique(sort(c(bks,bksNew))) bks.idx =unique(sort(c(bks.idx,t))) idx.3 = which(bks == bksNew) tv2=c(idx.3-1,idx.3,idx.3+1) bks.3 <-bks[tv2] for(i in 1:2){ t1 <-which(A[,1]==bks.3[i]) t2 <-which(A[,1]==bks.3[i+1]) slope <-(A[t2,3]-A[t1,3])/(bks.3[i+1]-bks.3[i]) for(j in 1:ludat.ext){ if(bks.3[i]<=A[j,1] & A[j,1]<=bks.3[i+1]){

Table 1 :

 1 Mean and standard deviation of absolute errors in approximating empirical probabilities of subintervals(, x] for the pH dataset of size 60

	Sl. No. Method	No. of	Mean of	Standard deviation
			bins	absolute errors	of absolute errors
	1	KHist	6	0.0144153	0.01650711
	2	ewHist	6	0.01726549	0.02629165
	3	eaHist	6	0.02865438	0.02337923
	4	dHist	6	0.01658409	0.01769767
	5	essHist	5	0.02288205	0.01701354

Table 2 :

 2 Mean and standard deviation of absolute errors in approximating empirical probabilities of subintervals (, x] for the duration-times dataset of size 299 Sl. No. Method No. of bins

	Mean of abs errors	s.d. of abs errors

Table 3 :

 3 Mean and standard deviation of absolute errors in approximating empirical probabilities for subintervals(, x] for the unemployment-rate-2020 dataset of size 3192

	Sl. No. Method	No. of	Mean of absolute	Standard deviation
			bins	errors	of absolute errors
	1	KHist	12	0.00429684	0.00394688
	2	ewHist	12	0.00666956	0.00983799
	3	eaHist	12	0.02050246	0.01490316
	4	dHist	12	0.00457148	0.00521596
	5	essHist	11	0.00257418	0.00390527

Source of Unemployment-rate-2020 data: Economic Research Service, U.S. Department of Agriculture, https://www.ers.usda.gov/data-products/county-level-data-sets/.

Table 4 :

 4 Mean and standard deviation of absolute errors in approximating empirical probabilities for subintervals(, x] for the delays dataset of size 931

	Sl. No. Method	No. of	Mean of absolute	Standard deviation
			bins	errors	of absolute errors
	1	KHist	13	0.004492525	0.005345538
	2	ewHist	13	0.01728035	0.04135553
	3	eaHist	13	0.01790002	0.01088608
	4	dHist	13	0.005233305	0.007919291
	5	essHist	13	0.004093359	0.0048635

Acknowledgments

The authors thanks Dr. Sujan Chandra and Dr. Saptarshi Mondal of Bethune College, Kolkata for their helpful comments and suggestions that led to improvements in this article.

Dataset 4. Delays data. This dataset is considered by [START_REF] Denby | Variations on the histogram[END_REF]. All the histograms in Figure 4 indicate that the data distribution is bimodal with a long tail at the right. All the histograms show the tail well. The essHist displays a false spike near the value 600; the edf indicates this falseness. The ewHist fails to show the increases in the modal regions and thus fails to show the modes precisely. From Table 4, we see that essHist is the best, KHist is the second best in approximating empirical probabilities, but the difference is insignificant. Giving a penalty to essHist for showing a false spike, we may conclude that KHist is the overall best. For this dataset, the essHist allows at the least thirteen bins (taking alpha = 0). dubnbins=nclass.Sturges(dat), plot=TRUE){ #dat is the numeric data vector; dat may include NA terms # n is the total no. of data values # dcdp is the discrete component defining percentage of n # h is the common width of bins for Sturges rule # gdm is the gap defining multiplier of h # gcm is the gap capturing multiplier of h # dubKd is desirable upper bound of Kolmogorov distance # dubnbins is the desirable upper bound of no. of bins dat (bks, counts, density, mids, dcvv, dcfv) names(result) <-c("breaks", "counts", "density", "mids", "discrete_component","discrete_component_frequency")


Rofiq Aunur

Muljarto

Jean-Michel Salmon

Brigitte Charnomordic

Patrice Buche
email: patrice.buche@inra.fr

Anne Tireau

Pascal Neveu

A generic ontological network for agri-food experiment integration -Application to viticulture and winemaking

Keywords: ontology network, data integration, viticulture, winemaking 1. Introduction

This paper presents an ontological approach of observational data integration across complementary sub-domains, i.e., agriculture production and food processing, with an application to viticulture and winemaking process. The two main steps in this approach are i) to integrate preexisting ontologies to create a so-called ontology network and ii) to populate the ontology network with actual experimental data from different sources. The Agri-Food Experiment Ontology (AFEO), a new ontology network was developed based on two existing ontology resources, i.e., AEO (Ontology for Agriculture Experiment) and OFPE (Ontology for Food Processing Experiment). It contains 136 concepts which cover various viticultural practices, and winemaking products and operations. AFEO was used to guide the data integration of two different data sources, i.e., viticulture experimental data stored in a relational database and winemaking experimental data stored in Microsoft Excel files. Two potential uses by researchers of viticulture-winemaking integrated data using AFEO are shown. The first one is about wine traceability and the second one is related to the influence of grape varieties, irrigation practices, and different winemak-

suggested by analysis tools, instead of standard data representations (e.g., relational database schema); and (iii) the terms and concepts used to label data are not standardized, neither within nor across scientific disciplines and research groups [START_REF] Bowers | Scientific Workflow, Provenance, and Data Modeling Challenges and Approaches[END_REF]. The difficulty of organizing available data and knowledge in a unified way not only limits research productivity but also reduces data traceability [START_REF] Gardner | Ontologies and semantic data integration[END_REF].

Research experiments are commonly divided into some sub-domains, such as agriculture production, post-harvest, and food transformation process. Even though the explicit relation between them is clearly understandable, each of these has different objectives, scopes, and circumstances. For instance, the agricultural experiments are normally performed in the fields, in which external factors have a significant contribution while food processing experiments are generally carried out in the laboratory with more controllable environments.

From a practical point of view, they require different methods for collecting and organizing observational data that would lead to differences in the data format or structure and in the way the data are stored. The heterogeneity also occurs due to the vast scope of agri-food domains, ranging from plant cultivation up to the final processed food product. Each discipline uses its own knowledge expression, terms, concepts and semantic relations that might cause some difficulties to share the observational data.

Studies in the last two decades have shown that ontologies represent a flexible way to link the information contained in heterogeneous data sources within or across domains [START_REF] Gardner | Ontologies and semantic data integration[END_REF][START_REF] Seedah | Approach to classifying freight data elements across multiple data sources[END_REF]. Ontologies also provide the common concepts for data integration, thus opening the possibility to draw more comprehensive conclusions and to view data from different perspectives. Ontologies also allow certain types of automated reasoning to be performed in order to fulfil some specific requirements. The capabilities of data and knowledge sharing as well as reasoning will help to develop more advanced Information Systems able to manage heterogeneous data sources and to design platforms for more collaborative and accurate scientific data analysis.

The contribution of this work is to provide a method to prepare and to integrate data sources prior to further analysis in order to answer complex questions that require access to various agri-food scientific data sources. This method works out in viticulture and winemaking to solve complex questions using heterogeneous experimental data sources. To achieve this purpose, we developed the Agri-Food Experiment Ontology (AFEO), a new ontology network resource, based on two ontology resources, i.e., AEO1 (Ontology for Agriculture Experiment), which is also an original contribution of this paper, and OFPE2 (Ontology for Food Processing Experiment). The AEO and OFPE are ontologies that have been developed separately in research laboratories as generic knowledge representations of two respective sub-domains, i.e., agricultural production and food transformation process. By following the NeOn [START_REF] Suárez-Figueroa | The NeOn Methodology for Ontology Engineering[END_REF] methodology, we integrated these two ontologies into an ontology network, in order to facilitate data integration across these complementary sub-domains. An ontology network [START_REF] Suárez-Figueroa | The NeOn Methodology for Ontology Engineering[END_REF] is a new ontology engineering concept, which allows ontology re-use and avoids custom-building new ontologies from scratch.

Although in this paper the proposed ontology is specialized and tested for viticulture and winemaking experiments, the core elements of AFEO are fairly generic and might be adapted to other food products. Furthermore, the ontological definitions (concepts and relations) can be used to impose and preserve a logical structure for new types of scientific data, that may appear due to new sensors, protocols and analyses. This paper is structured as follows: Section 2 gives a brief survey on recent work related to scientific data integration and agri-food ontologies; Section 3 describes the global agri-food experiment ontology design process, introduces the two ontology resources used, their integration and specialization to viticulture and winemaking experiments; Section 4 presents how the new proposed ontology network is instantiated to integrate two different data sources: Section 5 is dedicated to discussion and a potential use in the domain of viticulture and winemaking; Finally, in Section 6, conclusions are drawn and further work outlined.

State of the art

The works on ontologies have increased recently not only in computer science but also in various domains, including agri-food related domains. This is driven by the need to communicate and share knowledge with common understanding. This section is divided into two subsections: i) scientific data integration with respect to an ontological approach and ii) current work on agri-food ontologies.

Scientific data organization and integration

Over the recent years researchers have faced significant problems to manage scientific data due to their increasing volume and complexities. This causes researchers to spend quite a bit of time to manage and integrate scientific data rather than to directly focus on their analysis [START_REF] Madin | An ontology for describing and synthesizing ecological observation data[END_REF] /* BRIGITTE: AJOUT REF PHENOME */. Scientific data are generally collected from measurements directly linked to real-world phenomena [START_REF] Bowers | A Conceptual Modeling Framework for Expressing Observational Data Semantics[END_REF]. Within the agri-food domain, crossdisciplinary scientific data are required to explore complex and temporal aspects of food quality and the impact of practices and operations.

The need for a more adaptable mechanism to organize scientific data has been addressed in the literature, both in non-ontological based approaches such as, LabKey Server [START_REF] Nelson | LabKey Server: an open source platform for scientific data integration, analysis and collaboration[END_REF] and SciPort [START_REF] Wang | SciPort: an adaptable scientific data integration platform for collaborative scientific research[END_REF]; and in ontological based approaches such as proposed in [START_REF] Luduscher | Managing scientific data: From data integration to scientific workflows*[END_REF], [START_REF] Madin | An ontology for describing and synthesizing ecological observation data[END_REF], [START_REF] Leonelli | Integrating data to acquire new knowledge: Three modes of integration in plant science[END_REF], [START_REF] Bowers | Scientific Workflow, Provenance, and Data Modeling Challenges and Approaches[END_REF], [START_REF] Li | An ontology-centric architecture for extensible scientific data management systems[END_REF] and [START_REF] Fox | Ontology-supported scientific data frameworks: The Virtual Solar-Terrestrial Observatory experience[END_REF]. Some of these approaches are targeted to specific scientific domains while the others are developed to be more generic and extensible. The non-ontological approach mostly relies on data models, such as database or XML schema, where attributes and relationships of domain concepts are captured in standardized structures. The ontological approach has some additional advantages in terms of data interoperability and knowledge reasoning [START_REF] Daraio | The advantages of an ontology-based data management approach: openness, interoperability and data quality[END_REF][START_REF] Imran | Reference ontologies for interoperability across 29 multiple assembly systems[END_REF][START_REF] Arch-Int | Semantic ontology mapping for interoperability of learning resource systems using a rule-based reasoning approach[END_REF][START_REF] Lousteau-Cazalet | A decision support system for eco-efficient biorefinery process comparison using a semantic approach[END_REF].

To the best of our knowledge, we did not find an ontological approach to represent scientific experiments as well as observational data which fulfill all our needs. An ontology of scientific experiments, the EXPO [START_REF] Soldatova | An ontology of scientific experiments[END_REF], has been proposed to formalize the generic concepts of experimental design, methodology and result representation. However, this ontology does not provide a clear explanation about scientific data representation. Neither does this ontology describe how to manage a set of experiments in which several interrelated experiments have to be conducted in a given order. The Extensible Observation Ontology (OBOE) has been developed to serve as a formal and generic conceptual framework for describing the semantics of observational data sets (i.e., data sets consisting of observations and measurements) [START_REF] Madin | An ontology for describing and synthesizing ecological observation data[END_REF]. The basic concepts of the observational model consists of five classes and six properties [START_REF] Bowers | Scientific Workflow, Provenance, and Data Modeling Challenges and Approaches[END_REF]. This ontology can be applied to various types of observations. Nevertheless, it is more suited to representing scientific data which are generated from measurement by sensors. It does not provide other types of observational data such as expert judgements or results from a calculation procedure.

Agri-food ontologies

In order to fulfill the needs of representing complex knowledge, sharing common understanding within or across scientific domains and reusing domain knowledge in agri-food sectors, some ontologies have been proposed, either very general or more specific. Some researchers focused on building ontologies to conceptually model agricultural practices related to crop productions, such as, hilly citrus production ontology [START_REF] Wang | An ontology-based approach to integration of hilly citrus production knowledge[END_REF], precision agriculture ontology [START_REF] Song | Study on Precision Agriculture Knowledge Presentation with Ontology[END_REF], crop-pest ontology [START_REF] Beck | A Crop-Pest Ontology for Extension Publications[END_REF] and potato ontology [START_REF] Haverkort | Organizing Data in Arable Farming: Towards an Ontology of Processing Potato[END_REF]. Meanwhile, some works concentrating on food taxonomy have also been carried out, such as FOODS (Food-Oriented Ontology-Driven System) [START_REF] Snae | FOODS: A Food-Oriented Ontology-Driven System[END_REF] and wine classification [START_REF] Graça | Ontology building process: the wine domain[END_REF].

The valid definition of concepts and a complete taxonomy for agricultural practices and food processing are important to model agri-food experiments.

Most of the above ontologies refer to the terms or concepts listed in AGROVOC.

AGROVOC is a multi-lingual vocabulary developed by the Food and Agriculture Organization (FAO) of the United Nations and covers divers areas including food, nutrition, agriculture, fisheries, forestry, environment etc [START_REF] Rajbhandari | The AGROVOC Concept Scheme A Walkthrough[END_REF]. Some ontologies extend these concepts in order to accommodate their data sources according to the target domains, such as shown in [START_REF] Wang | An ontology-based approach to integration of hilly citrus production knowledge[END_REF], [START_REF] Beck | A Crop-Pest Ontology for Extension Publications[END_REF], and [START_REF] Haverkort | Organizing Data in Arable Farming: Towards an Ontology of Processing Potato[END_REF].

Another part of the agri-food domain that recently attracted the attention of researchers is related to food traceability. It is driven by a growing interest in developing systems for the food supply chain. Some essential works in this domain have been carried out, such as The Food Track and Trace Ontology (FTTO) [START_REF] Pizzuti | Food Track & Trace ontology for helping the food traceability control[END_REF] and TraceALL [START_REF] Salampasis | TraceALL: a semantic web framework for food traceability systems[END_REF]. Even though the FTTO is dedicated to food traceability management, this ontology provides representative food concepts that also become valuable resources for food processing experiments. This ontology includes four core concepts: actor, food product, process and service product.

The ontologies mentioned above have proven useful in their own domain.

However those ontologies mostly cover one sub-domain, for example only agricultural practices or only food processing. The question of data integration across complementary sub-domains often has not been discussed yet in the Agri-food sector.

The global Agri-food experiment ontology design approach

In this section, we explain how we built an ontology network (AFEO), starting from two complementary existing ontologies (AEO and OFPE), in order to integrate heterogeneous data sources, both from field experiments and from food processing processes. To design AFEO ontology, we have followed the NeOn methodology [START_REF] Suárez-Figueroa | The NeOn Methodology for Ontology Engineering[END_REF]. NeOn provides methodological support for constructing an ontology network (AFEO in our case), when different pre-existing resources must be re-engineered in order to be reused for a new purpose. NeOn permitted us to design iteratively the AFEO ontology network based on some of the nine scenarios proposed in the methodology which cover commonly occurring situations. The section is divided into three parts. The first part defines the requirements associated with the desired result, the AFEO ontology network. The second part presents the scope of both selected ontology resources (AEO and OFPE) as inputs of the ontology integration process. The third part describes the ontological transformations used to integrate AEO and OFPE ontologies into AFEO in order to fulfill the requirements. Main OWL 2 (Web Ontology Language, second edition) ontological constructs used in this paper are presented in [START_REF] Group | OWL 2 Web Ontology Language Document Overview (Second Edition) W3C Recommendation 11[END_REF].

AFEO ontology requirements

Following NeOn scenario 1 (From specifications to implementation), we established the ontology requirements (called OR in the rest of the paper). AFEO must • model a global food chain linking the biomass production process to the biomass transformation process (OR1),

• represent experimental observations all along the integrated process (OR2),

• be able to be specialized for a given food chain which is, in this paper, viticulture and winemaking (OR3).

Description of the initial ontologies

Following NeOn scenario 3 (Reusing ontological resources), AEO and OFPE ontological resources must be inspected in order to determine if they are good candidates to fulfill the AFEO requirements and to analyze their granularity.

AEO and OFPE ontologies were built separately for different intended communities. AEO serves as a representation of expert knowledge in the field of agricultural practices while OFPE was developed to represent the knowledge related to food processing experiments. It is the reason why they have been selected as their union should satisfy OR1 requirement presented in section 3.1.

The present section describes both ontologies, in terms of their concepts and relations, in order to determine if some knowledge is missing to fulfill AFEO requirements. AEO is an ontology aimed to represent objects related to agricultural practices. It is based on three main concepts, AgriExperiment, ObservedAgriEntity, and AgriActivity (Figure 1). AgriExperiment is a concept that represents experiments carried out by researchers. ObservedAgriEntity represents objects that are observed and followed during field experiments while the AgriActivity represents common activities or operations performed during experiments.

Agricultural Experiments Ontology (AEO)

Some important semantic relations have been defined between those concepts as shown in Table 1. Object property includes plays an important role in this ontology. It is used to represent the relation between spatial locations, e.g., Far-mArea a concept that represents the area of agricultural land used for farming.

This type of relation also applies to Plot, Sub-plot and Micro-plot which are subclasses of CultivatedArea. Each plot may be composed of several subplots and each subplot has two or more micro-plots. By defining includes object property as a transitive object property, we can easily navigate between locations. This object property also represents the multi-scale aspect of locations that is useful for tracking the origin of a particular product. Relations among main classes in this ontology can be grouped into two parts, i.e., product transformation and temporal aspects of operations. Product transformation can be described either by using a transitive object property Before (or its inverse After ) or object property hasInput and hasOutput. The Before links between different products, in particular between classes InputProduct, In-termediateProduct, and FinishedProduct (see Figure 2). To describe temporal aspects of operations, this ontology uses the concepts defined in the Ontology of Time proposed in [START_REF] Hobbs | An ontology of time for the semantic web[END_REF]. Examples of use of these temporal relations are presented in Table 2.

Ontology for Food Processing Experiments (OFPE)

AEO and OFPE re-engineering for integration

After inspection, the two selected ontology resources presented in Section 3.2.1 and Section 3.2.2 have been considered valid by domain experts for their respective intended domains, i.e. biomass production and food processing. However, when both are directly merged, the result is not entirely suitable to support the objective of this work which focuses on agri-food experimental data integration. Indeed, OR1 requirement is not completely fulfilled because the linkage between production and transformation is not done. is enlarged to the alternative AgriActivity class of AEO. By using these formal extended semantic relations, the ontology linking between AEO and OFPE can be built and OR1 requirement is now fulfilled. Figure 4 shows with an example how these extended semantic relations are applied. Another interesting point illustrated in Figure 4 refers to the practical application of complex temporal relations between operations. For example the Crushing is performed before the AlcoholicFermentation, the PumpingOver has to be done during the Maceration, etc.. By using these semantic relations, a particular sequence or itinerary of operations (experiments) can be investigated.

The ability of finding a specific sequence of products and operations as well as linking to agricultural activities and entities is a strong point of AFEO ontology network because it gives a reliable way to build a connection between observational data belonging to interrelated experiments. AFEO4 (resp. AEO5 and OFPE 6 ) ontology is available on AgroPortal, derived from BioPortal [START_REF] Noy | BioPortal: ontologies and integrated data resources at the click of a mouse[END_REF] for agronomical ontologies.

Ontology population with viticulture and winemaking experimental data

In a domain specific ontology development stage, an ontology instantiation (population) is an important step. The main task is to semantically annotate all related resources based on the proposed ontology. AFEO, result from Section 3, can be seen as an agri-food experiment knowledge layer that acts as a container for viticulture and winemaking experimental data integration. From a practical point of view, this ontology network needs to be instantiated with actual experimental data so that specific data queries can be performed to support further statistical analysis. This section presents how AFEO has been instantiated in order to integrate the experimental data from various stages of agri-food experiments. The first part describes two different data sources used in this work and the second part explains the principles of the ontology population step. Excel files. To the current date, more than 500 Microsoft Excel files have been collected. These files can be classified into two groups: i.e,

• a group that represents different operations during the winemaking process. Each file consists of a single sheet that contains a table of operations used during a set of winemaking experiments, started from harvesting to bottling. The table also contains the attributes of each operation;

• a group that records observational data concerning the different product features. Each file consists of three sheets, where each sheet represents observational results of some attributes for a particular product stage, such as grape, must, must after alcoholic fermentation, and finished wine.

Ontology instantiation process

Both data sources have to be transformed into uniform format based on AFEO ontology network. Consequently, the Resource Description Framework (RDF) format has been chosen to represent these data. The RDF is a standard model for data interchange and metadata processing [START_REF] Cyganiak | RDF 1.1 Concepts and Abstract Syntax[END_REF]. It has features that facilitate data linking even if the underlying schema differ. The RDF can be seen as a graph data model that uses URIs to name two nodes as well as the relationship between them. Due to the different source data formats, we developed two specific scripts using the Python language as illustrated in Figure 5.

The first script creates instances by performing some queries to the viticulture database and transforming them to RDF format. The second script is specialized for making instances from the Microsoft Excel winemaking experimental data files. Both of them were developed guided by the AFEO ontology network. RDF data are stored in a triplestore, a specific database for storing and retrieving RDF triples through semantic queries expressed in SPARQL.

Results and discussion

The RDF data produced in Section 4.2 are viticulture-winemaking integrated data that contain objects and activities/operations along with observational results from various experiments. These data can be used in many ways by querying them according to the user requirements. This section presents two examples on how this integrated data can help viticulture and winemaking researchers to find some related data prior a statistical analysis. The first part describes a practical use related to wine traceability and the second part explains how to extract and analyze interrelated observational data between viticulture practices and wine qualities.

Wine traceability

Wine is a food product whose value is generally determined by three groups of characteristics, i.e., appearance, flavour, and aroma. In the recent years, wine consumers are more and more oriented to consider detailed information about those characteristics as well as the overall process from the grape to the bottle [START_REF] Cimino | Enabling Traceability in the Wine Supply Chain[END_REF]. The information is used to confirm the wine identity (authenticity)

and to ensure it is produced transparently in order to avoid fraud and toxicological issues [START_REF] Palade | Wine traceability and authenticity A literature review[END_REF]. The viticulture-winemaking integrated data generated from Section 4.2 can be queried in order to get such traceability information, giving valuable knowledge about the entire process from viticulture practices through selected winemaking operations, until finished product delivery. Figure 6 shows a screen shot of the query result which lists instances of finished wine, their input products, sub-plots and vineyards where the grapes are planted, and their grape varieties. In Query 1, the After object property is used in order to trace all existing products during winemaking process. By using the After, which is defined as a transitive property, this SPARQL query performs an inference to determine link between BerryGrape instance (t) as an input product and FinishedWine instance (w ) as the final product, whatever the number of intermediate products and associated operations. Figure 6 highlights some information about wine traceability that might help researchers to know global information about the origin of finished wine products. For instance, we can see that, from the same berry grape lot, can be produced two different finished wine products: wt 12001 and wn 12001 are finished wine instances that have the same input product, i.e., g 12001. This indicates that probably there were different treatments during the winemaking process, that may affect the characteristics of the final product.

Influence of viticulture practices on grape and wine qualities

As said above, wine quality can be analysed by three groups of characteristics. Each group can be further detailed by various attributes. For example, the appearance is determined by the color attribute along with other visual features such as clarity and fluidity, while the wine flavour has some basic attributes, such as sweetness, acidity, bitterness, fruit flavour, etc. These attributes are influenced by various interrelated factors, both viticulture practices (e.g., grape variety, location, vintage, etc.) and winemaking selected operations (e.g., crushing method, maceration, pressing, yeasts added, etc.). To illustrate the interest of viticulture-winemaking integrated data, we now present one set of experiments that has been conducted in the Pilotype project, funded by OSEO innovation and the Languedoc-Roussillon regional council. This project includes multi-site experiments located in the south of France. The same experimental design was set up in seven sites across the Languedoc Roussillon region in order to test for the effects of vine stress status and winemaking protocol on grape potential and wine quality in contrasted environmental conditions. We discuss here a subset of these experiments. Three grape varieties are being studied, i.e. Merlot, Syrah and Cabernet Sauvignon; and two different winemaking methods, i.e., with an innovative hot pre-fermentation maceration and without it (classical method). In the experimental plots, the wine water status has been monitored by different means: on-line sap flow sensors, predawn leaf water potential and DeltaC13 at harvest time. The last one, which is a global indicator of the water stress experienced by the vine, will be used in the following. Many quality parameters resulting from physico-chemical analyses are available to assess grape composition at harvest time, must composition and finished wine composition. Among them, let us take the example of the glutathione (GSH) concentrations in wine and berry grape. GSH, a natural tripeptide found in grapes and wine, is a powerful antioxidant that protects wines from oxidation and loss of aroma or flavor. Glutathione levels fluctuate during production, as the compound can be absorbed by yeast and then released after fermentation. If final GSH levels are low in wines, they will experience faster loss of fresh varietal and fruity aromas, and poor ageing potential. By using the AFEO, this experiment can be represented semantically as visualized in Figure 7.

In order to perform a statistical analysis, some data sets need to be queried from the viticulture-winemaking integrated data, including all the RedWine A graphical analysis is then done to visually explore, by taking advantage of the links between viticulture and wine data, if the vine water status could have an impact on that influence. Figure 8 shows, for each of the three varieties, on the abscissa the grape GSH concentration and on the ordinate the corresponding wine GSH concentration. Circles correspond to the year 2012, and squares to the year 2013. The classical winemaking protocol is plotted in red, and the hot pre-fermentation maceration one in blue. The size of the symbols is proportional to the Delta C13 indicator: the higher Delta C13, the bigger the symbol and the less the vine was exposed to water stress. Plots visually confirm the increase of GSH in wine, for a given GSH in grapes, with the hot pre-maceration protocol, but they do not show any influence of the vine water status.

Conclusion

This paper presents an ontology-based approach for experimental scientific data integration across complementary sub-domains, i.e., agricultural practices and food processing, with an application to viticulture and winemaking process. The two main steps in this approach are i) to develop an ontology network and ii) to populate the ontology with actual experimental data from different sources. The ontology network -Agri-Food Experiment Ontology (AFEO)was developed based on two existing ontology resources, i.e., AEO (Ontology for Agriculture Experiment) and OFPE (Ontology for Food Processing Experiment). It contains 136 concepts which covers various viticulture practices, and winemaking products and operations. AFEO was used to guide data integration from two different data sources, i.e., viticulture experimental data which are stored as relational database and winemaking experimental data which are stored in Microsoft Excel files.

Results show the potential uses of the AFEO along with viticulture-winemaking integrated data to provide linked data to be used by researchers. Two practical uses are presented, i.e. wine traceability and the influence of grape varieties and different winemaking methods on GSH concentration. They give an idea of how data integration can support extended research questions which require data from different parts the Agri-food chain.

The development steps presented in this paper can also be viewed as an effort to decrease the gap between scientific disciplines, by allowing researchers from different disciplines to formulate their knowledge in a formal ontological form, in order to share it and to build more comprehensive and collaborative scientific researches. AFEO focuses on viticulture and winemaking objects and experimental activities. However, as indicated in Section 5 the weather and climate has significant influence on grape quality. Therefore in the future, aligning AFEO with an ontology that represents knowledge from the meteorological domain will allow a better analysis of viticulture and winemaking experimental results. Another interesting perspective is to specialize AFEO to other food products that require linkage from agriculture practices to food transformation process.

Figure 1 :

 1 Figure 1: Concept hierarchies in AEO.

Figure 2 :

 2 Figure 2: Core concepts and relations in OFPE.

  terials used by operations to transform particular product during process flow. The Operation class conceptualizes the knowledge related to the transformation activities. The concept of Attribute represents all features or qualities belonging to Product or Operation classes. Observation is an abstract model of activity where an instance of Attribute is measured. This class has an important role in representing measurement values of attributes collected from different experiments. Observation can be a single observation (SingleObservation) that means one time only measurement or a set of observation (MultipleObservation) where multiple measurements of a particular attribute (of product or operation) are needed. An instance of observation links to an instance of product or operation and to one or more instances of attribute through object property hasObservedObject and hasObservedAttribute.This observation instance also has method which is represented by Observa-tionMethod class and produces result depicted by ObservationResult that holds the values of measurement. In food processing the observation results come in various forms, such as values directly recorded by sensors, values from ex-pert judgement or values from a particular calculation. To accommodate those forms, this ontology provides three subclasses under ObservationResult, including SensorResult, ExpertJudgementResult, and CalculationResult (see Figure2).

(Figure 1 )

 1 Figure 1) which provides generic classes that mostly also exist in viticulture. Some specific classes have been added, such as CanopyManagement (sub-class of AgriActivity), GreenHarvesting (sub-class of Pruning), Vineyard (sub-class of CultivatedArea), GrapeVariety (sub-class of Genotype) and Grapevine (subclass of Plant).Figure 3 shows the new required specific classes under the Product and the Operation classes for winemaking. To illustrate the final structure of AFEO 3 , we present a part of the whole ontology in Figure 4. This diagram contains different viticulture entity and activity classes, winemaking specific classes of product and operation, and their semantic relations.

Figure 3 :

 3 Figure 3: Operation and product specialization of the AFEO for winemaking experiment.

Figure 4 :

 4 Figure 4: A part of the AFEO that represents viticulture and winemaking integration.

4. 1 .

 1 Data sourcesData sources used for this work can be divided into two groups, i.e., viticulture and winemaking experimental data. Both are temporal data, however they are different in terms of structure and storage formats.The viticulture experimental data were collected during several years of viticultural experiments from different vineyards in the south of France. These data contain information about vineyards, plots, sub-plots, grapevines, different treatments of experiment (for example irrigation, non irrigation, green harvesting, non-green harvesting, etc.), and a huge number of observations regarding the grape characteristics during the growing season. They are stored in a single relational database linked to Silex-VitiOeno Pilotype, a web application that manages viticulture experimental data.The winemaking experimental data contain information about different stages of the winemaking process, different wine products as well as a big amount of observational data about operations and products characteristics during process flow. These data were collected annually from the Unité Expérimentale de Pech Rouge, France, where the winemaking experiments were conducted. Unlike the viticulture experimental data, these data are recorded in the form of Microsoft

Figure 5 :

 5 Figure 5: Data population processing steps.

Figure 6 :

 6 Figure 6: List of finished wine instances and their origin

Figure 7 :

 7 Figure 7: Semantic relations linking GSH concentration in grape and red wine.

  instances and their corresponding BerryGrape instances along with their GSH values, all the Subplot and Plot instances as the wines origin, all the corresponding GrapeVariety instances, and all itinerary types which are used to identify what winemaking methods are used. Using the SPARQL query statements, data can be extracted from viticulture-winemaking integrated data. Based on the available data which cover two years experiments (2012 and 2013), the query provides the results as follow: there are a total of 40 instances of RedWine which are produced from 20 instances of the BerryGrape, 20 instances of the Subplot and 9 instances of the Plot as the origin of the BerryGrape instances. The RedWine instances are divided equally into two groups, 20 instances from the hot pre-fermentation maceration methods and the rest come from the classical method. The statistical study aims to determine if the winemaking protocol has a significant influence on the GSH wine concentration. As data do not follow a Gaussian distribution (as confirmed by a Shapiro test), the Wilcoxon test on paired samples is run. It highlights a significant (p-value <0.05) difference in GSH concentrations depending on the winemaking protocol: The hot prefermentation maceration influences the wine GSH concentration and increases it.

Figure 8 :

 8 Figure 8: Plots of GSH concentration in red wine versus GSH concentration in grape.

Table 1 :

 1 Some important object properties of AEO

	Property name Inverse	Descriptions
	includes	included	relation among cultivation locations (Far-
			mArea, CultivationArea and its subclasses)
	applies	appliedTo relation between classes under AgriActivity
			and some classes under ObservedAgriEntity.
			For instance, an instance of Fertilizing is ap-
			plied to an instance of Plot or SubPlot
	hasPart	partOf	relation between Plant class and Organ class
	hasLocation	locationOf relation between AgriExperiment and Culti-
			vationArea
	involves	involvedIn relation between AgriExperiment and AgriAc-
			tivity as well as ObservedAgriEntity.

Table 2 :

 2 Temporal relations between operations

	Relations	Inverse	Examples from winemaking
	Before(A,B)	After(B,A)	Crushing is performed after destem-
			ming
	Meets(A,B)	MetBy(B,A)	Draining is started after maceration
	Overlaps(A,B) OverlappedBy(B,A) Malolactic fermentation can be started
			before alcoholic fermentation is finished
	Starts(A,B)	StartedBy(B,A)	Alcoholic fermentation starts when
			Maceration is started
	Finishes(A,B)	FinishedBy(B,A)	Sulfitation finished malolactic fermen-
			tation
	During(A,B)	Contains(B,A)	Alcoholic fermentation occurs during
			maceration
	Equal(A,B)		Extraction of ethanol is started and fin-
			ished at the same time as alcoholic fer-
			mentation

outputs of food transformation process. The ServiceProduct represents all ma-

Table 3 :

 3 Class mapping between AEO and OFPE.

	AEO class	OFPE class Mapping
	Berry	Berry	owl:equivalentClass
	Bunch	Bunch	owl:equivalentClass
	AgriActivity Operation	owl:equivalentClass
	OR2 fulfillment The next step after linking AEO and OFPE is re-engineering

this new ontology network. Indeed, as presented in Section 3.2.1, AEO does not provide important concepts and properties with regard to observations, measurement data representation, as well as observed attributes. Contrary, the OFPE contains a specific part that is dedicated to accommodate observation activities. In order to fulfill OR2 requirement, we re-engineered the new ontology network by the following steps which implement scenario 8 (Restructuring ontological resources). Firstly, we re-used the semantic relation hasAttribute

http://agroportal.lirmm.fr/ontologies/AEO

http://agroportal.lirmm.fr/ontologies/OFPE

http://agroportal.lirmm.fr/ontologies/AFEO

http://agroportal.lirmm.fr/ontologies/AFEO

http://agroportal.lirmm.fr/ontologies/AEO

http://agroportal.lirmm.fr/ontologies/OFPE