Automated landmarking of bends in vascular structures: a comparative study with application to the internal carotid artery

Automated tools for landmarking the internal carotid artery (ICA) bends have the potential for efficient and objective medical image-based morphometric analysis. The two existing algorithms rely on numerical approximations of curvature and torsion of the centerline. However, input parameters, original source code, comparability, and robustness of the algorithms remain unknown. To address the former two, we have re-implemented the algorithms, followed by sensitivity analyses. Of the input parameters, the centerline smoothing had the least impact resulting in 6–7 bends, which is anatomically realistic. In contrast, centerline resolution showed to completely over- and underestimated the number of bends varying from 3 to 33. Applying the algorithms to the same cohort revealed a variability that makes comparison of results between previous studies questionable. Assessment of robustness revealed how one algorithm is vulnerable to model smoothness and noise, but conceptually independent of application. In contrast, the other algorithm is robust and consistent, but with limited general applicability. In conclusion, both algorithms are equally valid albeit they produce vastly different results. We have provided a well-documented open-source implementation of the algorithms. Finally, we have successfully performed this study on the ICA, but application to other vascular regions should be performed with caution.

Page 2 of 17 Kjeldsberg et al. BioMedical Engineering OnLine (2021) 20:120 conducted by non-experts within neuroradiology, which could cause differences in classification, and potentially influence the results [13][14][15][16][17]. Hence, a topic of interest is the development of a computationally inexpensive tool for automated and objective characterization of the ICA, referred to as landmarking. Previous methods have been presented by Piccinelli et al. [12] and Bogunović et al. [18], which rely on numerical approximations of the curvature and torsion, used to subdivide the vessel into separate bends, and are allegedly applicable to arbitrary tubular structures. However, to the authors' knowledge, there are no open source-implementations of the algorithms, and information about the input parameters for estimation of the geometric properties are unknown, limiting their applicability. Furthermore, the algorithms capability of capturing the underlying morphology irrespective of segmentation variability remains unknown. Therefore, our goal is to investigate the existing methods for automated characterization of the ICA, which will allow for objective, consistent, and operator-independent medical image-based morphometric analysis.
We will revisit automated landmarking, and organize the remainder of this paper as follows: we devote Sect. to the results, consists of three separate subsections. More precisely, in Sect. , we investigate the sensitivity of the algorithms to input parameters for estimation of geometric properties, in the pursuit of a set of parameters that produce consistent landmarking results. In Sect. , we perform verification of our implementations, and compare the results of the two algorithms. In Sect. , we test robustness of the algorithms. We present a discussion for the three subsections in Sect. , followed by limitations and implications. Concluding remarks are presented in Sect. , followed by our methodology in Sect. , including computation of the centerline, the relevant geometric properties, and a presentation of the two existing landmarking algorithms.

Piccinelli's algorithm
Qualitative results using Piccinelli's algorithm are shown in Fig. 1. Firstly, results of varying the resampling length r are shown in Fig. 1a, where we observe how the number of bends is increased from 5 to 15 as r decreases. Secondly, results of varying the smoothing factor are shown in Fig. 1b, where the two leftmost models have 8 and 7 bends, respectively, in contrast to 5 for the rightmost model. Finally, results of varying the number of iterations N are shown in Fig. 1c, where an additional 6th bend is detected for N = 50 , whereas an increase of iterations show no noticeable difference.
Quantitative results are presented in Fig. 2a, where we observe that the number of detected bends behaves inversely proportional to r, with a mean of 33 bends detected for r = 0.02 , in contrast to 3 bends for r = 0.2 . The results of varying are shown in Fig. 2b, where we observe a slight increase, followed by a decrease in the number of bends as the magnitude increases, varying around 6 bends. Finally, the results of varying N are shown in Fig. 2c, showing a steady decrease in detected bends as N increases, transitioning from a mean of 7 to 6 bends.

Bogunović's algorithm
Qualitative results using Bogunović's algorithm are shown in Fig. 3. Firstly, results of varying r are presented in Fig. 3a, where the leftmost model harbors an evidently short (red) bend, while the remaining models show no noticeable differences. Secondly, results of varying are shown in Fig. 3b, where the left-and rightmost model contain particularly short bends, in contrast to the default model in the middle. Lastly, results of varying N are presented in Fig. 3c, where there are no noticeable differences, and the bends are adequately detected, regardless of N.
Quantitative results are presented in Fig. 4. The results of varying r are presented in Fig. 4a, where we observe a steady growth in bend length towards r = 0.08 , while further increase contributes little to no value. The plot also shows how the lowest deviation appears for r = 0.1 , reflected by the CV, followed by a rapid increase as r increases. Low ( = 0.2 ) and high ( = 2.0 ) smoothing factors result in a shorter portion of the ICA being landmarked, shown in Fig. 4b. In contrast, around = 1.1 , the length averages at 60 mm, and harbors a minimum CV. When varying N, we observe a steady increase in deviation and decrease in length as N > 100 , shown in Fig. 4c. In contrast, for N ≤ 100 , the bends deviate much less and average around 60 mm in length. The lowest CV is attained at N = 20 , although for N = 60 and N = 100 the CV is similar. Verification and comparison of the landmarking algorithms

Verification
In Fig. 5a and b, we have applied our implementation to reproduce the original results by Piccinelli et al., specifically Fig. 4 in [12]. Similarly, in Fig. 5c, we reproduce the first landmarking result by Bogunović et al., shown in Fig. 5 in [19]. Albeit using only one model 1 , the correspondence between our and the original results suggests a successful implementation of the algorithm.  sub-optimal detection of the inferior (yellow) bend. However, the 2D projection of the models may have influenced the interpretation of the results. In Fig. 6b, the models in the lower row can be qualitatively compared against results in [19], including the incorrect detection of the posterior (red) and inferior (yellow) bend in model F14D, as originally pointed out by Bogunović et al. Comparing the upper row models with the lower row, the largest differences are harbored in the middle three models. The superior (blue) bend is captured as two bends with Piccinelli's algorithm, and captures the inferior (yellow) bend as two short bends for case F14C. In contrast, F14D is detected as five bends with Piccinelli's algorithm and provides a better landmarking.
Quantitative results are presented in Fig. 7, but omitting the incorrectly landmarked model. The mean bend length and standard deviation is presented in Fig. 7a, which shows largest differences between the algorithms for the superior and inferior bend, respectively. The two bends are close to twice the length using Bogunović's algorithm. In Fig. 7b, we show the CV for the respective bends, as defined in Equation 7. The results emphasizes the large relative deviance for the superior bend, where Piccinelli's algorithm produces a high variability with a CV of 58%. In contrast, Bogunović's algorithm has the highest variability for the posterior bend at 33%, although the overall variability is low.

Robustness of the landmarking algorithms
Qualitative results are shown in Fig. 8, where the alphanumerical characters are reflective of the respective participating teams of the former challenge. First, in the upper row of Fig. 8b, we have applied Piccinelli's algorithm. Overall, the algorithm detects anywhere from three to six bends. Starting at the first (blue) bend and comparing horizontally, there is slight variability to how far upstream the next interface is detected. Consequently, the second (green) bend has large variability in location and length. The Fig. 7 In a, a plot of mean length and standard deviation of the first four bends starting at the most proximal bend, traversing distally, for the models in Figure 6. In b, we have plotted the CV, per bend. We have excluded case F14D due to the incorrect landmarking with Bogunović's algorithm third (red) bend is located either as the anterior or posterior bend. Six of eight models detect a fourth (yellow) bend, detected as the posterior bend for all but one model (segmentation 19A). The only bend with a slight resemblance across all cases is the posterior bend, although it is captured as either the third (red) or fourth (yellow) bend. Therefore, allowing some leeway, there is a slight correspondence between bends in the cohort. Second, in the lower row of Fig. 8b, we have applied Bogunović's algorithm. Firstly, the superior (blue) bend is detected at indistinguishable location across all segmentations. Secondly, location and length of the anterior (green) bend is similar, with a tiny discrepancy in segmentations 24, 33, and 42, harboring a hardly noticeable, but slightly shorter bend. Thirdly, all cases appear to capture the same interface between the superior (blue) and anterior (red) bend. Finally, for seven of the eight cases, the posterior-inferior (redyellow) interface coincides, with case 16 being the exception, which is influenced by the flow extension at the model inlet. In addition, the inferior (yellow) bend of segmentation 38 is arguably too long, harboring two curvature peaks.
Quantitative results are shown in Fig. 9. The mean length and standard deviation for the three bends are presented in Fig. 9a, which highlights the particularly small deviation for the superior bend with Bogunović's algorithm. For the remaining two bends, both algorithms perform well at capturing consistently sized bends. Overall, the bends detected with Piccinelli's algorithms vary considerably more in mean length, compared to Bogunović's algorithm. In Fig. 9b, we present the CV for the three bends. The results further support the variability observed in the qualitative results, with large differences in CV between the algorithms. Piccinelli's algorithm shows high variability with a CV of 47% for the first bend. However, both the second and third bend lengths are consistent with a CV < 20% . For Bogunović's algorithm, the CV is generally low for all three bends, with a minimum of CV < 5% for the superior bend.

Sensitivity analysis
The two previous studies by Piccinelli et al. and Bogunović et al. have specified using Laplacian smoothing, but dedicated little attention to the centerline resolution, which is here shown to have the largest impact on the landmarking results. Therefore, to isolate and investigate the effects of centerline resolution on the geometric properties, and consequently on the landmarking results, we will be varying r for the representative model shown in Fig. 10a, keeping the remaining parameters fixed at   increase in the number of saddle-like points located in the vicinity of the main peaks. Between r = 0.1 and r = 0.25 , we observe a reduced number of extremum; whereas the peaks have completely diminished for r = 0.5 , represented by the orange curve. Figure 10d shows the overall impact r has on the number of peaks, which is considerably decreased as r is increased. Thus, values of r > 0.1 is shown to produce oversmoothed geometric profiles, following the centerline smoothing. In contrast, when r < 0.1 the geometric profiles are considerably noisy, creating an undesired amount of short bends regardless of the landmarking algorithm. Note that this analysis was performed for only one set of smoothing parameters. We therefore theorize that an adequate result might be obtained for different sets of centerline resolutions, using other smoothing parameters. Nonetheless, for centerlines representing models similar to the cohort used in this study, r = 0.1 is a reasonable choice. Considering parameters retrospectively suggested by Dr. Piccinelli 3 , and judging by the sensitivity analysis, values of ∈ [1.2, 1.5] appear to provide adequate results. Note that for > 2.0 Bogunović's algorithm often fails to identify any bends.
Choices of N have shown consistent results for N ∈ [20, 100] , while much higher values will contribute to further smooth out the centerline, and consequently reduce the number of curvature and torsion peaks.
For parameters within these suggested ranges, Piccinelli's algorithm is shown to produce an average of 6 to 7 bends. Furthermore, Bogunović's algorithm consistently produces the four bends, at a total length ranging from 60 to 70 mm. This is in good correspondence with the clinical measurements by Vijaywargiya et al., who reported an average length of 68.9 mm for the ICA siphon [20].

Verification and comparison of the landmarking algorithms
With the chosen set of parameters, we have verified our implementation of the landmarking algorithms. It should be noted that the verification was performed solely through qualitative analysis, and a more rigorous approach could include quantitative reference data if made available. Generally, software is verified through empirical analysis, and our implementation has shown to produce plausible results.
The comparison showed distinct differences between the algorithms, where Piccinelli's algorithm repeatedly produced several bends, whereas Bogunović's algorithm was less variable, consistently resulting in models with four bends, inherent in the algorithm design. As a result, we theorize that the two algorithms are not comparable in a metaanalysis. However, both work well for their purpose-capturing either geometrically defined bends or anatomical segments.

Robustness of the landmarking algorithms
Piccinelli's algorithm detects the ICA's major bends at comparable locations, but without correspondence between bends due to large variability for the first (blue) bend. In contrast, Bogunović's algorithm captures the first three bends at indistinguishable location and length, with an overall low variability. The comparison shows that Piccinelli's algorithm produces acceptable results, with similarly subdivided models, but is not robust enough to overcome the real-world interlaboratory differences. In contrast, Bogunović's algorithm is able to capture the underlying morphology irrespective of segmentation variability, although certain parameters are fitted to landmarking the ICA, thus at the cost of applicability to other vascular structures. Thus, for general tubular structures, we theorize that Piccinelli's algorithm is sufficient at capturing bends, although it is prone to slight variability as shown here, while Bogunović's algorithms is superior for carotid artery models.

Limitations
Despite drawing authoritative conclusions in the previous sections, this work has some limitations. Firstly, the set of parameters determined through the sensitivity analyses produced adequate and robust results in our study, which can plausibly also be used in future applications. That being said, these parameter choices are not unique, and there may exist other parameter combinations that produce equally plausible or better results.
Secondly, the verification was based on a qualitative comparison that arguably is suboptimal from a software engineering point of view. However, the software implementation of the previous studies was unavailable, and our open-source code produced adequate results.
Finally, the models used to study robustness were collected from a study with focus on aneurysm modeling pipeline consistency, and not accuracy of parent artery segmentation. Thus, the variability in segmentation may potentially be exaggerated, although these surface models were qualitatively similar to other studies [17].

Implications and future considerations
Setting the limitations aside, this study has shown how the two algorithms perform adequately in isolation and fulfill the respective authors' original purpose. It seems that Piccinelli's algorithm is conceptually independent of application, and can be applied to any arbitrary tubular structure, but is somewhat vulnerable to model smoothness and noise. In contrast, Bogunović's algorithm is robust and consistent, but with limited general applicability, as the threshold of the angles that separates each bend is specific to the ICA.
Having provided sufficient knowledge about the capabilities and limitations of both algorithms, combined with an open-source implementation, we would argue that the tools are readily available for others to use. The latter can potentially have a larger impact as many medical image-based studies are currently often limited by being operatordependent, and labor-intensive. Combined, these factors are the bottlenecks that hinder large cohort studies that are needed to cover the vast variability in human anatomy needed for clinical impact [21].
The current results also highlight how input parameters can affect morphometric analysis results of the ICA. Like in many other scientific communities, it is actually fair to question "[...] whether we know what we think we know. " [22]. Therefore, it may currently not be excluded that meta-analyses of the ICA are confounded by the previously mentioned bottlenecks and subjectively chosen parameters. Finally, and maybe most importantly, there is absolutely no guarantee that any of the algorithms actually reflect anatomical landmarks commonly used in radiology. Addressing the latter is however beyond the scope of this paper, and would require development of new and more sophisticated algorithms in collaboration with neuroradiologists.

Conclusion
This study provides an open-source implementation of the two existing algorithms for landmarking the ICA, and suggested parameters for models of similar morphology to the cohorts used in this study. Our investigation has also provided a comprehensive comparison of the algorithms, and shown their capability of capturing the vascular anatomy in the medical image irrespective of operator-dependent variability. Having provided in-depth knowledge about the capabilities and limitations of both algorithms combined with an open-source implementation, the tools are ready for others to use, although application to other vascular regions should be performed with caution.

Computation of the centerline
Landmarking the ICA was performed following the general workflow shown in Fig. 11. The starting point was a 3D model of the ICA, shown in Fig. 11a, from which the centerline was computed; see Fig. 11b. Following the methodology of previous work [12,18], the centerline was here a proxy for computing geometric properties of the model and was parametrized as follows: where t is the arc length parameter.

Centerline resampling using a cardinal spline filter
The surface mesh resolution determines the density of the Voronoi diagram from which the centerline points are computed, resulting in non-uniform spacing [23]. For a fair comparison between the models, we resampled the centerline using a cardinal spline filter to achieve a consistent spacing r between the neighboring points, as shown in Fig. 12. (1)

Centerline smoothing using a Laplacian filter
Computation of geometric properties relies on numerical approximations of higherorder derivatives, which are sensitive to noise from the discrete centerline. As a remedy, we could either smooth the discrete curve, or the resulting geometric profile, where we chose the former approach, as shown in Fig. 11c. We applied a Laplacian filter to the centerline, which performed the following iteration N times: where L(·) is the discrete Laplace operator, and is the smoothing factor.
To define a set of stable input parameters, we conducted a sensitivity analysis by varying r, N, and , as we were unaware of any specified values from previous studies.

Computation of curvature and torsion
The curvature of the parametrized centerline from Equation 1, was computed as follows: where the primes denote the derivatives with respect to t. Curvature is commonly interpreted to measure the deviation from a straight line. Geometrically, it is defined as the inverse of the radius of the osculating circle. Furthermore, following [24], torsion was computed as follows: Torsion can be interpreted to measure how sharply the curve is twisting out of the osculating circle. Of notice, is that the highest derivative is of second and third order for curvature and torsion, respectively.
Alternatively, we may represent the curvature as a vector through the use of two frames: the Frenet-Serret frame and the parallel transport frame [25,26]. In differential geometry, the Frenet-Serret formulas describe a particle's kinematic properties moving along a curve in three dimensions. Generally, the formulas defining the Frenet-Serret frame are as follows: (2) r(t) ← r(t) + L(r(t)), where T , N , B are the tangent, normal, and binormal vector, respectively. Of note is that N points towards the center of the osculating circle, meaning we could define the curvature vector as T ′ (t) = κN (t) , where κ is the scalar curvature. Furthermore, the curvature vector could be expressed in the parallel transport frame, in combination with any orthonormal basis {E 1 , E 2 } , as follows: Here, k 1 and k 2 are the components of T ′ (t) in the orthonormal basis. This representation of the curvature allowed for studying the torsion of a curve, but only computing the second derivative.

The landmarking algorithms
The two landmarking algorithms are conceptually similar, both following the outlined workflow in Fig. 11. However, there are differences between step c and d in Fig. 11. Piccinelli et al. identified locations of curvature and torsion extrema, and proceeded by defining a bend for each curvature peak enclosed by a proximal and a distal torsion peak. Bogunović et al. identified a set of anatomically inspired landmarks, and divided the vessel into a sequence of maximum four bends irrespective of the vessel length. By adopting the clinical nomenclature of Bogunović et al., the ICA was divided into the superior, anterior, posterior and inferior bend, colored blue, green, red, and yellow in Fig. 11e, respectively. Bogunović et al. defined bends as the curved parts of the centerline separated at a local curvature minimum. In contrast to Piccinelli et al., they expressed the curvature as a vector in the parallel transport frame, as defined in Equation 6. Hence, they detected bends by considering the trajectory of the curvature vector. As the curvature vector changes orientation, the basis vectors E 1 and E 2 remain stable along the curve, allowing for the measurement of the angle α between vectors. Using the curve representation in the (k 1 , k 2 )-space, four interfaces were detected from a proximal to distal direction with threshold angles of α = 45 • , 60 • , 45 • , and 110 • , respectively.

Data acquisition and software
We have used three separate datasets to test various aspects of the algorithms, that have previously been described by Piccinelli et al. [12], Bogunović et al. [18], and Valen-Sendstad et al. [16].
Piccinelli et al. used a subset of 34 models from the open-source Aneurisk database, where surface models are segmented from 3D rotational angiography images [27]. Similarly, we selected the first five consecutive cases where the ICA exceeded 70 mm to include the entire ICA siphon. Thus, we restricted our selection to models hosting at least four major bends, to improve consistency of comparison by reducing the variability within the cohort. Details of the data acquisition and processing are explained further in [28]. Bogunović et al. performed segmentation of vascular models from 3D rotational angiographic images following the approach in [19], that was made available to the authors upon request. The models corresponded to the geometries shown in Figs. 5, 7, and 14 of [19], which allowed us to replicate the previously reported results for verification of the implementation. Hence, we applied the algorithms to six of the provided models, one for verification and the remaining five for comparison.
In consistency with the previous section, we chose the models that extended beyond the carotid siphon from the 2015 International Aneurysm Computational Fluid Dynamics (CFD) Challenge, where 26 teams were provided medical images to study variability in segmentation and aneurysm hemodynamics [16,29]. This resulted in 8 of 28 submitted models for assessing robustness.
We have included our implementation of the two landmarking algorithms in the opensource Python framework morphMan [30], which allows for manipulating morphological features in vascular geometries [31]. The morphMan framework is an extension of the vascular modeling toolkit (VMTK) [32], and inherits functionality such as computation of centerlines, curvature and torsion.

Input parameter sensitivity analysis
To investigate the algorithms' sensitivity to the three input parameters used to estimate curvature and torsion, we performed a qualitative analysis on a representative model from [27], followed by a quantitative analysis performed on a cohort of 10 ICA models. The 10 models were collected from [27] and [19] as described in Sect. .
For the qualitative results we varied r = 0.10 ± 0.05 , = 1.2 ± 0.8 , and N = 150 ± 100 consecutively, while keeping the others fixed. Piccinelli's algorithm found an arbitrary number of bends, while Bogunović's algorithm detected a maximum of four bends. Therefore, we computed the coefficient of variation for the number of bends, and bend length, respectively, defined as: where µ is the mean and σ is the standard deviation. The CV was used as a metric to measure the algorithm's success, as we assumed there was a naturally low morphological variability in the ICA's bends, supported by previous clinical morphometric studies [20,[33][34][35].

Verification and comparison of the landmarking algorithms
We performed verification by comparing our results qualitatively against published results. Specifically, we reproduced Figure 4 in [12] and Figure 5 in [19], as they are the only visualizations of the respective algorithms.
Then, to see how the algorithms compared to each other, we performed a qualitative and quantitative comparison of the two algorithms using the same cohort of 10 models as in Sect. . Qualitatively, we considered the number of bends and their location. Quantitatively, we only included the four most proximal bends in our analysis to provide a fair comparison between the algorithms, and have presented the mean bend length with standard deviation, and their respective CV. For both verification and comparison,


Minimum Threshold Determination Method based on Dataset Characteristics in Association Rule Mining

The process of extracting data to obtain useful information is known as data mining. Furthermore, one of the promising and widely used techniques for this extraction process is association rule mining. This technique is used to identify interesting relationships between sets of items in a dataset and predict associative behavior for new data. The first step in association rule mining is the determination of the frequent item set that will be involved in the rule formation process. In this step, a threshold is used to eliminate items excluded in the frequent itemset which is also known as the minimum support. Furthermore, the threshold provides an important role in determining the number of rules generated. However, setting the wrong threshold leads to the failure of the association rule mining to obtain rules. Currently, the minimum support value is determined by the user. This leads to a challenge that becomes worse for a user that is ignorant of the dataset characteristics. In this study, a method was proposed to determine the minimum support value based on the characteristics of the dataset. Furthermore, this required certain criteria to be used as thresholds which led to more adaptive rules according to the needs of the user. The results of this study showed that 6 from 8 datasets, obtained a rule with lift ratio>1 using the minimum threshold value that was determined through this method.

Introduction
The current developments led to large quantities of data growth which were accessible from various locations everywhere at all times [1]. Data availability is a huge asset for an organization because it contains a lot of useful information. Therefore, Data Mining is a way to extract this useful information and patterns [1][2][3][4][5][6]. Furthermore, the Association rule is one of the most basic study topics widely used in Data Mining [1][2][3][4][5][7][8][9][10][11]. It is an important data analysis method that discovers and identifies interesting relationships between sets of items in a dataset and predicts association relationships for new data [7,8,12].
The basic concept of the association rule is to generate rules based on items with frequent occurrence in a transaction. This includes two main processes, namely the determination of frequent itemset and the process of forming rules. A frequent itemset is a collection of items that have a higher frequency of occurrence compared to the threshold value specified in the transaction. This value is also known as the minimum support. The real-time applications of the association rule have several challenges ranging from the presence of very large, multiple, and heterogeneous data sources to difficulty in the determination of the minimum support [7]. Furthermore, the first step in the association rule is to determine the minimum support value [13,14]. Currently, this value is determined by the user despite the difficulty associated with this process. Another difficulty is that the user is ignorant of the dataset characteristics to be searched during this process [3,6,11,[15][16][17][18].
The minimum support value has an important role in determining the value of several rules generated [3]. However, determining a wrong value leads to the failure of the association rule to obtain the required rule [19]. Furthermore, determining a value that is too low leads to the involvement of too many items in the rule formation process.
Conversely, when a value that is too high is obtained, fewer items are involved which leads to the loss of a lot of information. The minimum support values when compared in terms of two factors namely, time and memory showed that a value that is too low will require more of these two factors when compared to a higher value [6,11,20]. Currently, the method used to determine the minimum support is based on the intuitiveness of the user.
The association rule process is repeated through the change of the minimum support value when the rule obtained does not match. However, this does not guarantee that a rule will be generated with the input minimum support value.
Decision-makers are required to make the right strategic choices which lead to the adjustment of current conditions which are full of volatility, uncertainty, complexity, and ambiguity. This is known as the VUCA (Volatility, Uncertainty, Complexity, Ambiguity) world [21]. Furthermore, the current conditions also demand the adaptive transformation of the association rules to meet the needs of the users. Decision-makers have different criteria which are used to obtain the information they need. Therefore the rule formation process should pay attention to the criteria desired by the users to obtain adaptive Rules [22]. Furthermore, to meet these needs, the determination of frequent itemset should not only be based on the frequency of occurrence of an item but also involve another criterion called item utility [10,[23][24][25]. Therefore, the resulting rule will be adaptive according to the criteria desired by the user.
This study which proposes a method to determine the minimum support value based on the characteristics of the dataset and other criteria can also be used as assessments in the process of forming the rule. The main contributions of this study include: 1. The proposition of a method to determine the minimum support value based on the characteristics of the dataset.
2. The generation of a minimum support value-based not only on the frequency of occurrence of items but also based on certain criteria affecting the rule formation process such as price, profit, or item usability value.
3. The generation of a minimum support value certainly forms a rule that does not require the user to determine this value at the beginning.
This study is divided into several parts. Parts II, III, IV and V describe and explains related studies, proposed methods, experimental results and discussion and conclusions respectively.

Association Rule
The association rule mining was first proposed in a study by Agrawal [26,27]. This study developed a focus on different topics ranging from high utility itemset [23,25,[28][29][30][31], Top-K [5,11,32], Skyline [6,10,33], Multicriteria [34][35][36] and Meta association rules [37][38][39]. Furthermore, the main concept of association rule mining can be formally defined as follows: I = {i1, i2, . . ., im} is a set of items and D is a set of transactions T, where a set of transactions T is also a set of items, therefore, T ⊆ I. Furthermore, provided that A is a set of items, Transaction T is said to contain A if and only if A ⊆ T. Association rules are from A  B, where A ⊆ I, B ⊆ I, and A ∩ B = Ø. In addition, rule A  B has support in transaction set D provided that s% of transactions in D contain A ∪ B [4,22,40]. This support is shown by the occurrence frequency of items which is calculated by observing the ratio between the frequency of transactions containing itemset A divided by the total transactions. In general, it can be seen in the formula below [37]: Confidence is another threshold used in determining the rule apart from the support value. It is the ratio between the number of transactions containing items A and B divided by transactions containing item A for rule AB.
The confidence value of rule A  B is obtained by the formula [37]: Where: The general framework of the association rule is to extract a rule with a support value for an item that exceeds the minimum support and confidence value. Therefore, this rule exceeds the minimum confidence value specified by the user. In this case, it can be stated that A  B is included in the frequent and confidence category (strong rule) provided that Supp(AB) ≥ minsupp and Conf(AB) ≥ minconf respectively.
To evaluate rule, lift ratio can be used [35,36,[41][42][43][44][45][46][47][48]. Lift ratio is the ratio between the support value of the rule with the antecedent and consequent support value. The higher of lift ratio value, the more interest rule or called the strong rule. A rule is called interest and strong rule if the lift ratio value > 1 because it shows that is a positive correlation between the premise and conclusion of this association rule [36,48]. The lift ratio value can be calculated by the formula [36,[41][42][43]47,48]:

Minimum Support
The basic concept of the association rule requires the user to specify a minimum support value at the beginning.
This value usually applies uniformly to all items, although in reality, different items may have different criteria for assessing them. Therefore, studies about multiple minimum support which state that the support value should vary for different items have emerged [9,23,49,50]. However, the implementation of this system adds a task for the user, which is to determine the minimum support for each item.
Furthermore, the difficulty of determining the minimum support value by the user has led to a new field of study, namely association rules without the use of minimum support such as Top-K [5,11,19,32,51] and Skyline [6,10,33,52]. The Top-k association rule does not require the minimum support value because in this method the user is only asked to determine the k value, which is the number of rules that will be generated in the rule formation process. Therefore, it is easier for users to determine the k value because they explicitly know the number of rule results they want to obtain.
The Skyline algorithm was first proposed by Borzsony [52] and later developed by Goyal [33]. It is a point that is not dominated by other points [52]. This algorithm was combined by Jerry Chun-Wei Lin [10] and Jeng-Shyang Pan [6] to produce association rules. Furthermore, this study does not use minimum support but instead makes use of the maximum utility (utilmax) obtained from each iteration performed by the utility list structure.
Based on the results of the previous review [20], the association rules require a minimum support value to reduce the items involved in the rule formation process. Furthermore, the existence of this threshold can reduce the time and memory required in the rule formation process. Therefore, regardless of the term, starting from Minimum Utility, Maximum Utility to Minimum Support, this threshold is required for the association rule process. Meanwhile, processes without the threshold will involve all the items present and require more time and memory, which will lead to rules that may not be as desired.

The Proposed Model
To determine the minimum support value in the association rule, a special method is needed to determine the value according to the characteristics of the dataset which involves certain criteria according to the desires of the user. This study proposed an adaptive support method to answer these needs, as shown in Figure 1.

Algorithm.1 Adaptive Support Algorithm
In the adaptive support model, the determination of the minimum support value is based on several factors which include:

Characteristics of the dataset
In determining the minimum support value, the user should know in advance, the characteristics of the dataset that will be processed for rule formation. This is because several characteristic factors of the dataset will affect the suitable minimum support value. Furthermore, for an adaptive support mode, the factor used to determine the minimum support value is shown from the number of items contained in the transaction, the number of transactions, the average number of items in each transaction, and the support value for each item.

Specific criteria (utility for each item)
To be able to produce adaptive rules, a criterion is required as an assessment for an item known as a frequent itemset with the right to be involved in the rule formation process. Furthermore, these criteria can be determined by the user and each item has its own criteria values. For example, a user who wants to get a rule for the most expensive item has an involved criterion such as, the item price. In addition, another example is when a user wants a rule with the biggest profit then, the criterion for the item involved is the profit from each item.
Based on both types of inputs, the calculation process is carried out according to algorithm 1 to obtain adaptive support. The calculation stages are as follows: 1. Calculation of the support value for each item in the dataset with the following formula: 2. Calculation of the utility for each item in the dataset with the following formula: 3. Calculation of the average utility for the entire transaction with the following formula: () sup ||

Util d ave D
  [6] 4. Calculation of the minimum threshold value used for the rule formation process which is the average utility value divided by the total existing transactions through the following formula: sup min sup || ave D  [7] 5. Performance of the rule formation process with existing methods through the apriori algorithm, fpgrowth, or other algorithms

Data Experiment
The special dataset for the association rule case used in this study was obtained from SPMF [53]. The dataset criteria used can be seen in table 1.

Result
The proposed adaptive support method was carried out on 8 datasets according to  The trial of the proposed adaptive support method used two basic algorithms in the association rule, namely Apriori and Fpgrowth [10]. The Apriori algorithm used a level-wise approach and generated candidate items for each level [26]. Meanwhile, the fpgrowth algorithm used the pattern growth method but did not generate candidates for each level. After the elimination of itemset with minimum support, the next step was to obtain a Frequent Pattern-Tree [54]. The trial was carried out from the highest minimum support value at 100% and then repeated while a reduction of this value occurred. All minimum support values are not tested on all datasets because the number of rules is different. The more rules that are generated, the more difficult it will be in the decision-making process. For example, in the connect dataset with a minimum support value of 70%, it produces a rule 392,469,141 using the fpgrowth algorithm and consumes a lot of resources (runtime and memory) so the test is stopped. Table 3-6 shows the test results of each dataset for each minimum support value using the a priori and fpgrowth algorithms. The blue color in the table is the minimum support value proposed by the adaptive support method.     0  0  175  0  10%  1213180  0  0  168  0  20%  37757  0  1058700  0  77  0  30%  73  0  64794  0  44  0  40%  4  0  6297  0  7  0  50%  1431849  3  0  816  0  7  0  60%  121658  0  0  159  0  7  0  70%  6125  0  0  35  996275  0  4  0  80%  367  0  0  22  45541  0  0  0  90%  4  0  0  9  546  0  0  0  100%  0  0  0  2  0  0  0  0 Based on tables 3-6, it was shown that for each different dataset, the same minimum support value led to a varied number of rules. This was because of the dataset characteristics consisting of the number of items, the average item in each transaction, and the different density values. Furthermore, the trials that have been carried out showed that the higher minimum support value led to a smaller number of rules and runtimes and vice versa. The minimum support value generated by the adaptive rule method when compared with the results of trials using the fpgrowth and apriori algorithms is shown in Figure 2. adaptive support can generate a rule and if viewed from the quality, adaptive support produces a rule that has a lift ratio value > 1. In addition, with the proposed adaptive support value, users no longer need to guess the appropriate minimum support value that can generate rules. So that there is no longer a possibility that with the specified minimum support value, it does not get a rule, or the number of rules is 0 and must repeat the experiment with another minimum support value. Figure 3 shows that the smaller the minimum support value, the more rules are generated. The red line in Figure   3 shows the proposed minimum support value based on the adaptive support method.

Conclusion and Future Work
The minimum support value is important and has a big influence on the rule formation process in the association rule. The errors obtained when determining this resulting rule were not desired. Furthermore, the determination of this value was difficult especially if the user is ignorant of the dataset characteristics as a factor which was used as a reference in determining the minimum support value. This is because datasets with a high level of density required a larger minimum support value when compared to datasets with low density. This density level is the average value of the occurrence frequency of each item in the dataset. Therefore, an adaptive support model which determined the minimum support value based on the characteristics of the dataset was proposed. In addition, certain criteria leading to adaptive rules following the desires of the user were included.
From the study results on 9 datasets, 8 datasets obtained a rule based on the minimum support value suggested by the adaptive support model. In the future, the author will integrate the multicriteria system model [55] and this adaptive support method to obtain a completely adaptive rule model [22].


Publishing open-access bibliographical data on Ancient Greek and Latin texts: challenges, constraints, progression

We present here both some of our thoughts on methodology in relation to the specific constraints that complexify the ways of structuring and accessing bibliographical data in the Sciences of Antiquity, and the solutions adopted by the IPhiS-CIRIS project for dealing with these constraints. The project began in 2014 in a general scientific environment that was still being standardised and structured, with digital bibliographical resources in this disciplinary field becoming increasingly numerous, although of uneven quality and hard to access and/or private.

INTRODUCTION
The publication of bibliographical data on Classical and Late Antiquity 2 has a considerable history already, since it dates back to the early twentieth century with the publication in 1927 of the two volumes of an important retrospective bibliography entitled Dix Années de Bibliographie Classique (1914)(1915)(1916)(1917)(1918)(1919)(1920)(1921)(1922)(1923)(1924) [Ten years of Classical bibliography, 1914-1924, by Jules Marouzeau 3 . In keeping with the evolving needs specific to each discipline with regard to Antiquity, a number of specialised bibliographies have flourished with the intention of providing a comprehensive list of works published in their respective fields. Some of these bibliographies have since made use of electronic media for their circulation, continuing to maintain the paper version as their reference, while others have been digital from the outset. Thus each has its own classification scheme and indexing system, and sometimes even its own canonical forms of authority. Since most of these resources are proprietary, it is not their natural vocation to be mutually compatible: at best, certain practices tend towards a standardisation of formats and classification schemes. The work required in terms of referencing the data to make it interoperable has not yet been completed, although numerous initiatives demonstrate a desire to use common repositories. The IPhiS-CIRIS project ('Information Philologique -Savoirs Antiques' [philological information -ancient knowledge], Centre Jean Pépin, CNRS-ENS) is participating more particularly in defining a set of reference data of names of authors and titles of ancient works to be fed into a database of editions of ancient texts. When drawing up these files we come up against a number of difficulties: concurrent forms for the same entry, inexistent forms of the state of certain works in the existing repositories, duplicates, homonymic forms of titles or authors, dubious attributions of works to a particular author, controversial attributions to various authors, etc. Deciding on the forms of these tables and the links between them created a number of technical difficulties from the outset; these are characteristic of Antiquity and have not yet been fully dealt with in the computer modelling.

A blossoming of initiatives
There is today a large quantity of bibliographical resources in the field of Classical and Late Antiquity that is available -partly or fully -on the Internet. Mention may be made of L'Année Philologique, published annually since 2017 by Brepols, after having for a long time been distributed by Les Belles-Lettres: not only is this bibliography the only one to attempt to cover the group of disciplines encompassing Classical and Late Antiquity -it is also the oldest and largest bibliography listing studies on these authors and editions of texts, and a fee is charged for access. The other resources are specialised bibliographies in the form of regularly updated databases. There are many examples 4 , but we may mention here: • Base d'Information Bibliographique en Patristique (free access) 5 ; • Bibliographie papyrologique en ligne (free access) 6 ; • L'Année épigraphique (paywall) 7 ; • Syri.ac: An annotated bibliography of Syriac resources online (free access) 8 ; • Répertoire des sources philosophiques antiques (free access) 9 ; • Droits Antiques (free access) 10 .
New formats of shared bibliographical resources are springing up all the time, using software specifically designed for organising bibliographies. It is now possible, for example, to share collections and libraries in Zotero 11 . In addition, we are also seeing the appearance of digital libraries of ancient editions and manuscripts: each library has its own criteria for managing its collections of manuscripts and ancient editions, developing tools in-house that not only allow consultation but also, more often than not, prevent or restrict the downloading of data.
Mention should also be made of the massive but disorganised (and of very uneven quality) digitalisation work carried out by GoogleBooks / GoogleScholars, archive.org, HathiTrust (with restrictions on access from outside the US) projects, and the development of academic networks (such as academia.edu) for following up topics and researchers. These are new approaches to the publication and circulation of bibliographical data that -whatever we think of themcorrespond to new uses or new expectations in academic circles. Thus there is a host of initiatives in this field, but we are still at an experimental stage in terms of digitalising and structuring bibliographical data. There are a number of problems: firstly the large number of proprietary resources, and secondly the fact that the good quality open resources are still not well known outside digital humanities circles. Demand for the production of open data in fact involves producing data that meets not only the required technical standards but also scientific demands, always seeking to deliver data that is accessible to a wide public, whether or not its members are technologically informed. Thus it is necessary to bind together the political and scientific issue of access with the technical issues. This demands that we do not compromise on excellent scientific quality, ergonomics, ease of use, and good practices ensuring the continued existence of the tools, and it is sometimes difficult to maintain our stand.

The inexistent common portal for bibliography on Antiquity
In an ideal world, we might imagine that all these databases could be compiled into one vast bibliography of Antiquity, but so far there is very little interoperability among them. The problem is firstly one of quality, because of the absence of convergence among the strictly bibliographical structuring systems, such as the Dublin Core, which is used more than extensively in describing standardised bibliographical data, and the systems that describe ancient sources which use specific and sometimes contradictory characters. True interoperability among bibliographical databases would require a standardisation not only of the choices applied in describing the bibliographical resources themselves (articles, monographs, editions) but also of their material sources (manuscripts, papyri, inscriptions) and their textual sources (standardisation of titles and authors). It is important to underline the effort made by the Project Biblissima 12 to work on interoperability of a large variety of databases concerning history of books and libraries in the Middle Age and the Renaissance, including research tools for ancient authors and texts. We shall see below more specifically why true operability remains on a distant horizon with regard to the Sciences of Antiquity, and how we, for our part, have broached the issue. The problem is also one of quantity. Recent years have seen an inflation in both the bibliographical mass and the number of initiatives to make use of it, an immediate consequence of the bibliometric evaluation systems set up by the academic institutions. This burgeoning of scientific literature, even though it is a sign of the vitality of the research work being carried out, eventually wilts when faced with the defective referencing system that is in use. There is no longer any single bibliographical undertaking capable of coping with the entire quantity of scientific production 13 . We should also add that recent years have seen a renewal of scientific approaches in the field of Antiquity, with the emergence of areas of study devoted to cultures other than those of the Greco-Roman world in its strictest sense, and this in turn has led to numerous studies on the transmission and exchange of textual, literary, technical and philosophico-religious productions. However, the bibliographical tools that include these aspects are not yet particularly developed, and researchers are often faced with a fragmentation of resources, with access to each specialised bibliography creating yet another obstacle that needs to be overcome.

"Back to the source"
Rather than bemoaning the fact that we are not able to embrace the galaxy of scientific publications related to Classical Antiquity, we have, with the IPhiS-CIRIS project, opted for 12 https://biblissima.fr/; consulted on 23 April 2021. 13 While we cannot entirely subscribe to the political hypotheses put forward by Claude Calame in [Calame, 2006], we cannot but subscribe to his visionary description, set out as early as 1999, of the editorial frenzy that took hold of the academic world in general and the Sciences of Antiquity in particular and produced a situation in which no researcher is now able to claim to have knowledge of the entire annual production in his/her disciplinary field, however confident he/she may be. developing a tool in phase with these new methods, in terms of both content and ergonomics 14 . The first stage therefore involved refining this abundance of material in order to concentrate our efforts on a homogenous part of the publications. We chose to concentrate first on the editions of texts and then on those studies whose prime object is to identify authors and establish texts and their tradition. In doing so we introduced a new methodology: we chose to consider the text as the starting point for the architecture of our bibliographical database. However, there is nothing self-evident about identifying and referencing texts: there is no fixed form of titles 15 in Antiquity; many texts, in fragmentary form, have come down to us without any title, and others have been reworked and the various versions need to be differentiated, while others are no longer attributed with any certainty to a particular author, or were for a certain amount of time before scientific progress challenged their attribution, and so on. Our aim -on a small yet ambitious scale -was therefore reformulated at the start of the IPhiS project in 2014 as being: 1) to supply as complete as possible a bibliography of the editions of Greek and Latin texts from the time printing began up to the present day, including in the different states in which they are known (in their original language or in translation; in partial or complete form; treated as part of a larger set; etc.); 2) to supply this bibliography in a structured format that would allow the exchange of data with other bibliographical databases, whether specialised in any particular discipline or not; 3) to provide, as far as possible, access to the resource by indicating the link to an open-access digitalisation of the edition or, if it exists, to the manuscripts used as the basis for the edition, to make it easier for our users to find their way around the global landscape of digital resources concerning Antiquity 16 . The project has given rise to a working database, IPhiS, which is not open to the public, and to a web interface for published data once it has been validated by the CIRIS 17 team.

What constitutes an ancient text
Ancient texts, which form the core of our project, are above all shifting realities: between the initial form of a text published as the work of a given author and the form in which it has come down to us there are quantities of intermediate forms which we lump together in the reference title of the text 18 . There are any number of possible causes for an early text being deformed into the version of it we know today: the text may have been reworked by its original author and we are in possession of several concurrent versions; the author of the text may be uncertain or under debate; the text may not have reached us in its original or complete form, either by choice (quoted by another author, for example) or by accident (a fragmentary, defective or badly copied 14 We shall not set out again in detail here in the following pages the entire genesis of the project, which is well documented already. It was presented in detail at the Digit-Hum workshop in 2020 (https://hdl.handle.net/10670/1.dpif0n; consulted on 23 April 2021). We shall merely recall in this footnote all the active members of the project, all of whom contributed to the results presented in this text: Laurent Capron, Julie Giovacchini, Sébastien Grignon and Juliette Lemaire of the Centre Jean Pépin, and Bernard Weiss of the ARDIS unit (UPS2259) for implementing the computerised development of the various models. 15 See our description of the data model selected and choice of text as the principal node in [Giovacchini et al., 2017 p. 6]. 16 It has to be underlined that, although our goal is to provide bibliographical data about editions of texts, we also try to give a direct link to open access databases of texts like Perseus (http://www.perseus.tufts.edu/hopper/collection?collection=Perseus:collection:Greco-Roman; consulted on 23 April 2021). 17 https://ciris.huma-num.fr/ consulted on 23 April 2021. The public interface is available in four languages (French, English, German and Latin). Since the data are bibliographical data, they cannot be translated and remain in their original language. The content block reproduces most of the time the table of contents of the book. In some cases, we provide some comments about the edition; these comments are always in French. 18 See for example [Giovacchini, 2016 1 and 2]. manuscript), etc. However, all these forms refer to a single ideal conceptual philological object, which contains in it all the forms it has already been able to take and could still take in the future. The task of referencing these objects is ongoing, and no catalogue today can claim to be exhaustive or complete. Developments in the field of research also mean that this referencing cannot, by its very nature, be definitive, even if we seek to establish sustainable data: anyone could be caught out by an unexpected discovery that challenges an attribution or a title, or by the rediscovery of a text for which we thought we had reliable, constant information.

The problem of title
The question of the title of the ancient text is in itself a problem: in our efforts to draw up a list of titles we had to consider a number of realities that corresponded to the expression 'title'. Some texts -such as plays and novels -really do have a title. It is less evident when we are dealing with scientific, philosophical or religious treatises, since they would be qualified as '(treatise) on a particular subject', sometimes with a sub-title. This is then an explanatory title, but its form is not fixed and it may evolve, in copies that are made of it, by abbreviation, or by extension. Other texts have no other title than that given by a subsequent publisher according to their genre ('oration', 'speech', 'homily', etc.): these texts are often passed down to us in a corpus, within which they are numbered; this order becomes 'canonical' until new manuscripts are discovered, challenging the order by adding new texts or removing others, and we are then faced with duplicate or triplicate numberings. Most of the poetry that comes down to us from Antiquity is only known in anthologies and collections within which the poems are numbered, but the same poem, since it is included in several collections, is given several identifiers: we then choose to consider the compilation as the reference text, and the poem as a constituent part rather than as a text in its own right. Lastly, an incalculable number of texts have come down to us with no title at all, in isolation, sometimes only as a fragment: if their content is deemed important, they are given a title that quickly becomes the reference title. However, some of these titles are no more than designations of the accident as a result of which the text has come down to us: for example, what is designated as the 'Palatine Anthology' is a collection of poems which has come down to us via a manuscript found in the Palatine Library in Heidelberg 19 . We have sometimes chosen to propose a new, more meaningful title for a text which has a relatively meaningless title 20 . It is thus this multiplicity of situations that the field "title" covers. In our database we have made room for 'aliases' that retain the history of the titles, when they vary from one publisher to another, or from one piece of manuscript evidence to another, or simply because we give Greek texts a working title in Latin even though we are fully aware that the original title is the Greek one. Since we always provide for each text a cross-reference towards other repertories of texts, we often notice that these repertories don't use the same exact title for the same text. If there is no reason to reject all of these variant titles, we tend to keep the title given in the Thesaurus Linguae Graecae Canon 21 of texts or in the Library of Latin Texts 22 for classical texts, and the title given in the Clavis Clavium 23 for Christian texts.

Linking a text to an author
Another difficulty with referencing is that of creating a link between a text and an author. Two specific situations had to be taken into account in our bibliographical database: texts with no identified author, and texts whose presumed author is or has been disputed. In both cases, we must report the lack of precision or the ambiguity in our knowledge, without hiding anything.

Texts with no author
This first case appears simple, since it is possible to attribute a text with no author to an 'anonymous' author. However, the entry 'anonymous' in the table of authors would refer to just one person whose name has been lost! Our approach has therefore been to use collective headings in the 'creator author' field, making it possible to classify our texts in categories without concealing the loss of the name of their author, and providing the possibility of finding the text by means of a themed search. The headings and number of these collective entries are left completely up to us, but there is a tendency in academic circles to adopt common practices, and so we have tried to harmonise our headings with those used in other databases, particularly the Pinakes database 24 developed by the Greek section at the IRHT (CNRS -UPR 841) 25 . Thus these collective headings function as "supra-authors" and it would have been perfectly logical for us to attribute to each text, whether its author was known or not, a collective heading in addition to its possible author, in the same way as one would use markers or labels when organising index cards. We decided to only use this option in the case of unknown authors or for certain large-scale groupings in mainly early editions. Initially, we chose to use these names only in the case of texts without a known author, that is to say as an alternative generic author name. But we do not rule out modifying this parameter later and systematically assigning each text one or more of these names to allow a thematic search in the database.

Disputed attribution
The other situation is when texts have come down to us under the name of an author that subsequently proves to be incorrect, either specifically and deliberately -for example the many cases of religious authors whose work was banned but some of their texts continued to be copied under the name of another author who was authorised -, or as the result of an error in transmission caused by homonymy or confusion. Sometimes modern publishers of ancient texts took up such problems of attribution a while ago, and in some cases they have come up with a 24 https://pinakes.irht.cnrs.fr/; consulted on 21 April 2021. 25 List of our headings in the internal documentation for the database, produced by Juliette Lemaire: available at https://ciris.huma-num.fr/manuel/doku.php?id=manuelciris:anonymes&do=login; consulted on 21 April 2021. Collective headings in Pinakes are listed at: https://pinakes.irht.cnrs.fr/mode-d-emploi.html; consulted on 21 April 2021. solution. Thus some texts no longer circulate under the wrong author's name, and once the controversy has been deemed closed for several decades, we make no mention of this other than in a comment on the text. But much doubt still remains about many texts, and we felt it was necessary to report on this as a stage in academic research.
We therefore opted for creating the notion of 'disputed attribution' by mentioning specifically the bibliography involved in the controversy. It is therefore possible, in our database, to list a text under several authors and to mention which authors are accepted or rejected by modern publishers, with the corresponding bibliography. Apart from the fact that this provides additional access to the bibliographical data concerned, our solution makes use of the state of research and the importance of considering the uncertainty that sometimes surrounds the texts that have come down to us from Antiquity, by presenting such texts to the user on both the page for the author (Figure 1) and the page for the corresponding text ( Figure 2).

Geographical data
It is usual to designate certain Ancient authors by adding to their name that of a town or country to which they are attached by birth or the place of their main activity, particularly in cases of homonymy. Wherever possible we have preferred sequencing these two items of information, the one prosopographic and the other toponymic. However, this obviously supposes that the geographical data has been checked and crossed-referenced against the historical geography repositories. Where this was known, we linked each author to one or more places, possibly specifying the event associated with the place (birth, education, activity, death). Here again we made it possible to weight the reliability of the historical data by adding an indication of whether the data is certain or disputed. This specific data is displayed in an extension of the CIRIS application in a cartographic format 26 that we felt was more pertinent. For the time being, only the geographical data of the philosophical authors are being published; ultimately we hope to be able to provide this data for all the Ancient authors in the database 27 . 26 https://ciris.huma-num.fr/cartographie.php?langue=fr; consulted on 23 April 2021. See also Fig. 12 supra. The specific publication of this geographical data has constituted an appendix to the project which we present in the report [Giovacchini et al., 2020]. 27 We have chosen to display our biographic data in a modern map, with contemporaneous place names. This choice is a pedagogical one, and is directly focused on the accessibility of our tool for non-scholar users and particularly high school students.

A bibliography in its environment
For the files of both titles and authors, we rely systematically whenever possible on repositories that have already been checked and found reliable, to which we direct users (Pinakes, VIAF, DataBNF, etc), but if appropriate we also propose our own repository, which has our own structuring. Once we had opted for acknowledging the rightful place of uncertain data on bibliographical and philological objects with rather complex contours, presenting a classification meant both respecting the standards without which it is impossible to share data as well as making decisions reaching well beyond straightforward indexing or alignment, and therefore supposed a degree of scientific risk-taking. In the history of the IPhiS-CIRIS project, accessibility has played a structuring role. Initially, the project was constructed on the basis of an ambition to offer full open access, in reaction to the idiosyncratic and extremely constricting proprietary model of the Année Philologique 28 . Thus the notion of open access was directly correlated to the question of the structuring and display of the data. Opening up data is not simply the unequivocal gesture of lifting a barrier: rather it means from the outset thinking of the data as an element that may be shared or potentially improved or altered within a complex environment -what is often nowadays called a 'data ecosystem'. Which is tantamount to saying that accessibility is necessarily free of charge, but that is not its only feature. The project therefore exploits a dimension of structuring that is in fact already historically consubstantial with the Classical sources. Since the time of the very first publishers, Greco-Latin literary texts -because of their often incomplete or fragmentary state and the existence of successive versions that form overlays rather than replacements -possess systems of unique identifiers of varying complexity.

Many non-classicists from academia and beyond still express surprise that classicists have been aggressively integrating computerized tools into their field for a generation. The study of Greco-Roman antiquity is, however, a data-intensive enterprise.
Classicists have for thousands of years been developing lexica, encyclopedias, commentaries, critical editions, and other elements of scholarly infrastructure that are best suited to an electronic environment. Classicists have placed great emphasis on systematic knowledge management and engineering. The adoption of electronic methods thus reflects a very old impulse within the field of classics. The paper knowledge based on Greco-Roman antiquity is immense and well organized; classicists, for example, established standard, persistent citations schemes for most major authors, thus allowing us to convert nineteenth-century reference tools into useful electronic databases. Classicists are thus well prepared to exploit emerging digital systems. For many classicists, electronic media are interesting not (only) because they are new and exciting but because they allow us to pursue more effectively intellectual avenues than had been feasible with paper 29 .
Since the time of the monuments of German erudition in the eighteenth and nineteenth centuries, Classicists have always considered manipulation of the corpora as constituting a consultation, far beyond cursive continuous reading. Consultation supposes transversality and navigation; the corpora are explored and refer back to each other in an inchoative method that can never end. This mode of appropriation is necessary in as much as ancient texts are not units that are closed in on themselves but rather are open samples that are always subject to revision and rereading and above all that serve as sources for other texts. By its very nature, one Greco-Latin literary text refers to other texts in the present state of transmission: one text transmits other texts and is itself transmitted by others. (By 'source' we mean here the material source as well as the historical and literary source, both meanings mingling fairly imperceptibly in the case of texts of the Greco-Latin Antiquity period 30 .) Thus the very first step towards accessibility consists, as we have seen, of modelling this network of inter-generating texts, and making the text as a source the pivotal point or central table of the database. The second stage supposes adding to this central table a sufficient number of controlled identifiers to allow unambiguous navigation both inside and outside the database. These two gestures suppose a distancing from the usual structuring of a bibliography: departing from the traditional documentary model which constructs the reference around the modern edition and is not affected by fine granularity (fragment, extract, etc), considering the modern edition as the culminating point of a long historical process, one state of the text among others, neither the latest nor the 'best', and focusing attention on the source text identified as a sort of bibliographical invariable in its ideal form, whose actual occurrences are so many versions. This involves no more or less than applying the Lachmannian notion of archetype to the bibliography, albeit by shedding any naively realist posture 31 . It is supposed that a text was produced in a given period by a given author on a given subject; if the text in its empiric form is no longer accessible today, it has produced a certain number of historical avatars which all have in common a desire to be reproductions or indirect representations of the text, which must then be taken seriously as the focus, raison d'être and true purpose of these avatars. This is truly a matter of accessibility, since it is the only modelling that actually meets the expectations of the users of a bibliographical database; these users are primarily readers, as they read and carry out research on texts, but they are also authors who produce texts themselves. This departure from the usual bibliographical frame is also an interesting way of converging towards other schemes that are less strictly disciplinary and more generalist, with a view to strengthening the navigability of the data.

Semanticizing IPhiS
In 2019, the IPhiS database and its public web version (CIRIS) migrated from a local server on the Villejuif site to Huma-Num's Very Large Research Infrastructure (TGIR). The conditions for this migration were excellent, offering guarantees of incomparable permanence compared with the constraints of local hosting. The operation, although highly beneficial for the project, was dependent on one medium-term condition: it had to be possible for the Isidore 32 search engine to harvest the essential CIRIS data. Since Isidore functions according to the principles of the web of linked data, we had to 'translate' our traditional relational database in such a way as to make it compatible with a number of semantic constraints, which meant converting the main IPhiS data into searchable resources meeting the semantic standards accepted by Isidore 33 . 30 This is a problem that justifies the title of our job at the CNRS: the analysis of source, many examples of which are to be found in our team's research logbook; see for example [Capron, 2016c] and [Grignon, 2016.]. 31 An expression of this type of realism forms a common theme running through recent experiments carried out on citing Ancient sources; all the models proposed are based on historical breakdowns and undisputed nomenclatures that are deemed historical fact, whereas they are actually no more than reconstructions. Thus the most advanced tool available to date in terms of citation, the CapiTainS environment (presented for example in [Clérice, 2017]), proposes alignments that are technically extremely advanced, constructed on the basis of the CTS (Canonical Text Services) model, which in turn uses a text identification system that does not dispute the pertinence of the titles being aligned. Although in theory this system is indeed able to allow title variants to be taken into account by distinguishing works from versions of works, in fact it only does so marginally, as it excludes for example the possibility of fuzzy matches, variable divisions, and intertextual conversion. 32 https://isidore.science/ ; consulted on 23 April 2021. 33 There is nothing original in this process of semanticisation on our part. Indeed it is a process that has become banal: items of digital data are adapted to the constraints of the data web so that they will comply with the Isidore is a harvester and a tool of enrichment, but to be able to harvest and enrich it first needs to be able to recognise, identify and link. It is therefore necessary to propose data set out in a format it is able to interpret, and for the actual items of data to be described using metadata Isidore recognises. The Isidore documentation offers two options for preparing databases: • Propose data using an XML flow of standardised metadata using the OAI-PMH protocol associated with metadata in Dublin Core format. This method is suitable for use with documentary databases, corpora, scientific archives and document/data libraries. For example, a tool such as Omeka offers OAI-PMH via a module. 34 • Propose data using an XML sitemap flow pointing to webpages containing RDFa metadata. This method is suitable for research programme websites presenting corpora of documents or data, scientific blogs (but not Hypotheses.org), and webpages in general. 35 We 36 selected the first option, specifically adapted to our case, and decided to do so by making use of another tool proposed by the Huma-Num grid of services: a Nakala 37 depository. This solution supplied us with an OAI-PMH depository generated automatically by our posting in Nakala without having to incorporate the data directly in a database that was already substantial enough; it also enabled us to select more closely which sets of data were most pertinent for harvesting purposes. This option nevertheless raised other problems, and not all of them have as yet been completely resolved. The principle of a Nakala depository is relatively simple: it is an autonomous uploading area in which items of data are associated either manually or using an API with metadata standardised according to the grids of Dublin Core vocabulary, which is currently the most frequently used model for producing bibliographical metadata 38 . The first question that had to be asked was therefore whether the fields in the various IPhiS tables matched those of the Dublin Core vocabulary, with a view to being able to establish an equivalence between the two, this being a prerequisite for the possibility of interoperability between IPhiS and Nakala. If we compare the IPhiS data model with the Dublin Core vocabulary, we can see straight away that there are considerable convergences -which is perfectly natural and to be expected of a bibliographical database. The most important of these convergences is the adaptation in IPhiS of an important distinction, namely differentiating between the creator of a resource and a contributor to a resource. It is a particular feature of ancient texts that their transmission involves a number of participants who, although they are not all authors strictly speaking, have nevertheless made a not inconsiderable contribution to the elaboration of a given text up to its final state: these participants include publishers, printers, translators and commentators. The distinction between creator and contributor was from the outset an elegant solution in the data model for differentiating sufficiently clearly the various stages in the transmission of the text; we preferred this to the more traditional distinction between ancient and modern authors which is based on a vague and relatively inoperative temporal difference as we wish to distinguish not between periods but between interventions requirements of search engines, in a frame that is often institutional. We may note, for example, that the tool SKOS Play allowing the conversion of data into RDF/SKOS from an Excel spreadsheet was developed with funding from the Luxembourg State in order to produce public data in a semantic format (cf. [Francart, 2017]). 34 http://info.omeka.net/build-a-website/manage-plugins/oai-pmh-repository/; consulted on 23 April 2021. 35 https://documentation.huma-num.fr/isidore/; consulted on 23 April 2021. 36 The development and implementation work described in this section was carried out mainly by Bernard Weiss and Julie Giovacchini (ontology and mapping with the DCMI by Julie Giovacchini, scripts for automated supply to the Nakala API by Bernard Weiss); the tests were devised jointly by both these researchers. 37 https://www.nakala.fr/ consulted on 23 April 2021. 38 This vocabulary is described and documented on the website of the Dublin Core Metadata Initiative: https://www.dublincore.org/specifications/dublin-core/dcmi-terms/; consulted on 23 April 2021. on the texts. Thus the IPhiS data model allows the entry of an 'ancient' author as a contributor to a text on a par with a humanist or contemporary publisher.

Adapting to Nakala
For the actual uploading in Nakala, we had to overcome a number of relatively substantial technical constraints, which obliged us to delimit very clearly both what we wanted to display and our choice of metadata to accompany the display.
In the first place, Nakala is mainly intended to be used for uploading data in the form of files attached to metadata, and the main working interface is a visual interface that only allows the individual uploading of file after file. But our situation is very different: we want to post large sets of data in an automated way, by supplying the depository directly so that it updates itself at the same time as the database, which is designed to continue to receive data indefinitely. We therefore concentrated firstly on uploading the records of editions in the presentation proposed by CIRIS, as these constitute the most important and complete IPhiS data, leaving aside temporarily the direct display of the thesauruses of Ancient authors and texts. Our Nakala depository is envisaged as a place for displaying edition records which are considered as so many separate files, each comprising an image (PDF or screen capture of the page of the record in CIRIS) and a set of metadata (Figures 3 and 4 39 ). 39 The screen captures were generated at the time of the stage in the test of the procedure described in these pages, as the Nakala depository whose development we describe is not yet public. Also, in order to automate the process and upload large quantities, we had to access Nakala via its API 40 . Using a script, we recuperated the necessary files and metadata in IPhiS and then uploaded them in the API by using a 'post' request. This is the only way the depository can be updated automatically. The script, first developed in PHP, is still experimental, but once it has been stabilised, the next stage of the work will consist of proposing an open version in PHP and Python that can be adapted for use in other projects similar to ours. The Nakala API requires a particular formalism for the presentation of metadata, requiring us to adapt our requests to convert the fields in the IPhiS database in such a way as to produce metadata in JSON format, which is compatible with Nakala. This part of the work was relatively delicate and called for a number of arbitrations that were at times somewhat frustrating. For a very straightforward record, limited for example to very little metadata in addition to the compulsory metadata, we arrive at the following form: { "status": "published", "metas": [{ "value": "Ermarco -Frammenti", "lang": "it", "typeUri": "http://www.w3.org/2001/XMLSchema#string", "propertyUri": http://nakala.fr/terms#title },{ "value": { "givenname": "Hermarchus", "surname": "Philosophus", "orcid": null }, "propertyUri": http://nakala.fr/terms#creator },{ "value": null, "lang": null, "propertyUri": http://nakala.fr/terms#created },{ "value": "CC-BY-4.0", "lang": null, "typeUri": "http://www.w3.org/2001/XMLSchema#string", "propertyUri": http://nakala.fr/terms#license },{ "value": "http://purl.org/coar/resource_type/c_c513", "lang": null, "typeUri": "http://www.w3.org/2001/XMLSchema#anyURI", "propertyUri": http://nakala.fr/terms#type },{ "value": "Francesca Longo Auricchio -éd. (VIAF -7280456)", "lang": "it", "typeUri": "http://www.w3.org/2001/XMLSchema#string", "propertyUri": http://purl.org/dc/terms/contributor },{ "value": "https://ciris.huma-num.fr/noticeedition.php?langue=fr&id=54", "lang": "fr", "typeUri": "http://www.w3.org/2001/XMLSchema#anyURI", "propertyUri": http://purl.org/dc/terms/relation }] } Injecting this form into the API via a 'post' request produces the following display ( Figure 5): Thus the compulsory metadata in Nakala includes the notions of creator and created in respect of the date of creation. But these notions, in Nakala's internal logic as expressed in the API, apply not to the content of the data but to the data itself: the creator is the person who posted the data, and the date is the date of posting. If we maintain this idea in our display, the metadata then proves to be very poor, and harvesting is likely to prove of little pertinence, even though it is always possible to add further layers of metadata subsequently. For our type of bibliographical data, creating the possibility of carrying out a search on the basis of the name of the person uploading an item of data merely results in the creation of unnecessary noise and is probably a nuisance for users of both Nakala and Isidore. We therefore decided to circumvent this constraint and indicate as creator the creator of the intellectual content -so, as far as we are concerned, still a creator author, but an ancient author. However, in this case it is impossible to associate a creation date with this creator. This is because the date format for an Ancient work cannot be expressed as D/M/YYYY as required by Nakala's API. At the time of posting we therefore systematically need to associate a zero value to the compulsory created item of metadata. These constraints are offset by the possibility of incorporating a clickable link in the metadata items leading directly to the record in the database. Thus whether by visiting the depository directly or as a result of harvesting by Isidore, the user will always have the possibility of rapid access to the full record in its original place of publication, as the last metadata item visible in Figure 5 shows.

What we display in Nakala, and why
This obviously raises the question of the necessary redundancy of accesses to an item of digital data. The purpose of conversion is to produce a display which will, we hope, increase the visibility of the database -but which cannot take the place of direct consultation of the database if full information is required. Therein lies all the ambiguity of the application of semantic technologies to digital objects that are already natively relational: the overlay of relational logic, thought out as navigation or an explicit path from one resource to another, by an object logic in which the fine description provides the key but does not set out the entire path; thus the description increases the visibility of the resource in certain search tools, but does not take the place of direct exploration of the resource itself. In other words, full display in Nakala would require the construction of a semantic clone of our database, and that would be pointless. Nakala is therefore used like a magnifying glass, with the intention of making it possible for Isidore to harvest certain strategic metadata in order to increase in fine the flow of visits not to the Nakala depository but to the database itself. It is in this logic that the date of creation of the data or its creator becomes a useless item of information, which must be replaced by the creator of the intellectual content likely to be of interest to the user. These choices, summed up in Figure 6, which are still being implemented, are the final stage in a lengthy thinking process; before accepting these compromises it was necessary to start by exploring the hypothesis of systematicity. Would we have been able to display the complete set of IPhiS data directly in Nakala if we had wanted to? The answer is no, for the time being, because firstly if we had wanted to display not only the records for editions but also all the connected data in the IPhiS thesaurus, we would have fairly quickly reached the limit of the vocabularies accepted by the API, and secondly Nakala does not natively recognise the SKOS vocabulary. If we compare for example the IPhiS data and a set that is close not in terms of quantity but of type of object listed -the BNF data -we can see fairly well how DataBNF compensates for the shortcomings of qualified Dublin Core and FOAF with on the one hand certain elements of SKOS for the data in its thesauruses and on the other a specific ontology describing relations and objects specific to its resources and its display 41 . Similarly, a full IPhiS semantic display would suppose the creation of a specific ontology to express certain traits which, as far as we know, are not currently taken into account by the standard bibliographical ontologies. This is more particularly the case for the matter of incomplete texts, noted as fragments or pieces, or collections of texts, anthologies or corpora; it is also, and perhaps even more so, the case for describing the complex progression in order to distinguish between a text's creator, copyist, translator and publisher throughout its history. It is possible to construct this ontology, and we are able to propose an overview of it here, produced using Protégé software 42 (Figures 7 to 11).    Implementation of this ontology is not immediately desirable, since it would lead to a very significant technical constraint by causing, apart from the creation of one or more namespaces, the need to attribute a considerable number of URI because of the growing size of the database and manage the negotiation of content between the HTML and RDF versions for each item of data. This is a very real constraint, and one to which experts in the bibliographical semantic web have been drawing attention for quite some time 43 .

Conclusion
As we see it, it is not pertinent, because of the nature of our data on ancient texts, to only use tools such as Nakala to make sure that they are displayed and harvested. Our philological aims are as varied as they are complex; there is therefore always a constraint to either force their harmonisation so that it is not necessary to draw up over-heavy sharing schemas, or simplify them artificially so that they fit into categories that were not designed to accommodate them. 43 "The attribution of URI specific to your set of data for secondary entities is thus an additional burden since you will have to maintain them; however, it is also a security feature in terms of the consistency of your set of data. It all depends on how much you trust the sets of data whose URI you re-use, and the ease of discerning which entities you are manipulating within these external artefacts. If you create your own URI for secondary entities, you can always link them to the others at a later stage (see A.7)." [trans.] [Bermès, Isaac & Poupeau, 2013 paragraph 49]. See: https://www.cairn.info/le-web-semantique-en-bibliotheque--9782765414179-page-69.htm; consulted on 23 April 2021.
Happily, there are other less ponderous solutions for displaying data such as ours in the best possible way. Some are already virtually in place, as a result of our initial choice to cross our own data with as many external repositories as possible. The alignment work carried out with the VIAF, the Pinakes database authorities, dataBNF, or even, in the case of our cartographic extension, several geographical repositories, may ultimately make it possible to envisage entering IPhiS data via channels that are not strictly philological, either via a general bibliography or by using access paths that cease to have anything to do with the base material and are semantic by nature from the outset -or at least readily convertible into a semantic logic. What is more, we have long given CIRIS users the possibility of downloading a large part of the data in open format for their personal use. This is the case not only for the thesauruses of texts by ancient authors, which are directly downloadable in *.csv format in CIRIS, but also for the edition records that can be exported in RIS format, thereby making them compatible with most bibliographical management software. In the cartographic extension carried out using the open application uMap 44 , all the data for the maps can also be downloaded (Figure 12). Diversifying the ways of displaying our data does not in any way mean having to renounce full interoperability; quite the contrary, in fact: it means optimising this sharing by selecting, for each aspect of the items of data, the tool best suited to their display. It is important to take care in determining which item of data should be entrusted to which tool. Doing so takes advantage of the specific features of the items -their transmission is complex, they are charged with a scientific uncertainty that it is our duty to make known, and they represent a wealth of variety of types that it would be wrong to attempt to standardise. An effort still needs to be made regarding the data contained in thesauruses. Here we feel the choice to retain a firm barrier between back-and front-office remains pertinent, since this is checked data that must be subjected to tight editorial control, under an expert eye. That is why, while contributions to the IPhiS database are allowed, in order to enable external users to