dataesr/scientific-paragraphs-categorization huggingface dataset:
Datasets We performed our experiments utilizing a variety of attributed graph datasets ranging from small to medium graphs with small to large sets of items. Table  1  depicts the main characteristics of these datasets (see also  (Galbrun et   (Lazega 2001). It concerns 71 attorneys (partners and associates) of this firm who are the vertices of four networks. In the resulting data, each attorney is described using various attributes. 2 We consider the advice network which is originally a directed graph in a undirected version, so that two lawyers are connected if at least one asks for advice to the other one. • The CoExp dataset models a representative regulatory network for yeast obtained from Microarray expression data processed by the CoRegNet  (Nicolle et al. 2015)  program. In the CoExp dataset the vertices are co-regulators and they are linked if they share a common set of target genes.
2013). It represents a co-authorship graph built from a set of publication references extract from DBLP, published between January 1990 and February 2011 in the major conferences or journals of the Data Mining and Database communities. Three labels have been added to the original dataset based on the scope of the conferences and journals, respectively: DB (databases), DM (data mining) and AI (artificial intelligence). • Delicious consists of the social (friendship) network of the resource sharing system delicious where individuals are described by their bookmarks' tags. The dataset is publicly available and was obtained from the HetRec workshop  (Cantador et al. 2011 ) at Recsys 2011. 3 • DBLP. S was used in  Silva et al. (2012). It also represents a co-authorship network from a set of publication references extracted from DBLP.
Similarities and Differences in Pattern Selection Both the considered baseline methods, i. e. , MinerLC and COMODO output a set of pairs (pattern, vertex subset). However, in order to compare their outputs we have to consider the following differences: • In COMODO the vertex subset W is obtained as the extremities of the set of edges in which a pattern occurs and a pattern occurs in an edge whenever it occurs, in the original dataset, in both connected vertices. That is, for each edge we assign the set of common items of both nodes, such that a pattern always covers two nodes connected by an edge. As a consequence, W ignores isolated nodes in which p occurs. To obtain the same vertex subset in MinerLC (and MinerLSD) it is necessary to remove isolated nodes, which is enabled by applying a 1-core graph abstraction.
Parameters and Datasets For MinerLSD, it is important to note that in our experiments described below we did not have to use the minimal support s, since the local modularity threshold is efficient enough to strongly reduce the number of patterns. Below, we consider the following pattern quantities, where the (closed pattern, support set) pairs (c, e) are output by MinerLC unless specified; also, we consider a given local modularity threshold lm. • #c the number of pairs (c, e). • #lme: the number of pairs (c, e) such that oe(MODL)(e) ≥ lm. • #nec: the number of (necessary) pairs (c, e) a top-down search has to consider to ensure that no pair with oe(MODL)(e) ≥ lm is lost. See "Pruning: Efficiency of the Local Modularity Estimate" section for details and results on #nec. • #lm the number of pairs (c, e) such that MODL(e) ≥ lm • #lmeSD: the number of pairs (c, e) such that oe(MODL)(e) ≥ lm as generated by COMODO.
Impact of Closed Patterns in Reducing the Search Space MinerLSD searches a space of closed patterns while COMODO searches the whole pattern space. Therefore, we will investigate the impact of the closure reduction, for each local modularity threshold lm. For that, we first consider the quantity #lme of core closed patterns with a local modularity estimate above lm, as provided by MinerLSD, when using 1-cores. We consider then the quantity #lmeSD of patterns developed by COMODO using the same threshold. Table  2  reports #lme and #lmeSD for our datasets under investigation. We observe two very different situations. In the Lawyers and CoExp datasets there is a large difference between #lmeSD and #lme, while there are considerable but not so strongly expressed differences in the other datasets compared to the former.
Large differences typically occur when items have strong dependencies hence leading to a large reduction of the search space when applying a closure operator. For instance, in the Lawyers dataset vertices are described by various numeric attributes. In our representation, a single numeric attribute x leads to a set of x ≤ s i and of x > s i items with various thresholds s i. This allows to include interval constraint as x ∈] s j , s k ] within patterns. However there are then several equivalent patterns in which the same interval is represented in various ways. For instance, consider 4 thresholds s 1 ,. , s 4 , the interval x ∈] s 2 s 3 ] is represented by x > s 2 , x ≤ s 3 , x > s 1 , x > s 2 , x ≤ s 3 and x > s 1 , x > s 2 , x ≤ s 3 , x ≤ s 4. The latter is the only one found in a closed pattern.
k-core sizes of the various networks Before considering how reducing support sets to k-cores affects the number of closed patterns in each dataset, we consider the various networks and compute their k-core sizes for a range of values of k. This pre-analysis aims to evaluate which level of k we should use in our experiments. For small datasets for which computing closed patterns does need much resources this is not that important. However, for large datasets with many attributes, i. e. , potentially large numbers of closed patterns, it is much better to have a rough guideline for selecting appropriate parameters for optimizing the computational effort. In Fig. 2  we display the k-core sizes for a range of values of k, for each dataset. As we will see below, the small but densest networks for which local-modularity-based pruning has a weak efficiency, namely coExp and Lawyers, also exhibit a (relatively) slow decay with respect to increasing k values, whereas for the other (larger) datasets we observe a quite considerable decrease in terms of the k-core sizes.
Pruning: Efficiency of the Local Modularity Estimate For investigating the efficiency of pruning using the modularity estimate, we compare our proposed algorithm MinerLSD to the MinerLC algorithm, which applies no optimistic Fig. 2  k-core sizes of the networks associated to our datasets versus k estimate pruning. For the other baseline, i. e. , COMODO we already investigated the efficiency of MinerLSD which showed a considerable reduction in the number of considered patterns, cf. , section "Impact of Closed Patterns in Reducing the Search Space". Regarding the number of output patterns, both actually yield the same numbers, if a postprocessing step of COMODO is applied for keeping only the subset of closed patterns (as discussed in section "Similarities and Differences in Pattern Selection"), i.
Whenever #lm is far from #nec this means that there does not exist any good optimistic estimator. Whenever #lm is close to #nec which in turn is far from #lme this means that there could be some optimistic estimator that is much better than oe(MODL). By computing these numbers, we can then state separately for each dataset whether the oe(MODL) estimate is efficient in pruning the search with respect to the best possible estimator nec and whether nec would be efficient in pruning the search, if such an estimator would be found.
Small Datasets In a first step, we first considered several rather small datasets using no minimal support parameters, and a 1-core abstraction in MinerLSD aiming to provide a comparable setting for COMODO. We also checked the number of patterns retrieved by COMODO with additional postprocessing as discussed above -only keeping the closed patterns. We used parameters that do not limit the enumeration in COMODO, i. e. , for an exhaustive search only using the local modularity threshold for pruning. Likewise, for MinerLSD, we select and count vertex subgroups whose induced subgraphs satisfy a local Fig. 3  Detailed Estimated/Observed Modularity Distributions: We consider the unlabeled graph of the dataset. We generate 100 random subgraphs of the unlabelled graph picking randomly half of the vertices.
For each random graph, we compute the local modularity of the abstract 5-core subgraph and we report the survival distribution of the local modularity over the 100 experiments (in orange), i. e. , for each local modularity (lm) level, the probability of having at least that level in our sample. In blue, we report the (empirically observed) survival distribution of the local modularity, i. e. , the respective MODL values of the core subgraphs of the abstract patterns discovered using the 5-core abstraction modularity threshold lm. In this way, we could confirm (again) that the final number of output patterns is the same for both algorithms, as discussed above. Figure  5  depicts the results of the applied five datasets, with the detailed results in Table  3. Overall, the local modularity estimate is efficient in pruning the pattern exploration, on different levels.
For instance, in the Lawyers dataset, MinerLSD finds #c=3221 patterns at level lm=0. 005 and most of them, i. e. , 2929, have an oe(MODL) value above 0. 005, not too far from the #nec = 1792 patterns any top-down search would have to  have to be developed and 144 do have a local modularity above 0. 005. When the local modularity threshold increases, #lme keeps being close to #lm. Overall, the Lawyers dataset displays moderate pruning efficiency, still allowing to avoid to develop many nodes, and this is also the case for the S50 and CoExp datasets. In contrast, DBLP. C and DBLP. P indicate a very efficient optimistic pruning in terms of the numbers of patterns. Tables  4  and 5  show the runtime results of MinerLSD for the larger of the small datasets (Lawyers, CoExp, DBLP. C, DBLP. P, runtime in seconds).
Here, we observe that Min-erLSD is either in the same range or slightly faster than MinerLC for the small datasets, i. e. , for Lawyers and CoExp. For DBLP. C, we observe a strongly reduced number of patterns, while the runtimes are always in the same range, especially for stronger (graph-)constraints. Here, we considered k-cores, k = 1, 2, 3, 5, 7. Therefore, while strongly reducing the number of patterns the additional computation using the estimate still keeps the runtime of the algorithm in the same range as MinerLC most of the times. In contrast to the other smaller datasets, for the larger DBLP. P dataset we observe an increase in the runtime of MinerLSD compared to MinerLC. However, this can be explained by some special characteristic of DBLP. P. The DBLP. P dataset contains an extremely limited number of labels (32) which are used in the dataset.
Medium Size Datasets Overall, MinerLSD detects closed patterns with the benefit of pruning using the oe(MODL) ≥ lm condition, i. e. , only developing the #lme nodes according to Table  2. Furthermore, applying both the k-cores and local modularity constraints makes it possible to find some balance between the k-core and the local modularity constraint to apply when facing large datasets that are difficult to mine. This is investigated on the two datasets LastFM and Delicious, i. e. , those with the largest number of closed core patterns when considering the 1-core and no local modularity thresholds  -these were not investigated in Tables  2  and 3 , respectively. For these medium sized datasets, we performed experiments using 1-cores, 2-cores, 3-cores, 5-cores and 7-cores with local modularity thresholds 0.
01,0. 02, 0. 03, 0. 04, 0. 05, and 0. 15; the results regarding the number of closed patterns and the total CPU time (including pruning/optimistic estimation) are shown in Fig. 6  (runtimes in seconds). The benefit of applying local modularity constraints in the resulting number of closed patterns is, as expected, quite impressive. When no constraint (outside the 1-core) is applied, MinerLC in comparison finds 1,555,292 and 11,833,577 closed patterns, respectively. For MinerLSD, in the LastFM case there are no strong differences when using 1-cores, 2-cores and 3-cores while we know from Fig. 2  that using 4-cores does have an important effect. Corresponding results are also observed for larger sizes of the respective k-cores. Regarding the Delicious dataset, we observe a smaller number of patterns at local modularity levels 0.
e. , with respect to the applied k-cores. Using the appropriate modularity thresholds the runtime can be considerably decreased which enables new approaches already for medium sized datasets, e. g. , concerning pattern exploration. Specifically, if we compare the extra computation performed by MinerLSD for computing the estimate, in the Delicious case, the benefit is immediately obvious: MinerLSD is always much faster than MinerLC. The LastFM dataset shows a somewhat different picture: with weaker core-constraints and at local modularity level of 0. 01 MinerLC (which does not consider local modularity) is (slightly) faster than MinerLSD. This is not that surprising, since MinerLSD has to compute local modularity estimates and local modularities for all the developed patterns during search.
However, first this happens only for weak constraints, and second, when using MinerLC all these computations (in fact much more as there is no pruning), would have to be made anyway in post-processing fashion for obtaining the patterns according to a local modularity threshold. Furthermore, the runtime behavior of LastFM here is similar to DBLP. P and can also be explained by the smaller number of labels compared to Delicious. Overall, this shows that if we consider appropriate local modularity thresholds MinerLSD already allows the analysis of larger datasets, especially in terms of larger sizes of the labels, while comparable results (with respect to MinerLC) are usually obtained for weak (graph-)constraints. However, the efficient pruning of MinerLSD is important, e. g. , for exploration, and also for the processing of larger datasets, as we will also discuss in the next section for large datasets.
Large Datasets In this section, we present experiments of MinerLSD on two large datasets, namely DBLP. S and DBLP. XL (see Table  1  for their characteristics) to further explore the scalability of MinerLSD when using both k-core and local modularity constraints. Again we do not use any threshold on the pattern supports. In Table  7 , we report the results on DBLP. S and DBLP. XL with the same local modularity thresholds as in the previous section and applying k = 1, 2, 3, 5, 7 and 7 k-core constraints, respectively. The scalability of MinerLSD depends obviously on the size and density of the network but also heavily depends on the size of the attribute set and on the average number of labels per vertex. DBLP. XL is then a real challenge as it is a large network made of 929,937 vertices related by 3,461,697 edges and described by more than 90,000 items, with an average number of 10.
16 labels per vertex. The efficiency of the optimistic pruning is then of primary importance. As can be seen in the results table, optimistic estimate pruning using local modularity is quite effective in achieving an efficient pattern mining approach. For both datasets, we observe large reductions in the number of patterns, while focussing on the interesting ones according to the applied local modularity interestingness measure and the utilized local modularity thresholds. In particular, the results for DBLP. S indicate the enormous pruning efficiency -here the dataset for weaker constraints cannot be handled by Min-erLC at all, where the computation did not terminate after 36 h. The DBLP. XL results indicate the same trend. Overall, this indicates the huge impact of optimistic estimate pruning using local modularity as provided by MinerLSD for handling large datasets.
Structural Pattern Set Analysis In the following, we analyze the results of the proposed pattern mining method Min-erLSD in more detail, focussing on different graph statistics. We report exemplary results on three datasets with different characteristics as outlined in section "Datasets", i. e. , the Lawyers, the CoExp, and the DBLP. C datasets. We consider all patterns above a given local modularity threshold, combined with different core abstractions. For computing the graph statistics, we analyze the respective induced subgraph W of each pattern, and consider the following: (1) the vertex count N W , (2) the edge count E W , (3) the scaled density (cf. ,  (Lancichinetti et al. 2010 )) of subgraph W, i. e. , the ratio of E W divided by the number of edges of a complete graph with the same number of vertices as W and multiplied (scaled) by the total number of vertices; this measure approximately estimates the average degree of the nodes contained in the community, cf.
,  (Lancichinetti et al. 2010). (  4 ) Furthermore, we also consider the fraction of outgoing edges, i. e. , the edges connecting nodes contained in the pattern with others not being part of the pattern subgraph, to the set of edges E W. The results are shown in Tables  8, 9 , 10 and 11. Considering the results shown in Tables  8  and 9  we observe that, as expected, increasing numbers of k tend to focus on larger communities, which is especially the case for weaker core constraints and larger local modularity thresholds. In particular, we observe those trends for the local modularity for the Lawyers and the DBLP. C datasets, while this is also pronounced for CoExp regarding stronger constraints. For the DBLP. C network, in particular, we observe a rather strong effect. Overall, with no constraints quite small patterns are detected.
When the k-core constraint and the local modularity threshold are increased, then larger patterns are detected which are also considerably denser than those with no constraints. This can clearly be observed in Table  10  for increasing k-core and local modularity threshold values. Furthermore, when we consider the ratio of outgoing edges vs. in-edges of a pattern shown in Table  11 , then we also observe the trend that the proposed approach focuses on selecting denser pattern subgraphs with a stronger connectivity structure in terms of the links within the subgraph, i. e. , the in-edges. This is especially obvious for higher k-core and local modularity threshold values, as exemplified by the CoExp and DBLP. C datasets, e. g. , for k = 5 and lm = 0. 04 where the number of in-edges strongly "dominates" the number of outgoing edges.
Lawyers Dataset In order to demonstrate the effectiveness of the pattern exploration and selection methodology using abstract closed pattern with k-cores and local modularity, we exemplify that with the two patterns shown in Fig. 7. Here, we show two similar patterns in terms of Jaccard similarity (0. 52) considering the nodes of the respective pattern-induced subgraphs. While the patterns are very similar regarding the overlap  and their size, they have quite different local modularity values referring to their connectivity structure. The left pattern described by 35 < Age ≤ 65 AND Seniority < 5 AND Status = Partner, with a size = 24 of the set of nodes in its subgraph, is considerably denser with a local modularity of MODL = 0. 058, compared to the pattern on the right; the latter is described by Age < 40 AND Seniority ≤ 30, with a size = 23 of the pattern support and a local modularity of only MODL = 0.
DBLP. C Dataset In order to show the impact of pattern selection and k-core abstraction, we first consider the local Modularities on k-cores with increasing k. For analyzing the impact of the k-cores we firstly consider the empty pattern, thus only focussing on the abstraction by the applied k-core. For the local modularity values of the empty pattern, for k = 2, 3, 4, 5 we observe MODL = 0. 0075, 0. 0430, 0. 0915, 0. 1223, respectively. Thus, we observe the clear trend that increasing k yields patterns with higher connectivity structures as shown by the increasing local modularity values; similar trends are obtained for the other datasets. This complements our results in the last section, where we discussed, how increasing k for the k-core abstraction together with increasing local modularity thresholds focuses on larger and more "interesting" patterns as measured by the local modularity quality function.
The latter allows to strongly reduce the number of patterns while focussing on essential parts of the graph which leads to more interesting high quality patterns. For our experiments we used a number of datasets with different characteristics, also ranging from small to large datasets in order to estimate the scalability of MinerLSD. Overall the result indicated effects that were always positive, and sometimes even crucial, for allowing to handle even rather complex and large datasets with reasonable pattern set sizes and computational effort -without using any minimum support threshold. Specifically, the results of our experiments show the efficiency of the presented method. Furthermore, we have presented exemplary results showing the benefit of pattern selection and abstraction which demonstrate the efficacy of the proposed MinerLSD approach.
(Soldano and Santini 2014)1Itrepresents148 friendship relations between 50 pupils of a school in the West of Scotland; the labels concern the students' substance use (tobacco, cannabis and alcohol) and sporting activity. The values of the corresponding variables are ordered (see(Soldano and Santini 2014)for details). • The Lawyers dataset concerns a network study of corporate law partnership that was carried out in a Northeastern US corporate law firm from 1988 to 1991 in New England.
(Soldano and Santini 2014)1Itrepresents148 friendship relations between 50 pupils of a school in the West of Scotland; the labels concern the students' substance use (tobacco, cannabis and alcohol) and sporting activity. The values of the corresponding variables are ordered (see(Soldano and Santini 2014)for details). • The Lawyers dataset concerns a network study of corporate law partnership that was carried out in a Northeastern US corporate law firm from 1988 to 1991 in New England al. 2014)), which have been previ- ously used in pattern mining tasks on attributed graphs. For each dataset, we indicate the number of edges (|E|), vertices (|V |) and labels (|L|), the average vertex degree (deg(v)) and average number of labels per vertex (|l(v)|) in the table. • S50 is a standard attributed graph dataset used in a previous work about graph abstractions (.
Endnotes1 Available at: http://www. stats. ox. ac. uk/~snijders/siena/s50_data. htm 2 Available at: https://www. stats. ox. ac. uk/~snijders/siena/Lazega_lawyers_data. htm 3 https://grouplens. org/datasets/hetrec-2011/ 4 https://lipn. univ-paris13. fr/MinerLC/.
Objective: To update the health economic evaluation of pirfenidone in the treatment of idiopathic pulmonary fibrosis (IPF) compared to all available alternatives strategies (Best supportive care -BSC and nintedanib), based on a cost-utility model previously validated by the CEESP's (French Committee for Economic Evaluation) in 2014. Methods: A standard Markov cohort model, adapted to French methodology guidelines, was used to simulate the therapeutic management and the course of IPF patients (including potential adverse events) using the collective perspective. Cost-effectiveness was evaluated regarding life years (LY); quality-adjusted life-years (QALY); average cumulative costs; the incremental costeffectiveness ratio (ICER) expressed in cost per QALY gained. Data were retrieved from trials, meta-analysis, literature, health insurance and hospitalisation databases, and national tariffs.