dataesr/scientific-paragraphs-categorization huggingface dataset:
2. Here, we consider at the beginning all transactions containing the item. Then, we pick all those not containing the item  but the item , and so on. Next, the pseudo-code of our algorithm using a decomposition-based method for enumerating all CHUIs is summarized in Algorithm 2. The algorithm, coined as SATCHUIM (SAT based Closed High Utility Itemset Mining), takes a transaction database  and a minimum utility threshold , and it outputs all the closed high utility itemsets in. Notice that the decomposition technique applied to the database  provides some significant advantages. First, splitting the whole database into independent sub-bases can reduce significantly the size of the original problem. Also, the algorithm does not need to generate candidate sets since the reduced database does not contain any low utility itemset, i.
e. , each itemset that has utility lower than TWU is discarded. The algorithm follows an order over the set of items appeared in  by counting items occurrence, i. e, items are sorted in increasing order of their support. Obviously, the splitting strategy is performed before the solving process. At each iteration, each item   is fixed to be in the itemset and the encoding is restricted only to transactions containing   , denoted. Then, if the TWU of the item   is less than the  threshold,   is discarded and it will not belong to the set of HUIs. In the next iteration, we ignore in the current sub-database all items having TWU less than. Then, the function encode_huim_cnf is called over    in order to encode the problem into CNF. Finally, the enumeration of the models of the CNF formula is performed using the function DPLL_Enum (Algorithm 1).
Again, we use the decomposition strategy for a scalability reason. In fact, we have shown in our previous work  [34]  that a SATbased approach cannot scale to large datasets, e. g. , Chainstore and Kosarak, since the CNF encoding of such transaction databases is huge and cannot be resolved by the SAT solvers. Hence, in this paper we applied the decomposition-based technique described previously to achieve efficiency by reducing the size of the CNF encoding without losing completeness.
Experimental setup Experiments are performed on a computer with an Intel Xeon quad-core machine with 32GB of RAM running at 2. 66 Ghz. To evaluate the practical performance of our approach, experiments were carried on seven real-life datasets commonly used in the HUIM literature: Chess, Mushroom, Connect, Kosarak, Foodmart, Accidents and Chainstore  [35]. These datasets have various characteristics and represent data taken from real-life scenarios. For each benchmark, we report in Table  4  the number of transactions (#Trans), the number of items (#Items), the number of items per transaction or average transaction length (AvgTransLen), and the density. 2 he density factor has a direct impact on the computation time of mining algorithms. In our experiments, both sparse and dense datasets were used for performance evaluation.
For each dataset, we fix a timeout of 2 h. We conducted two experiments to evaluate the performance of our proposed approach. In the first experiment, we compared our SATHUIM algorithm to the two most efficient specialized approaches for enumerating HUIs  [14] : EFIM  [22] , and D2HUP  [20]. Moreover, in the second set of experiments, we compare our SATCHUIM method against three baselines for mining closed HUIs, namely EFIM-Closed  [28] , CHUD  [25] , and CHUI-Miner  [29]. For these baselines, we used the Sequential Pattern Mining Framework (SPMF, for short) open-source data mining library  [35]  written in Java. Our algorithms are implemented in C++ and we used the MiniSAT solver  [36]  to enumerate all models of the CNF encoding. In our experiments, for the minimum utility threshold values, we follow the work of Zida et al.
Results for HUIs enumeration In this experiment, we run each method on each database while comparing the algorithms' running time for different minimum utility thresholds. Fig. 3  reported the comparative results, i. e. the CPU time, of our method SATHUIM against the two specialized ones. Note that for our algorithm, the computation time includes the time for generating the CNF formula and that for enumerating all models (i. e. , the HUIs). The empirical results show the feasibility of our SAT-based approach. As illustrated in Fig. 3 , it is clear that the performance of all algorithms depends on the dataset characteristics. In fact, all approaches need more time to discover the set of HUIs from large databases. In addition, the minimum support threshold  has a strong influence on the performance of algorithms.
Results for CHUIs enumeration In this subsection, we turn to the empirical evaluation of our SATCHUIM algorithm and compare it to three baselines, namely, EFIM-Closed  [28] , CHUD  [25] , and CHUI-Miner  [29]  for enumerating closed high utility itemsets from transaction databases. Fig. 4  shows the execution times of the different algorithms. According to these experimental results, our proposal achieves a good performance in 5 out of 7 databases for different minimum utility threshold values. As we can also see from the results, our algorithm remains competitive with the best baselines for Mushroom and Chainstore databases. Notably, the required time for our SATCHUIM algorithm to find all CHUIs increases when the  value decreases on Chess, accidents, connect and foodmart. In contrast, the running time remains almost constant when  threshold varies for the datasets Chainstore, kosarak and Mushroom.
In terms of average CPU time and for low values of , SATCHUIM surpasses CHUD by about 163 and 9 times on Chess and Kosarak datasets , respectively. Likewise, SATCHUIM surpasses CHUI-Miner by about 147 and 3 times on Chess, kosarak, respectively. In addition, our algorithm is up to 60 times faster than CHUI-Miner, while CHUD took too long time to terminate on the dataset Connect. From the scalability point of view, we observe that our proposed SAT-encoding is able to scale for all the minimum support threshold values under the time limit for large datasets; while CHUD and CHUI-Miner algorithms not able to scale on the datasets accidents, Connect and Chainstore under the time limit. Overall, the empirical evaluation confirms that our SATCHUIM algorithm is very promising. Finally, Table  5  provides the variation of the number of generated patterns as well as the number of propositional variables and clauses used to encode the problem for both classical HUIs and closed HUIs.
The main observation is that the number of found itemsets highly depends on the selected threshold values: it decreases when the utility threshold increases and vice versa. Furthermore, the number of patterns can be limited when the minimum utility threshold is large. Let us also mention that the CHUIs is smaller compared to the set of HUIs. For instance, for Chess dataset the number of HUIs is equal to 428023, while the number of CHUIs is about 114660. According to the experiment results shown in Table  5 , we can observe that the number of clauses can exceed 400 millions (i. e. , Kosarak dataset). Note that this number corresponds to the sum of the number of clauses of the different sub-problems generated by our decomposition technique. Despite this large number of clauses and variables, our approach remains efficient and scale on all datasets in a reasonable time.
Sample transaction database. Definition 1 (Support of an Itemset). Let  be a transaction database. We define the support of an itemset  as the number of transactions in  that contain , i. e. , ()= |  ∕  ⊆. (,   ) ∈ |. Definition 2 (Utility of an Item/Itemset in a Transaction). Given a transaction database , the utility of an item  in a transaction (,   ) ∈ , denoted by (,   ), is defined as (,   ) =   () ×   (,   ). Then, the utility of an itemset  ⊆  in a transaction (,   ) ∈ , denoted by (,   ), is defined as:.
is checked (line 9) to verify its consistency. A comparison to  is then performed to continue the search or to backtrack. Such checking can be easily accomplished by considering the value ∑  If all literals are assigned without contradiction, then  is a model of the CNF formula (line 12). Obviously, each found model of  ℎ gives rise to a (closed) high utility itemset from the transaction database (line 13) by restricting the model to variables encoding items.
SAT based Closed High Utility Itemset Mining (SATCHUIM) Input: : a transaction database, : a user-specified utility threshold Output: : the set of all closed high-utility itemsets of   = ⟨ 1 , … ,   ⟩ ← ();  ← ∅; for  ∈ 1. do if    (  ) <  then continue; end    ← {(  ,   ) ∈  |   ∈   };  ← ∅; for  ∈ (   ) do if    (,    ) <  then  ←  ∪ {}; end end  ← _ℎ_ (   , ) ∧    ∧ ⋀ Proposition 3 (Correctness). Let  be a transaction database. SATCHUIM returns all closed high utility itemsets of.
Let  be a transaction database and  an itemset in. is called a closed itemset if there exists no itemset  ′ such that  ⊂  ′ , and ∀(,   ) ∈ ,  ∈   →  ′ ∈. Example 2. Let us consider again the transaction database given in Example 1. Then, the utility of the itemset {𝑎, 𝑐} is 𝑢({𝑎, 𝑐}) = 𝑢({𝑎, 𝑐}, 𝑇 1 ) + 𝑢({𝑎, 𝑐}, 𝑇 2 ) + 𝑢({𝑎, 𝑐}, 𝑇 3 ) = 5 + 14 + 5 = 24. Definition 4 (Closed Itemset).
is checked (line 9) to verify its consistency. A comparison to  is then performed to continue the search or to backtrack. Such checking can be easily accomplished by considering the value ∑  If all literals are assigned without contradiction, then  is a model of the CNF formula (line 12). Obviously, each found model of  ℎ gives rise to a (closed) high utility itemset from the transaction database (line 13) by restricting the model to variables encoding items. Algorithm 1: DPLL_Enum: A backtracking search procedure for models enumeration Input: 𝛷: a CNF formula, 𝜃: a minimum utility threshold Output: 𝑆: the set of models of 𝛷 𝛥 = ∅ ; /* interpretation */ 𝑆 = ∅; if (𝛷 ⊧ 𝑝) then return 𝐷𝑃 𝐿𝐿_𝐸𝑛𝑢𝑚(𝛷 ∧ 𝑝, 𝛥 ∪ {𝑝})) ; /* unit clause */ end if (𝛷 ⊧ ⊥) then return 𝐹 𝑎𝑙𝑠𝑒 ; /* conflict */ end if 𝑐ℎ𝑒𝑐𝑘_𝑢𝑡𝑖𝑙𝑖𝑡𝑦_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒(𝜃) == 𝑓 𝑎𝑙𝑠𝑒 then return 𝐹 𝑎𝑙𝑠𝑒; end if (𝛥 ⊧ 𝛷) then 𝑆 ← 𝑆 ∪ {𝛥} ; /* new found model */ return 𝐹 𝑎𝑙𝑠𝑒; else end 𝑝 = select_variable(𝑉 𝑎𝑟(𝛷)); return 𝐷𝑃 𝐿𝐿_𝐸𝑛𝑢𝑚(𝛷 ∧ 𝑝, 𝛥 ∪ {𝑝}) ∨ 𝐷𝑃 𝐿𝐿_𝐸𝑛𝑢𝑚(𝛷 ∧ ¬𝑝, 𝛥 ∪ {¬𝑝}); return 𝑆; =1∑∈  (,   ) and by subtracting (,   ) each time   becomes false.
Algorithm 2 : 2 SAT based Closed High Utility Itemset Mining (SATCHUIM) Input: : a transaction database, : a user-specified utility threshold Output: : the set of all closed high-utility itemsets of   = ⟨ 1 , … ,   ⟩ ← ();  ← ∅; for  ∈ 1. do if    (  ) <  then continue; end    ← {(  ,   ) ∈  |   ∈   };  ← ∅; for  ∈ (   ) do if    (,    ) <  then  ←  ∪ {}; end end  ← _ℎ_ (   , ) ∧    ∧ ⋀ Proposition 3 (Correctness). Let  be a transaction database. SATCHUIM returns all closed high utility itemsets of. ¬𝑝 𝑎 𝑗 ∧ ⋀ ¬𝑝 𝑏 ; 1≤𝑗<𝑖 𝑏∈𝛤 𝑆 ← 𝑆 ∪ 𝐷𝑃 𝐿𝐿_𝐸𝑛𝑢𝑚(𝛷, 𝜃); end return 𝑆;.
, 2017b (Dadar et al. , , 2017c)) , we have compared burden and distribution of WMHs across 11 diagnostic cohorts: cognitively intact elderly (CIE), subjective cognitive impairment (SCI), mild cognitive impairment (MCI), vascular MCI (V-MCI), Alzheimer's dementia (AD), vascular AD (V-AD), frontotemporal dementia (FTD), Lewy body dementia (LBD), cognitively intact elderly with Parkinson's disease (PD-CIE), cognitively impaired Parkinson's disease (PD-CI), and mixed dementias as well as between men and women in each group. To our knowledge, this is the first study that consistently compares the distribution of WMHs across all these neurodegenerative disease populations using a large dataset (N=976) acquired consistently with a harmonized protocol.
MRI data All CCNA participants were scanned using the Canadian Dementia Imaging Protocol, a harmonized MRI protocol designed to reduce inter-scanner variability in multi-centric studies  (Duchesne et al. , 2019). The following sequences were used to detect WMHs: -3D isotropic T1w scans (voxel size = 1. 0 × 1. 0 × 1. 0 mm 3 ) with an acceleration factor of 2 (Siemens: MP-RAGE-PAT: 2; GE: IR-FSPGR-ASSET 1. 5; Philips: TFE-Sense: 2) -Fluid attenuated inversion recovery (T2w-FLAIR) images (voxel size = 0. 9 × 0. 9 × 3 mm 3 ), fat saturation, and an acceleration factor of 2. Table  1  shows the acquisition parameters for each sequence and scanner manufacturer. A detailed description, exam cards, and operators' manual are publicly available at: www. cdip-pcid. ca.
MRI data All preprocessed and registered images were visually assessed for quality control (presence of imaging artifacts, failure in registrations). WMH segmentations were also visually assessed for missing hyperintensities or over-segmentation. Either failure resulted in the participant being removed from the analyses (N = 9). All MRI processing, segmentation and quality control steps were blinded to clinical outcomes. Note that the provided data was already quality controlled by the CCNA imaging platform for presence of imaging artifacts, and only scans that had passed this quality control step were collected and used for this study. In final, 976 participants' MRIs were entered in our analysis (see Table  2  for details).
DISCUSSION In this study, we compared the distribution of WMHs across eleven distinct neurodegenerative disease diagnostic groups using COMPASS-ND dataset from the CCNA acquired consistently with a harmonized protocol. Our results showed significantly greater WMH burden in all cognitively impaired and dementia groups compared with matched controls, whereas the cognitively intact PD (PD-CI) and SCI groups had slightly higher but non-significant differences. As expected, the highest burden of WMHs was found in the mixed dementia group, followed by V-MCI and V-AD (Table  1 ). In patient groups that were not diagnosed with comorbid cerebrovascular pathology, the PD-CI, LBD, and FTD groups had the highest WMH loads. Interestingly, even the AD group not diagnosed with comorbid vascular pathology had significantly greater WMH burden than the controls, though this difference was much smaller (Tables  1  and 2 ).
, 2017). Low et al. have also reported left-dominant occipital WMH burden in AD patients which was higher than that observed in MCI and control groups, as well as an association with poorer global cognition, memory, language, and executive functions among cognitively impaired participants (MCI and AD)  (Low et al. , 2019). There are established regional brain asymmetries in the frontal and occipital lobes which are also phylogenetically evident and have been detected in older primates  (Toga and Thompson, 2003). These differences might also indicate differences in the evolutionary development of these lobes, leading to differences in susceptibility to neurodegeneration and presence of white matter pathology. The image processing and WMH segmentation pipelines used in the present study have been developed and validated for use in multi-center and multi-scanner studies of aging and neurodegenerative disease populations and have been previously used in such applications  (Anor et al.
To tackle this challenge, a database, called BaGaTel, has been built, guided by a process and observation ontology in food science, PO² ontology  (Ibanescu, Dibie, Dervaux, Guichard, & Raad, 2016)  and hosted by the PLASTIC platform INRAE (https://www6. inrae. fr/pfl-cepia/). This database gathers data in the field of reformulation of dairy products taking into account their nutritional, sensory and environmental properties, using a consensual model and a shared structured vocabulary (available online at http://agroportal. lirmm. fr/ontologies/PO2_DG/?p=summary). Data from a total of 65 different projects have been imported in BaGaTel (list available at http://plasticnet. grignon. inra. fr/portailbagatel/); 693 samples, 450 methods, 297 materials and 1045 measured characteristics are included, up to November 2020.
The data are either nonpublished but used with the permission of the authors or are extracted from the literature. The database is continuously enriched with data from new articles in the field. This database has already been successively used to (i) find correlations between one rheological parameter, the Young's modulus and one sensory descriptor, i. e. , firmness in hard cheeses, (ii) estimate missing experimental data due to this correlation and (iii) estimate the environmental impact for specific foods, for which a process was described in BaGaTel  (Pénicaud et al. , 2019). In the present paper, we aim to demonstrate that the BaGaTel database can be successfully used (i) to gather data obtained in different projects that used similar methodologies and (ii) to reach a critical number of samples from similar food products differing in composition, to better understand the relationships between physico-chemical data and sensory perception.
Data preparation Specific queries were done to export data from the BaGaTel database. We searched for samples, which had data on composition, rheological properties and sensory profile analyses. In BaGaTel, 271 samples are characterised by rheological data, 365 samples by sensory data, while 228 samples by both sets of data. However, the composition and structure of the dairy products and the measured variables were often very different. We thus restricted our query to hard cheeses and related model cheeses. For such types of cheeses, the materials and methods used for rheological analyses were comparable (data available in BaGaTel) and the bulk of sensory description can be considered as quite similar. We finally selected 68 cheese samples (hard-type model cheeses) from six different projects.
These samples had been characterised for their composition (lipid, protein, water, sodium ions), sensory properties (salty, fatty, springy, hard/firm, crumbly, sticky, melting, granular, dry), rheological properties (Young modulus, fracture stress, fracture strain, work at fracture) and chewing activity parameters (total muscular work, number of chewing cycles, chewing duration). The whole data set (2021-01-22_cheese-compo-rheo-senso_Guichard-V3. tab, sheet whole-dataset) is available on-line  (Guichard et al. , 2020). The description of the samples, data, associated metadata, experimental, material and analysis methods, together with the scatter-plots of the values in the different projects (Figs. S1-S5), are available in a co-submitted data paper  (Guichard et al. , 2021). The information concerning the different projects (title, abstract, coordinator, scientists involved, DOI of publications) are available on line in the database website (http://plasticnet.
The final list of composition variables is the following: water, protein, lipid, Na +. We also added three variables. Lipid/DM is the ratio of lipids per dry matter and represents the impact of lipids in the lipid/protein network and food texture. Na + /water is the amount of sodium ions in the water phase and should better represent the concentration in sodium ions available for the taste receptors. The ratio moisture-in-non-fat-substances (MNFS) is a useful variable in cheese manufacturing and is used in the classification of cheeses  (Codex Standard 283-1978, FAO). It gives an estimation of the water/ protein ratio and influences a wide range of textural characteristics  (Lucey, Johnson, & Horne, 2003). The values for these variables in the different samples were calculated and uploaded in the database.
Multiple linear regression The data extracted from BaGaTel had missing values for several parameters. MLR (XLStat, Addinsoft, Paris, France) was applied to estimate missing values. In addition to Young's modulus (YM) and fracture stress (FS), other rheological parameters such as fracture strain (CS) and work to fracture (WF) were available for several samples. Thus, we estimated the missing values for CS and WF, separately, using multiple linear regression (MLR) with the following variables: Na + , lipid, protein, water, lipid/DM, YM, FS. Considering sensory profiles, the descriptor hard/firm was estimated with MLR based on the following variables: Na + , lipid, protein, water, lipid/DM, YM, FS, but crumbliness and stickiness were estimated separately with the same variables, excluding lipid because of strong multicolinearity.
The dataset with the estimated data (2021-01-22_cheese-compo-rheo-senso_Guichard-V3. tab, sheet: dataset+estimated-data) and the parameters of the MLR used for the estimation (2021-01-22_cheese-compo-rheo-senso_Guichard-V3. tab, sheet: missing-data-estimation) are available on-line  (Guichard et al. , 2021). Another alternative would be to use the missMDA (R package), which performs PCA on incomplete data sets  (Josse & Husson, 2016). We performed PCA with the two methods and calculated the RV coefficient, which is of 0. 992, confirming that, in our case, with only few missing data, the mode of estimation has very little impact on the PCA results. We thus used the data estimated using MLR.
Principal component analysis Principal component analyses (PCAs) were performed on different subsets of data to highlight the relationships between food composition, food rheology and sensory perception. PCAs were performed with XLStat (Addinsoft, Paris, France). On the total dataset of 68 samples, a PCA was done on the 7 variables of composition, two sensory descriptors (salty and hard/firm) and two rheological parameters (YM and FS). We also performed PCA on two subsets, one subset of 32 samples (Adi, Lawrence, PraSel and Tarrega projects) with a sodium ion content below 5 g kg -1 , and a second subset of 36 samples (Adi, Boisard, Lawrence, Phan and Tarrega projects) with a sodium ion content higher than 5 g kg -1. As for some projects, measurements on chewing behaviour were obtained (Total muscular work, Number of chewing cycles, Chewing duration), we also performed two additional PCAs, using only the samples with data on chewing behaviour, to assess (i) the impact of chewing behaviour on sensory perception and assess (ii) the hypothesis formulated by  Lawrence et al.
Data set of 68 samples and 11 variables A PCA was done on the set of 68 samples containing data for the two sensory descriptors hard/firm and salty (estimated data for hard/firm in Phan project), available online (2021-01-22_cheese-compo-rheo-senso_Guichard-V3. tab, sheet: dataset_PCA-68samples). The map of the samples (Fig. 1A, B ) shows that there is a good overlap of the samples from the different projects. Figure  1C ,D represents the map of the variables on the three main dimensions, which account for 81. 26 % of total information. On axis 1, water content (negative part of axis 1) is opposed to sodium ion and lipid contents (positive part of axis 1). On axis 2, protein content (positive part of axis 2) is opposed to lipid/DM content (negative part of axis 2). The sensory descriptor hard/firm is located on the positive part of axis 2 close to the protein content and opposed to moisture-in-non-fat-substances (Fig.
723) with sensory hardness (graphic representation in Guichard et al. , 2021: Fig. S6 ). Because of the large differences in sodium ion content in our dataset and since several authors found different conclusions as a function of salt content, the initial set of samples was divided into two subsets according to the sodium ion content (below or above 5 g kg -1 sodium ion). Two other PCA analyses were performed on these subsets of samples.
Data set of 28 samples with data on chewing behaviour Data on chewing behaviour are available in four projects  (Boisard, Lawrence, Phan and Tarrega projects). A subset of these samples with the data on chewing activity was selected (2021-01-22_cheese-compo-rheo-senso_Guichard-V3. tab, sheet: dataset_chewingactivity). Because it was previously observed that the relationships between saltiness and chewing behaviour were highly dependent on salt content  (Lawrence et al. , 2012b) , PCAs were performed on two subsets of samples according to their sodium ion contents. The aim of this analysis was to increase the number of samples compared with the Lawrence project  (Lawrence et al. , 2012b). The added samples had a different composition and especially a lower amount of water and a harder texture, so that they required a more intense chewing activity.