dataesr/scientific-paragraphs-categorization huggingface dataset:
In other words, the training dataset used to prepare the CA for online learning might not be large enough to "fill" all cells in the grid. In such a case, it becomes necessary to "evolve" the grid several times (generations) until all cells are assigned a state. In this evolving process, each cell calculates its new state by applying the update rule over the cells in its neighborhood. All cells apply the same update rule, being updated synchronously and at the same time. Here lies the most distinctive characteristic of CA: the update rule only inspects its neighboring cells, being the processing entirely local (Figure  1 ).
Proposed Approach: CURIE We delve into the ingredients of CU RIE to act as drift detector. As shown in Figure  3 , its detection mechanism hinges on the evidence that a recent number of mutations in the neighborhood of a cell that has just mutated, may serve as an symptomatic indicator of the occurrence of a drift. CU RIE builds upon this intuition to efficiently identify drifts in data streams by fulfilling the following methodological steps (Algorithm 1): -First, the CA inside CU RIE is created by setting the value of its parameters (detailed as inputs in Algorithm 1), and following the characteristics of the given dataset (lines 1 to 5). -A reduced number of preparatory instances of the data stream [(X t , y t )] P -1 t=0 ) is used to initialize the grid of CU RIE. This grid is seeded with these instances, and then CU RIE is evolved for several iterations (generations) by applying the local rule until all cells are assigned a state i.
, G} d ; radius r for the neighborhood operator; radius rmut; maximum number of allowed mutants n muts allowed; time period mutation period; sliding window W of size P. Output: Trained CU RIE producing predictions yt ∀t ∈ [P, ∞) Preparatory process (6 -10) with instances in W the preparatory process is carried out by seeding the grid with the instances stored in the sliding window W (line 28). Finally, after detailing the ingredients of CU RIE to act as drift detector, we would like to highlight two improvements over  [25]  that positively impact on the learning of data distribution: -If the predicted and the true label do not equal each other, the cell state in CU RIE is always changed to the class of the incoming instance. Otherwise, if the age of the cell state (T age ) was considered, this could impact on drift detection resulting in more detection delay.
-In CU RIE there is always one state assigned to each cell, thus it is not necessary to check the state of the closest cell among those with assigned state to provide a prediction. The cost of assigning one state to all cells of the grid is insubstantial; it is just carried out at the preparatory process and when drift is detected. And so we achieve a more simple method that does not need to check the surroundings (neighborhood) of the cell when no state is assigned. The source code of CU RIE is available at https://github. com/TxusLopez/ CURIE.
Experimental Setup In order to assess the performance of CU RIE, we have designed several experiments with synthetic datasets configured with both abrupt and gradual drift versions. Since drift detectors usually base their detection mechanisms on the prediction results of a base learner, both detection and classification are often set to work together. As it has been already mentioned, CU RIE does not use the prediction of the base learner. Instead, it estimates the occurrence of the drift by looking at the changes that occur in the neighborhood of cells deployed over a grid that represents the distribution fo data. In our experiments we have accordingly combined three well-known base learners (HT, NB and KNN) with five popular drift detectors including our proposed detector (corr. DDM, EDDM, PH, ADWIN, and CURIE).
Datasets In order to assess the performance of a drift detector by measuring the different detection metrics, we need to know beforehand where a real drift occurs. This is only possible with synthetic datasets. The scikit-multiflow framework  [30]  allows generating several kinds of synthetic data to simulate the occurrence of drifts. Concretely, we have generated 20 diverse synthetic datasets (10 abrupt and 10 gradual) by using several stream generators and functions, and with a different number of features and noise. They exhibit 4 concepts and 3 drifts at time steps 10, 000, 20, 000, and 30, 000 in the case of abrupt datasets, and at time steps 9, 500, 20, 000, and 30, 500 in the case of gradual ones. In the latter case, the width of the drift is 1, 000 time steps. All generated data streams have 40, 000 instances in total.
Next, the details of the datasets: -With Sine generator: it is ruled by a sequence of classification functions. Sine A refers to abrupt cases and Sine G to gradual ones. In the case of Sine F1, the order of the functions is SINE1 ,reversed SINE1, SINE2, and reversed SINE2. For Sine F2 the order is namely, reversed SINE2-SINE2-reversed SINE1-SINE1. Therefore, Sine stream generator provides 4 different datasets: Sine A F1, Sine A F2, Sine G F1, and Sine G F2. They consist of 2 numerical features without noise, and a balanced binary class. -With Random Tree generator: it is ruled by a sequence of tree random state functions. The parameters max tree depth, min leaf depth, and fraction leaves per level were set to 6, 3, and 0. 15 respectively. RT A refers to abrupt cases and RT G to gradual ones.
In the case of RT F1, the order of the functions is 8873-9856-7896-2563. For RT F2 the order is reversed 2563-7896-9856-8873. Therefore, Random Tree stream generator provides 4 different datasets: RT A F1, RT A F2, RT G F1, and RT G F2. They consist of 2 numerical features without noise, and balanced binary class. -With Mixed generator: it is ruled by a sequence of classification functions. Mixed A refers to abrupt cases and Mixed G to gradual ones. In the case of Mixed F1, the order of the functions is 0-1-0-1. For Mixed F2 the order is reversed 1-0-1-0. Therefore, Mixed stream generator provides 4 different datasets: Mixed A F1, Mixed A F2, Mixed G F1, and Mixed G F2. They consist of 4 numerical features without noise, and a balanced binary class. -With Sea generator: it is ruled by a sequence of classification functions.
Sea A refers to abrupt cases and Sea G to gradual ones. In the case of Sea F1, the order of the functions is 0-1-2-3. For Sea F2 the order is reversed 3-2-1-0. Therefore, Sea stream generator provides 4 different datasets: Sea A F1, Sea A F2, Sea G F1, and Sea G F2. They consist of 3 numerical features, a balanced binary class, and with the probability that noise will happen in the generation of 0. 2 (probability range between 0 and 1). -With Stagger generator: it is ruled by a sequence of classification functions. Stagger A refers to abrupt cases and Stagger G to gradual ones. In the case of Stagger F1, the order of the functions is 0-1-2-0. For Stagger F2 the order is reversed 2-1-0-2. Therefore, Stagger stream generator provides 4 different datasets: Stagger A F1, Stagger A F2, Stagger G F1, and Stagger G F2.
They consist of 3 numerical features without noise, and a balanced binary class. Finally, as it is explained in section 3. 2, it is necessary to create "bins" by splitting each grid dimension by the values of the features. For Sine and RT datasets we have used 20 "bins" per dimension, while for the rest of datasets we have used 10 "bins'. The values have been found experimentally, just knowing that a small grid is not capable of representing the data distribution (e. g. the grid of Figure  1 ). Here, we would like to warn other researches by underlining that CURIE exhibits at this moment a drawback that should be considered. Due to its exponential complexity, we recommend the use of CURIE in datasets with a low number of features. This setback can be tackled by carrying out the search over the grids cells by parallelizing this process.
Methods and Parameters As for CU RIE we have assigned one grid dimension to each feature of the dataset at hand. We also note that we have used a reduced number of instances to warm up the learning-detection schemes, and also CU RIE (see Algorithms 1 and 2). The number of instances for this purpose usually depends on the memory or processing time restrictions. In our experiments we have considered a very low number of them in order to simulate a very restrictive real-time environment (see parameter P in Table  1 ). In all of them, CU RIE has been configured with a von Neumann's neighborhood rather than opting for its Moore alternative. A von Neumann's neighborhood is linear in the number of dimensions of the instance space, and therefore scales well for problems of high dimensionality. In addition, a Moore's neighborhood includes more neighbors, thus we would have to potentially apply the local rule over more cells.
Statistical Tests We have statistically compared the detectors in all datasets by carrying out the Friedman non-parametric statistical test as described in  [11]. This test is the first step to know whether any of the detectors have a performance statistically different (in prequential accuracy, RAM-Hours, µD, and M CC) from the others. The null hypothesis states that all detectors are statistically equal, and in all cases was rejected. Then it is necessary to use a post-hoc test to discover in what detectors there is a statistical difference (in prequential accuracy, RAM-Hours, µD, and M CC), and we used the Nemenyi post-hoc test  [31]  with 95% confidence to compare all the detectors against all the others. The results are graphically presented showing the critical difference (CD) represented by bars and detectors connected by a bar are not statistically different.
Results and Discussion For the sake of space, we only present the mean results in Table  2. Detailed results are provided in https://github. com/TxusLopez/CURIE. Figure  4  presents the evaluation of the concept drift detection methods based on the results of the Table  2. In Table  2  we observe that CURIE and ADWIN achieve the best pACC metric with 0. 83. However, CURIE is the worst in terms of RAM -Hours with 0. 0009449. Here, in favor of CURIE, it is worth mentioning that it is competing with well-established detectors whose code have been optimized and tested by the community in the scikit-multiflow framework  [30]. Probably, future versions of CURIE will be more competitive in terms of this metric. Regarding detection metrics, CURIE is the best with 465. 45 for µD and 0. 37 for M CC.
According to the ranks of Figure  4 , ADWIN, DDM and CURIE are the best detectors in terms of pACC, yet no statistical differences between them. Regarding the RAM -Hours metric, CURIE and DDM are the worst detectors, with no statistical differences between them. However, in what refers to µD and M CC, CURIE, ADWIN, and EDDM are the best detectors, yet again no statistical differences between them. The conditions of the Nemeneyi test have been very tight (95% confidence for 5 detectors in 20 datasets) and it is difficult to achieve statistical differences. Even so, CURIE has shown to be an interpretable drift detector competitive in terms of predictive performance (pACC) and detection metrics (µD and M CC), without depending on the output (class prediction) of the base learner. Moreover, CURIE provides competitive metrics for abrupt and gradual drifts, being this issue very controversial in the drift detection field, as it was shown in  [17].
Conclusion and Outlook This work has presented CU RIE, a competitive and interpretable drift detector based on cellular automata. Until now, cellular automata have shown to be suitable solutions for data mining tasks due to their simplicity to model complex systems, being robust to noise and a low-bias method. Besides, they are computationally complete with parallelism capacity, and they already showed competitive classification performances as data mining methods. This time, we have focused on their capacity to detect concept drift. They have revealed themselves as suitable detectors that achieve competitive detection metrics. They have also allowed base learners to exhibit competitive classification accuracies in a diversity of datasets subject to abrupt and gradual concept drifts. They are suitable candidates to represent data distributions with a few instances, being this ability welcomed in data stream mining tasks where memory and computational resources are often severely constrained.
Moreover, CU RIE can act as an all-in-one approach, in contrast to many other drift detectors which are based on a combination of a base learner method with a detection mechanism. As future work, we aim to extend the experimental benchmark to more synthetic and real datasets in order to extrapolate the findings and conclusions of this study to different types of drift and more realistic applications. Applying ensemble approaches or even networks of cellular automata are also among our subjects of further study.
Acknowledgements This work has received funding support from the  ECSEL Joint Undertaking (JU)  under grant agreement No  783163  (iDev40 project). The JU receives support from the  European Union 's  Horizon 2020 research and innovation programme , national grants from  Austria ,  Belgium ,  Germany ,  Italy ,  Spain  and  Romania , as well as the  European Structural and Investment Funds. Authors would like to also thank the  ELKARTEK  and  EMAITEK funding programmes  of the  Basque Government (Spain).
Only a few countries conducted systematic, on-the-ground inventories  19, 23. For most countries data are either only available for a few well-studied forests  [24] [25] [26]  , or are limited to the distribution of potential (=unconfirmed) primary forests, typically predicted statistically or via remote sensing  [27] [28] [29]. Despite past efforts for harmonizing data  24, 30  , only recently has the first map of primary forests been released for Europe  31, 32  together with a first assessment of their conservation status  21. In a previous effort, we assembled a first European Primary Forest database (EPFD v1. 0) that included 32 local-to-national datasets, plus data from a literature review and a survey, resulting in the mapping of a total of ~1. 4 Mha of primary forest  31. This was only about one fifth of the estimated 7.
3 Mha of undisturbed forest still occurring in Europe, excluding Russia  10. Also, most of the data collected in our v1. 0 database were not open-access, and could thus not be used without the explicit consent of their respective copyright holders. Here, we build on those efforts to progress further towards a complete map of Europe's primary forests. First, we secured permission from all data holders to release all data with open-access. Second, we aggregated and harmonized 16 additional regional-to-continental spatial datasets to now cover a total of 48 independent datasets. The EPDF v2. 0 contains 18,411 non-overlapping primary forest patches (plus 299 point features) covering an area of 41. 1 Mha (37. 4 Mha in European Russia alone; Fig. 1 ) across 33 countries (Table  1 )  33. Key improvements of this new database include (a) filling major regional gaps, including European Russia, the Balkan Peninsula, the Pyrenees and the Baltic region, (2) mapping potential primary forests for Sweden and Norway (additional 16,311 polygons and 2.
Based on our own interpretation of commonly used forest terms, we deliberately excluded terms such as "unmanaged" (meaning: not under active management), "ancient" (never cleared for agriculture) or "natural" (stocked with naturally regenerated native trees). These terms indicate conditions that are necessary, but not sufficient for considering a forest as primary. Finally, we refined our search using geographical and subject filters. The literature search returned 129 candidate papers. After screening their content, we added 23 additional primary forest stands (10 in European Russia, 13 in the rest of Europe), from 13 studies (four from European Russia, and nine from the rest of Europe). Building the EPFD v1. 0 31 involved reaching out to 134 forest experts. For v2. 0 we contacted an additional 75 experts with knowledge on forests or forestry, and invited them to add spatially-explicit data on primary forests to our database.
We focussed on experts from geographical regions poorly covered in v1. 0. We received 56 answers, which led to the incorporation of 16 new datasets in our map. Given the context-dependency of definitions used in regional mapping projects, new datasets were only included if we could find an explicit equivalence between country-specific forest definitions and our definition framework  35. This was done after discussing with data contributors the criteria and categories used for constructing their datasets, which we then mapped onto our definition framework. Depending on the datasets, these criteria included: (1) forest age or structural variables  19, 23, 36  , (2) legal designation  25  or year since onset of protection 37 , (3) time since last anthropogenic disturbancee  38  , or (4) the lack of human impacts and infrastructures  39.
We integrated all data into a geodatabase, which contains primary forests either as polygons (if information on the forest boundary was available) or point locations (when having only an approximate centre location). We set 0. 5 hectares as minimum mapping unit, although only a few of the datasets already contained in v1. 0 contained polygons smaller than 2 ha (i. e. , the minimum mapping unit originally used). If available, we included a set of basic descriptors for each patch: name, location, naturalness level (based on  35  ), extent, dominant tree species, disturbance history and protection status. In total, our map harmonizes 48 regional-to-continental datasets of primary forests (Online-only Table  1 ). All data is open-access  33  , except for three datasets that we kept confidential, either for conservation or copyright reasons.
These datasets are: 'Hungarian Forest Reserve monitoring' (ID 17, custodian: Ferenc Horváth); ' Ancient and Primeval Beech Forests of the Carpathians and Other Regions of Europe'  40, 41  (ID 34, copyright: UNESCO), and 'Potential OGF and primary forest in Austria' (ID 48, custodian: Matthias Schickhofer). Additional non-open access polygons also exist for the dataset 'Strict Forest Reserves in Switzerland' (ID 30, custodian: Jonas Stillhard). These data are here referred to for transparency, but are neither included in the statistics and summaries reported here, nor in any of the remote-sensing analysis below. Post-processing. To provide common descriptions for all features contained in the geodatabase, we integrated the basic descriptors detailed above with a range of attributes derived by intersecting all polygons or points of primary forests with layers of: 1) biogeographical regions, 2) protected areas, 3) forest type, and 4) forest cover.
We used the map of biogeographical regions  42  to assign each primary forest point or polygon to one of the following ten classes: 1. Alpine, 2. Arctic, 3. Atlantic, 4. Black Sea, 5. Boreal, 6. Continental, 7. Macaronesia, 8. Mediterranean, 9. Pannonian, 10. Steppic. Similarly, we derived information on protection status and time since onset of protection for each primary forest polygon or point based on the World Database on Protected Areas (WDPA -https://www. protectedplanet. net). We simplified the original IUCN classification to three classes: 1. strictly protected -(IUCN category I); 2. protected -(IUCN categories II-VI + not classified); 3. not protected. This is a conservative aggregation recognizing the fact that, in certain contexts, logging and salvage logging are allowed inside national parks, at least in the buffer zone.
3. This yielded 14,300 polygons covering a total area of 2. 4 Mha. For Norway, even though we were able to include two datasets of confirmed primary forests, additional primary forest is expected to exist. Therefore, we derived a map of potential primary forests, based on the "Viktige Naturtyper" dataset from the Norwegian Environment Agency 47 , which maps different habitat types of high conservation value both inside and outside forested areas. We extracted all polygons larger than 10 ha classified as "old forest types" (="gammelskog"), i. e. , forests that have never been clearcut and are in age classes of 120 years or older. This yielded 2,103 polygons covering a total area of 0. 1 Mha. Importantly, these layers were neither directly integrated in our composite map, nor used to calculate country level statistics as they only represent a first approximation of the primary forest situation in these countries, so far without ground validation.
Data Records The EPFD v2. 0 33 is composed of 48 individual datasets (Online-only Table  1 ) and the two layers of potential primary forests for Sweden and Norway. We integrated the 48 datasets into two composite feature classes, after excluding all duplicated\overlapping polygons across individual datasets. 1) EU_PrimaryForests_Polygons_OA_v20 • Composite feature class combining the forest patches classified as "primary forest" based on polygon data sources described in Online-only Table  Fig. 3  Workflow and data sources for the map of potential primary forests in Sweden. Data on woodland key habitats derive from  60  (see also: https://www. skogsstyrelsen. se); forest with conservation value from  61, 62  , forest core areas from  63  , continuity forests from  64, 65  , protected mountain coniferous forests from  66  , clear cuts and fellings from https://www.
skogsstyrelsen. se. The individual datasets are also included in the geodatabase, inside the feature dataset 'European_ PrimaryForests'. The whole database is stored in Figshare (https://doi. org/10. 6084/m9. figshare. 13194095. v1)  33. The file format is ESRI personal geodatabase (. mdb). Each feature class in the geodatabase follows the structure described in Online-only Table  2. A full description of each individual dataset is reported in the metadata file 'DATASET_overview_v2. 0_20201030. docx' , available at the same link.
technical Validation We benchmarked our data against country-level statistics on primary forest extent. Although we had no direct control of the raw data contained in our database, the fact that all our information on primary forest locations derives either from peer-reviewed scientific literature, or was field-checked by trained researchers and/or professionals suggests high data reliability. We made sure to have a common understanding with data contributors about forest definitions [i. e. 34, 35 ,], and only included a dataset in the EPFD if we could find an explicit equivalence with the forest definitions we used. Additional information on the harmonization process is reported for individual datasets in the metadata accompanying our geodatabase. An additional, wall-to-wall validation of our database using remotely-sensed information is currently impossible.
Remote sensing data only cover the last 35 years, and even if high resolution laser ranging (LIDAR) might become available in the future, at the moment no reliable workflow exists for mapping primary forests from such multi-sensor data. The alternative is field work, which is clearly unfeasible given the huge area covered by our database, the large number of polygons, and the cost and time effort that would be required for a statistically valid ground sample of data. Still, remote sensing data can be helpful for checking whether a patch of primary forest underwent human disturbance after it was delineated and that is why we implemented a semi-automatic procedure based on Landsat satellite-image time series (1985-2018) (see below). Benchmarking against country-level statistics. Our database contains most of the geographical information currently available on primary forests in Europe, but we do not claim this data is complete.