dataesr/scientific-paragraphs-categorization huggingface dataset:
Cone Model The Cone Model proposes to describe the volume inside which the electromagnetic radiation is strong enough to be detected as a cone, characterized by a height and an opening angle varying with shower energy. The Cone Model allows for a purely analytical computation of the radio footprint at ground, and thus provides a very fast evaluation of the trigger condition, while it also allows for an easier understanding of the effect of ground topography on shower detection. The parametrization of the cone height and opening angle as a function of shower energy needs to be computed once only for a given frequency range. This was done as follows for the 50 -200 MHz band considered in this study: 1. We simulate with the ZHAireS code the electric field from one shower at different locations set at fixed longitudinal distances L from the X max position (see Figure  4  for an illustration).
The amplitude dispersion at a given Ω value is due to interplay between Askaryan and geomagnetic effects leading to an azimuthal asymmetry of the signal amplitude. For a shower energy E = 1. 5 × 10 8 GeV (in blue) from the E ν = 10 9 GeV dataset, we find for instance (Ω j min ; Ω j max ) = (0. 1 • ; 1. 7 • ) in the aggressive case and (0. 8 • ; 1. 2 • ) in the conservative one. Cone Model is therefore only an approximate method. The distribution of the electric field amplitudes as a function of the angular distance to the shower axis is shown for illustration in Figure  5  for the plane j located at a longitudinal distance L = 59 km. As the Cherenkov ring induces an enhancement in the amplitude profile for Ω ∼ 1 • , we actually compute two values of the angle Ω j : Ω j min and Ω j max , thus defining the angular range inside which the electric field amplitude is above the detection threshold.
Acknowledgments We are grateful to  Clementina Medina  and  Jean-Christophe Hamilton  for suggesting this study. This work is supported by the  APACHE grant  ( ANR-16-CE31-0001 ) of the  French Agence Nationale de la Recherche. We also thank the  France China Particle Physics Laboratory  for its support. The simulations were performed using the computing resources at the  CC-IN2P3 Computing Centre (Lyon/Villeurbanne -France) , partnership between  CNRS/IN2P3  and  CEA/DSM/Irfu.
In this case, the use of topological and geographical information enhances the proposed algorithm. Towards this end, many studies proposed a Hidden Markov Model (HMM) to take into account the measurement noise  [9]. The authors in  [10]  introduce a HMM to robustify the proposed MM algorithm. The HMM incorporates the topological and the geographical road network information in the transition state to ensure the temporal connectivity between links. A more recent approach presented in  [11]  utilizes the HMM for the MM task. In essence, the two approaches are similar, except for the HMM modeling. Indeed, in  [11]  the transition from one 'link' or segment to another must obey some rules, these rules include the dynamics of the vehicles and the legal and logical connectivity of the road map. In a more specific way, the latest developments use the OpenStreetMap (OSM) database to perform the MM.
Thus, in this paper, we present a complete solution for the overall localization problem. Unlike existent work, this contribution distinguishes by the information-driven approach. Indeed, we exploit the available data from the OSM map in order to extract prior about the road geometry. This strategy allows us to focalize the region of interest in the recognition procedure and ultimately reduce the computation complexity. In addition, we propose a probabilistic model that will ensure the geometric coherency between lanes marking. Finally, the main contributions can be summarized as follows: 1) An enhanced map matching method based on OSM datasets and a Hidden Markov Model 2) An ego-lane detection based on a prior OSM map and a vision based recursive recognition ego-lane marking in an information-driven fashion.
OVERALL LOCALIZATION ALGORITHM In this work, we present an end-to-end algorithm for ego localization as highlighted on Figure  1. The algorithm is intentionally divided into three modules: Road-level localization (RLL), Ego-lane level localization (ELL) and Lane level localization (LLL). This split allows us to be in phase with the current literature. Moreover, the pipeline of the algorithm allows to have modular algorithms that can be changed in the future without changing the entire algorithm architecture. In the following, we will first introduce our map-matching module based on OSM datasets, then we will use this map as a prior for our ego-lane marking detection in order to locate the vehicle within its lane. Once the egolane level localization is performed, we will proceed to the identification of the ego-lane in the road.
Road-level localization (RLL) In this section, we present our road-level localization algorithm using OSM datasets. As shown in Figure  2  the proposed module is an upgrade of our work presented in  [12]. Indeed, an HMM is added to robustify the proposed Map-Matching. Therefore, the algorithm is divided into two different stages: • Discrimination stage elimination of incongruent links based on distance, orientation difference between vehicle steering, and links heading. Additionally, a third factor was implemented, it is based on the maximum speed allowed on the road. • Selection stage in the case where the remaining candidate links are greater than one, we proceed into a selection procedure based on multiple probabilistic criteria to eliminate the ambiguity. Fig. 2 : Overall algorithm for the RLL using GPS data and OSM in order to extract the correct road and the corresponding number of lanes.
n 1 n 2 , u 0 = 0 and we take σ 0 = 0. 25. If the Way W i and W j are connected then we introduce a criterion based on  [39] , this criterion depends on the Fig. 4 : Example of road network to illustrate the transition probability calculation. In this example the number of Way candidates is the same between two consecutive frames with ∆θ being the vehicle's heading change over time, ∆ψ the Way's heading change between the two Ways W i and W j and β a chosen coefficient. Once the Way selected, the number of lanes is extracted from the OSM database.
REAL-WORLD EXPERIMENTAL RESULTS The different parts of the localization algorithm have been introduced in the previous section. In order to prove the effectiveness of the presented algorithms, real-world experiments have been carried out. To do so, we tested our algorithm on real driving datasets. The first one was collected in the region of Clermont-Ferrand in France, where we drove our acquisition vehicle on two lanes and three lanes road in a national highway. In order to collect these datasets, the acquisition vehicle was equipped with a front camera, with the addition of an IMU and a classic GPS receiver. The data have been stored on a bag using using ROS. In addition to that, the ego-vehicle provides information about its own odometery. Finally, these datasets will be made available for researchers 1.
In the following, they will be referred to as "2-lanes" for two lanes road and "3-lanes" for three lanes road (1000 images frames). Furthermore, we wanted to compare the performances of our algorithm to the literature on more challenging scenarios. Naturally, we turned our attention to the KITTI datasets  [47]. Although these dataset contain few lanechanging scenarios, we will however use some part of those in order to show the effectiveness of our RLL module. In addition, we tested our algorithm on some datasets referred to in  [19]. Unfortunately, all the data were not ready yet. We were able to test on some of them, noted as the A4-Highway Italy, for a total of 9528 frames. The collected datasets were manually annotated in a per-frame basis in order to determine the correct ego-lane classification.
In the following, we will refer to these datasets as "4-lanes". Each part of the ego-localization: RLL, ELL and LLL will be tested on the presented datasets, the results will be discussed in terms of accuracy. In the end, the overall algorithm will be discussed in terms of computation time. In order to assess the presented RLL algorithm, the correct Way has been manually annotated for each GPS frame. The resulting ground truth was compared with HMM-MM. The results are summarized on Table  2. As highlighted, the Map-Matching with the addition of the HMM improves the overall accuracy precision. This can be explained by the inclusion of the topology of the road network in the HMM. Indeed, the transition states are governed by the connectivity between links. Furthermore, we test the reliability of our algorithm in more challenging scenarios.
Thus, we used the well-known KITTI  [47]  database in urban scenarios. The used sequences are the following: "sequence_2001_09_26_0001" and "se-quence_2001_09_26_0001". Even if the two sequences were taking in urban areas, the correct map-matching obtained shows the effectiveness and the robustness of our proposed RLL algorithm in varying scenarios. Finally, it can be noticed that for the "4-lanes", the GPS datasets have not been mentioned. Indeed, practically the entirety of the datasets is on the same Highway. Thus, the results on MM would not be relevant. As discussed in  [48]  [13], in most of the work presented in the literature, the aim is to find the white strips in the image without seeking for consecutive elements of lane marking. Cnversely, in our work, we are more interested in the curvature of the lane marking than the white strips.
To overcome this issue, we would have to determine the localization of the detected vehicle relative to the ego-vehicle, which is not the case since we use solely images as input. Finally, despite that the authors 2 in  [19]  did not take into account the lane change scenarios and designed empirically the HMM. Nevertheless, we manage to outperform their results on the same datasets. Indeed, they achieved 77% correct classifications, where we were able to reach 85. 35% on 9528 frames. Some ELL in different images are presented in Figure  15. The presented results have been carried using Python 3. 7 under a Dell G3 3579 Core i7 8th generation equipped with an NVIDIA GeForce GTX 1050 Ti. The computation time results presented in Figure  16  shows that even if the entire algorithm was coded in Python, real-time implementation is possible.
CONCLUSION In this paper, we presented an end-to-end ego-vehicle localization. Starting from Road-level localization (RLL) using OSM datasets and a classic GPS receiver, to the Ego-lane level localization (ELL) using a recognition lane marking in an information-driven fashion and finally, a Lane-level localization (LLL) using the well-known YOLO detector in a probabilistic framework composed of a Bayesian Network and Hidden Markov Model to correctly determine the egolane in the road. The distinction from other work lies in the overall aspect of the ego-localization that has been tackled 2. The authors would like to acknowledge the authors of  [19]  for their help with their datasets. in stock in the paper. In addition, this work is distinguished by the information-driven approach. For our future work, we are currently working on adding detectors from different sensors, i.
ACKNOWLEDGMENT This work has been sponsored by  Sherpa Engineering  and  ANRT  ( Conventions Industrielles de Formation par la Recherche ). This work has also been sponsored by the  French government research program Investissements d'avenir through the RobotEx Equipment of Excellence  ( ANR-10-EQPX-44 ) and the  IMobS3 Laboratory of Excellence  ( ANR-10-LABX-16-01 ), by the  European Union  through the program Regional competitiveness and employment 2014-2020 (FEDER -AURA region) and by the AURA region.
Introduction Clustering  [1] [2] [3]  is probably the most powerful unsupervised tool to identify a structure in a collection of unlabeled data. It can be formally defined as the process of organizing the data into groups whose members are similar in some way and different from the members of other clusters. Many methods were developed in the past and the topic has been continuously investigated  [4] [5] [6]. One of the recurrent challenges is related to the search for solutions to manage cluster complexity (variation in size, shape, density, overlapping, noise. ) The era of big data has raised additional issues  [7]  for clustering. Most of the popular clustering algorithms were developed at a time when datasets were small or medium. Large datasets are intractable using these algorithms due to memory constraints or runtime issues.
Improving and accelerating existing algorithms can help but is only a partial and limited solution in terms of scalability  [8] : a new class of scalable processes for clustering is required. The main trend is to split the dataset and to handle the subsamples separately. Graph based structures  [9, 10]  can be used: the BIRCH algorithm  [11]  is based on a clustering feature tree structure. Other approaches implement incremental algorithms  [12] [13] [14] [15] [16]  or divide-and-conquer  [17, 18]  strategies. In this context sampling, also known as instance selection in the machine learning community, appeared as an interesting alternative. The goal is to select a sample that behaves like the whole, i. e. without losing any valuable information  [19, 20]. Sampling techniques  [21, 22]  have been explored and studied in many works  [23].
Beyond uniform random sampling, to deal with data variety and to keep the sample size small, sampling algorithms were designed to account for the data structure, e. g. the density distribution  [24, 25]. Unfortunately, the price to pay for this efficiency is that the use of the algorithms is restricted to moderate size datasets. Stratification and progressive sampling are two ways to combine data splitting and sampling  [26, 27]. In the stratification case, the dataset is split into strata, then an instance selection algorithm is applied to each stratum and the resulting sample is the union of the samples selected from each stratum. The complexity, both in time and in space, is reduced but all the strata are considered. Progressive sampling  [28]  consists, from a starting sample, in using increasing random samples until the model accuracy no longer improves.
The learning algorithm, of which clustering is a good example, is generally embedded in the incremental process  [29] , meaning that the process is designed for a specific learning algorithm. The sampling schedule to be used with progressive sampling techniques is still an ongoing issue of research. Available schemes may either yield oversized samples or take too long when the sample size grows too slowly. It is worth mentioning that the progressive sampling approach does not require all the dataset to be analyzed. This work proposes a sampling for clustering that inherits from both progressive sampling and stratification concepts. The dataset is split into strata that are statistically representative of the whole. The stratum size is designed for clustering purposes. The progressive characteristics do not require all the strata to be analyzed: the process ends when a stopping criterion is reached.
The rest of the paper is organized as follows. Section 2 summarizes the state of the art about progressive sampling and stratification approaches. The proposed algorithm is introduced in Section 3 and its behavior with respect to two sensitive parameters, the stratum size and the stopping criterion, is illustrated using benchmark synthetic datasets. Numerical experiments using synthetic and real world datasets are reported in Section 4. First, the proposed framework is compared to the sampling algorithm applied to the whole set and, second, to other progressive sampling schemes. Finally, the main conclusions and open perspectives are stated in Section 5.
Related work Sampling, also called instance selection in the machine learning community, is applied to speed up processes, especially clustering algorithms. Samples often provide sufficient accuracy with far less computational cost than clustering the whole dataset. Working with a reduced but representative sample proved necessary as the algorithms became more sophisticated to handle complex data and as the data size grew with the big data era. Three kinds of strategies have been recently developed: sampling algorithms for moderate size datasets, stratification strategies for large datasets and progressive sampling for very large, even unloadable, datasets. The first method to appear was random sampling, driven by the sample size parameter. Its main drawback is that there is no relationship between size and data structure.
To ensure a good representation of the data, random sampling has to overestimate the sample size. Many methods were developed since this basic algorithm, either in a supervised learning context (the reader is referred to  [23]  for a recent review), or to deal with unsupervised tasks, such as clustering. In this case sampling algorithms became more and more complex to handle arbitrary shapes or densities. A review can be found in  [30]. Recent algorithms are useful for knowledge discovery and data structure identification. They are mainly based on density  [31] , distance  [30]  or combine the two concepts  [32]. Even if the new developments include an optimization effort, they are slower than uniform random sampling and their use is restricted to moderate size datasets. To deal with large datasets, stratification strategies (not to be confused with stratified random sampling  [33] ), were introduced.
Dense areas are obviously represented in the strata while regions corresponding to noisy data are likely to be diluted in the whole set of strata. This way, they have less opportunity to be represented in the final set. The algorithm proposed in  [38]  is driven by the sample size. To get the target size, the stratification strategy is recursively applied on the sampling result. In a supervised framework, the sample size is reduced using ensemble classifier concepts  [39]. As each stratum is independently managed, a parallel implementation is possible. The Map-Reduce paradigm  [40]  provides a robust framework to process huge datasets using clusters of machines. Progressive sampling was developed in parallel with stratification strategies  [41, 28]. While the two concepts share the division into strata, the main difference is that using progressive sampling there is no need to examine all the strata but a stopping criterion is required.
The Probably Close Enough criterion (PCE)  [41]  formalizes this idea when the whole dataset can be processed: In the unsupervised case, this is achieved using a statistical test to compare the two distributions. The most common ones are the Chi-square or the divergence tests. The latter was used in  [48] , where it was concluded that: ''Unfortunately, the divergence test appears to be very conservative in practice, and the sample size yielded by this scheme often turns out to be nearly 50% of the whole, which is absolutely impractical for real very large data. " The criterion may be specific to a given clustering algorithm: the sampling cost of the k-means is part of the whole stratification process in  [49]. For supervised tasks, the quality function is generally based upon the classification accuracy.
PrðQðXÞ À Q ðSÞ > eÞ 6 d ð1Þ When the whole dataset is unloadable or not available, only a sequential analysis is possible  [50]. Chernoff inequality is also useful in this particular case where the expected value of the random variable is unknown. A relative error about E½X is considered, instead of an absolute one  [51]. These concepts have been used in applications dealing with query size estimation for relational databases  [52]  or to track clusters in evolving datasets  [53]. In  [54]  the authors used the evolution of the quality criterion to make the decision about convergence: jQ iþ1 ðSÞ À Q i ðSÞj 6 e ð2Þ where i and i þ 1 are two consecutive iterations. The proposal aimed at determining the additional sample size needed at each iteration until Eq. (  2 ) is satisfied. For the next iteration, s iþ1 , to meet Eq.
P½X < k < d ð4Þ Combining these two constraints, the minimum size is given in Theorem 2. Theorem 2. Let k be the number of clusters, let q P 1 define the minimum cluster size with respect to the whole dataset size, n : c min ¼ n kq. The probability that any group includes fewer items than k is less than d (0 6 d 6 1) when the stratum size satisfies: s P kkq þ kq ln 1 d þ kq ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2k ln 1 d þ ln 1 d 2 s Proof. The theorem was published in  [56]. As the number of clusters is usually unknown, a cautious attitude is to overestimate it. In the remainder of this study, the product kq is set at 20. The probability d is set at 0:01. Therefore, the stratum size depends on k which represents the minimum number of points per cluster in the sample.
Description of the algorithm The process is summarized in Algorithm 2. The inputs of the algorithm are the dataset, the sampling algorithm and two parameters that drive the process: the stratum size and the threshold, q th , that serves as a stopping criterion. These parameters are studied in the experimental section. Algorithm 2. Progressive sampling 1: Input: X (dataset), s (stratum size), A (sampling algorithm), q th 2: Output: q S (selected subset S & X) 3: S 0 ¼ £; f ¼ n=s; q ¼ 0; t ¼ j ¼ 1, stop = bf false 4: fW i g = Partition(X,s) X ¼ [ f i¼0 W i 5: T 0 = StratumSampling(W 0 , ¼ CP t ðTt Þ C P tÀ1 ðTt Þ Costs computed according to Eq. (  7 ) 13: end if 14: if (q P q th ) 15: stop = true (continued on next page)  The partition into strata is achieved in line 4. As previously described, three sets of data are needed at a given iteration, t: the current stratum, T t , is used as a validation set, the previous one, T tÀ1 is part of the candidate set of representatives jointly with the set of already selected representatives S tÀ1.
This probability is computed according to the within group distance and to the representativeness of the sample item, assessed by the number of items in the whole set it represents. This algorithm is fully driven by a unique parameter: the sampling cost. The lower the cost, the more accurate the representation and the larger the sampling set. The ProTraS parameter cost is 0:1 and the threshold is q th ¼ 0:99. The accuracy is assessed by the difference in the center locations between the partitions given by the k-means algorithm applied to the sample, c i , and to the whole set, c j. This difference is weighted by the cluster sizes w i and w j. The value is divided by the space dimension, p, as shown in Eq. 8. The distance, d m , is the Manhattan distance, and n is the size of the dataset. acc ¼ X k i¼1 ðw i þ w j Þ min c j d m ðc i ; c j Þ 2np ð8Þ The randomly chosen initial values, one for each dimension, of the centers are the same for the two sets as suggested in  [58].
Process stability The first experiment aims to check the stability of the process. Tests were conducted with a wide range of dimensions and dataset size. The results are illustrated using data of 200000 items in 15 dimensions. For each stratum size, 50 runs were carried out for a number of clusters from 2 to 7. The number of iterations achieved by the proposal was also analyzed. Table  1  shows the results. Each value is the average over the 300 trials (50 runs for each of the 6 numbers of clusters). The stratum sizes of 258; 504; 1531 and 2706 correspond to a minimum number of points for the smallest cluster, i. e. 2; 10; 50 and 100. The results show a great stability with all the indices. The accuracy is good for all the configurations in average. The variations in the standard deviation are due to the k-means random seeding.