dataesr/scientific-paragraphs-categorization huggingface dataset:
Time-lapse CSEM signals In order to identify time-lapse signals in our dataset related to the thermal stimulation of the RN-15/IDDP2 well, we have calculated the amplitude and phase change of the polarization ellipse of the horizontal electric field between the monitor and baseline surveys (Fig. 16 , phase not shown). We focused on the stations located along the aforementioned profile as it crosses the producing reservoir and the RN-15/IDDP-2 well. For the stations with a high signal to noise ratio and therefore high repeatability (stations 09, 14, 18, 19), no clear and consistent time-lapse anomaly related to the RN-15/IDDP-2 thermal stimulation can be identified. Indeed, observed time-lapse anomalies are random and stay within the measurement error. The only significant anomalies occur at frequencies where the signal to noise and hence repeatability is poor (e.
Greater depths of penetration can surely be achieved using more powerful transmitters (e. g. longer dipole, higher currents) as recently developed for offshore CSEM systems  (Hanssen et al. , 2017). In addition, the resistivity of the overburden has to be taken into account as more resistive overburdens can often lead to greater depths of penetration (3-4 km) with similar CSEM systems  (Coppo et al. , 2016). As shown on the Reykjanes example, MT data provides a good alternative to increase the depth of investigation (> 2-3 km) when CSEM data is of limited use. For monitoring purposes, the challenge is however to obtain a highly repeatable MT dataset  (Abdelfettah et al. , 2018). Continuous MT and CSEM monitoring surely provides a good way to control the quality of the measurements by correlating them with subsurface phenomena but it also represents a huge logistical challenge for long term monitoring.
Careful survey planning and execution allows to reduce the large number of parameters influencing survey repeatability to the level of external noise of the baseline and monitor surveys. As it can be artificially influenced, it offers the possibility to adapt the survey design to increase the chance of detecting the time-lapse signals of interest. On the contrary, little control is possible on the MT signal to noise ratio and hence repeatability. The time-lapse EM survey acquired over the Reykjanes geothermal reservoir provides the basic information for deciding when and how an EM monitor survey must be performed for the monitoring of the Reykjanes reservoir but also for the definition of the monitoring strategy of similar high-enthalpy geothermal reservoirs. Monitoring high-enthalpy geothermal reservoir development with CSEM and/or MT techniques is still at its infancy but we believe that by careful survey design and by applying dedicated data acquisition, processing and imaging techniques, sufficient data repeatability can be achieved to monitor resistivity changes associated to fluid movements in the deep geothermal reservoirs.
Acknowledgments The IDDP-2 was funded by  HS Orka, Landsvirkjun, Orkuveita Reykjavíkur , and the  National Energy Authority in Iceland , together with  Statoil , the Norwegian oil and gas company. The IDDP-2 and our project have received funding from the  DEEPEGS  project, European Union's  HORIZON 2020 research and innovation program  under grant agreement No  690771. We would like to thank  HS-ORKA  for providing access to the MT dataset over the Reykjanes geothermal field. We are also very grateful to  Steinthor Nielsson ,  Stephan Audunn Stefansson  from the  Iceland Geosurvey (ISOR)  for their logistical support during the EM surveys. We would like also to thank  Eva Schill ,  Nadine Haaf  from the  Karlsruhe Institute of Technology, Germany ,  Mariane Peter-Borie ,  Florent Beaubois  and  Esteban Pineda  for their unvaluable help during the field work.
-Definition of SimLife technology. "SimLife" technology is based on (Figure  1 ): -A fresh body from the Gift of the Body to Science. Cannulas are introduced into both femoral arteries and the left common carotid artery for circulatory input, and into both femoral veins and the left internal jugular vein for venous outflow. The distal limb vasculature can be excluded limiting vascularization to the trunk only, or one or two limbs can also be perfused. A pressure-recording catheter in the arterial system is inserted into the right common carotid artery and advanced to the aortic arch. A tracheostomy allows ventilation. A gastric tube allows aspiration of the stomach contents. Emptied of its native blood, the body is initially frozen and then thawed for eventual training use. -A technical module that animates the body uses three synchronous pumps connected to arterial catheters (arterial revascularization by simulated blood at 37° C) and another pump asynchronous with the previous ones for ventilation.
Time series classification is a task that aims at classifying chronological data. It is used in a diverse range of domains such as meteorology, medicine and physics. In the last decade, many algorithms have been built to perform this task with very appreciable accuracy. However, applications where time series have uncertainty has been under-explored. Using uncertainty propagation techniques, we propose a new uncertain dissimilarity measure based on Euclidean distance. We then propose the uncertain shapelet transform algorithm for the classification of uncertain time series. The large experiments we conducted on state of the art datasets show the effectiveness of our contribution. The source code of our contribution and the datasets we used are all available on a public repository.
In some applications, uncertainty cannot be neglected and has to be explicitly handled  [16]. Shapelet based methods are one of the best approaches that have been developed for time series classification. A shapelet is a subseries that is representative for a class of time series. These methods are especially appreciated for their interpretability, their robustness and their classification speed  [23]. A typical shapelet-based approach for classification can be summarized in three steps: This work is funded by the french Ministry of Higher Education, Research and Innovation, the LabEx IMobS3 and the CNRS PEPS project TransiXplore. Thank to the UEA & UCR Time Series Classification Repository which provides the datasets used for our experiments. • the first step is the extraction of shapelets.
This step can be seen as a feature selection, • the second step is the shapelet transformation. Here, the feature vector of each instance in the dataset is computed, • the third and last step consists in training a supervised classifier using the generated feature vectors. Almost every time series classification methods are built by coupling a similarity measure with a supervised classifier. We follow this pattern in this paper to build an uncertain time series classifier. We are not aware of any existing method in the literature for the classification of uncertain time series. Our contribution is as follows, we first propose an uncertain dissimilarity measure based on Euclidean distance. Secondly we use it to build the uncertain shapelet transform algorithm, which is the shapelet transform algorithm adapted to the classification of time series with available uncertainty information.
B. Related work on similarity measures for uncertain time series Given two uncertain time series, a probabilistic similarity measure computes the probability that the magnitude of the similarity between them is not greater than a user defined threshold  [6]. They are mostly used in the context of time series database querying. For multiset-based UTS, MUNICH  [2]  can be used. For pdf-based UTS, PROUD  [16]  can be used. Unlike probabilistic similarity measures, uncertain distances compute the dissimilarity between uncertain times series. When the distribution of the uncertainty is known DUST  [16]  can be used to compute the distance between UTS. Otherwise, the dissimilarity measure FOTS  [18]  can be used. A common limitation of FOTS and DUST is that they define the distance between two uncertain time series as a real number, without any uncertainty information on that number.
[8]  also shown that coupling shapelet transformation with a good classifier, particularly an ensemble classifier, significanly improves the classification accuracy. An optimization of shapelet transform classification has been proposed by  [5]. It reduces the execution time of the shapelet selection step, and optimizes the shapelet evaluation for multiclass classification. The greatest limitation of shapelet-based classification approaches is their time complexity during the training step, which is in the order of O(n 2 m 4 ), where n is the number of time series in the training dataset and m is the length of the longest series. Despite the high time complexity of shapelet algorithms, they are very appreciated because they are easy to interpret, robust to outliers and fast at classifying a new instance.
A. Definition of concepts Definition 4 (Uncertain subsequence): An uncertain subsequence S of an uncertain time series T is a series of l (its length) consecutive uncertain values in T. S = Ŝ ± δS = {t i+1 ± δt i+1 ,. , t i+l ± δt i+l } 1 ≤ i ≤ m -l, 1 ≤ l ≤ m, m = |T | (7) Definition 5 (Uncertain dissimilarity): The dissimilarity between two uncertain subsequences S and R is the uncertain distance between them d = U ED(S, R) = U ED(R, S) (8) The dissimilarity between an uncertain time series T and an uncertain subsequence S is the dissimilarity between S and the subsequence of T that is the most similar to S. It is formally defined as follows: U ED(T, S) = min{U ED(S, R) | ∀R ⊆ T, |S| = |R|} (9) Definition 6 (Uncertain separator): An uncertain separator sp for a dataset D of uncertain time series is an uncertain subsequence that divides D in two parts D 1 and D 2 such that: D 1 = {T |U ED(T, sp) ≤ , ∀T ∈ D} D 2 = {T |U ED(T, sp) > , ∀T ∈ D} (10) As in  [8] , the quality of a separator is measured using the information gain (IG).
B. Uncertain shapelet transform classification Our algorithm for uncertain time series classification is an extension of the shapelet transform algorithm  [8]. Given a dataset D of uncertain time series, the first step is to select the top k best uncertain shapelets from the dataset. This step is achieved using the procedure described by Algo. 1, which takes as input, the dataset D, the maximum number of uncertain shapelets to be extracted k, the minimum and the maximum length of an uncertain shapelet M IN and M AX. This algorithm uses three subprocedures: C ← ∅; Q ← ∅ 3: for i ← 1, n do 4: cands ← GenCand(T i , M IN, M AX) 5: qualities ← AssessCand(cands, D) The next step after the top-k uncertain shapelets selection is the uncertain shapelet transformation. This step is done using Algo. 2, which takes as input the dataset D, the set of the top-k uncertain shapelets S and the number of uncertain shapelets k.
For each uncertain time series in the dataset, its uncertain feature vector of length k is computed using U ED. The i th element of the vector is the U ED between the uncertain time series and the uncertain shapelet i. Because the uncertainties add up during the transformation, the uncertain feature vectors are such that the scale of the best guesses is smaller than the scale of the uncertainties. It is very important to have everything on the same scale. The second for loop of Algo. 2 performs the standard normalization of the transformed dataset. We use D:j to represent the list of the best guesses of uncertain dissimilarities between every uncertain time series and the j th uncertain shapelet, and δD :j is the list of the corresponding uncertainties. The scaled and transformed dataset is finally returned by the algorithm.
Algorithm 2 Uncertain Shapelet Transformation function USHAPELETTRANSFORMATION(D, S, k) for i ← 1, n do temp ← ∅ for j ← 1, k do temp j ← U ED(T i , S j ) end for D i ← temp j end for for i ← 1, n do for j ← 1, k do best ← Dij -mean( D:j ) std( D:j ) delta ← δDij -mean(δD:j ) std(δD:j ) D ij = best ± delta end for end for return D The transformed dataset end function The third and last step is the effective classification. A supervised classifier is trained on the uncertain transformed dataset, such that, given the feature vector of an unseen uncertain time series, it can predict its class label. Since the uncertainty have been propagated, the training process can be aware of uncertainty by taking it as part of the input. More specifically, best guesses are features and uncertainties are features of best guesses, and thus are metafeatures.
There exists many supervised classifiers in the literature for the classification of uncertain tabular data  [1] ,  [9]. We have decision tree-based methods  [13] ,  [20] , SVM-based methods  [4] ,  [10] ,  [22]  and Naive bayes-based methods  [14] ,  [15]. Since the transformed data is an uncertain tabular data, uncertain supervised classifiers can be used for the classification step. Furthermore, any supervised classifier can be used as soon as the transformed dataset is formatted in a way that is accepted by that classifier. If instead of U ED, one of the existing metrics from the state of the art (DUST, MUNICH, PROUD or FOTS) is used, the classifier would not be able to learn while being aware of uncertainty in the input since the output of these metrics are apparently 100% reliable; most importantly, it would not be possible to take advantage of an uncertain classifier.
Fig. 1  gives an overview of the classification process. During the training step, top-k uncertain shapelets are selected and an uncertain supervised model (illustrated here by a decision tree for simplicity) is trained on the uncertain transformed dataset. During the test step, the uncertain shapelets extracted during the training step are used to transform the test set, and the trained model is used to predict the class labels of the test set according to the result of the transformation. We call this model UST for Uncertain Shapelet Transform classification. Since the number of shapelet candidates of length l in the dataset is bounded to n × (m -l + 1), the subprocedures used by the Uncertain Shapelet Transform algorithm do not last forever; the rest of the algorithm are for loops, and thus the UST algorithm ends.
The algorithm also evaluates all possible shapelet candidates and keep only the k best ones. In term of time complexity, it is the same time complexity as the original shapelet transform (ST) which is O(n 2 m 4 ). In fact the differences are the dissimilarity computation and the transformation process. UST uses UED to compute the dissimilarity, while ST uses the Euclidean distance (ED). The time complexity of UED is O(n) + O(n) which is asymptotically equal to O(n), the time complexity of ED. The scaling of the transformed dataset does not change the complexity order of the transformation process as well.
To discretize I (using Eq. 5), we fixed the value of k to 100. Larger values of k lead to best approximation of I, however slow the classification process. We tried several values of k, but k = 100 worked better. We have also used a relaxed version of the stochastic ordering: given two random variables X and Y , we have X ≤ st Y if the number of values t in I such that CDF X (t) > CDF Y (t) is greater than the number of values t in I such that CDF X (t) ≤ CDF Y (t). For the interval ordering, we say that x ≤ y if P r[x ≤ y] > 0. 5 3) supervised classifier: This is the model used to classify the transformed dataset in the last step of UST. We used the classical Gaussian Naive Bayes (GNB) and the Uncertain Gaussian Naive Bayes (UGNB) models. We implemented UGNB following  [15]. We choose these classifiers for their simplicity, we want to evaluate UED, the importance of propagating uncertainty following by the use of a classifier that takes uncertainty into account during its training phase.
For each model, the parameter M IN and M AX are set to 3 and m -1 respectively, where m is the length of the uncertain time series in the dataset being processed. Because of the high time complexity of the algorithm, we have used a time contract to limit the execution time of each model. After the evaluation of an uncertain shapelet candidate, the next candidate is evaluated only if there is time remaining in the contract; otherwise the shapelet search is ended. Because FOTS is more time consuming than ED, UED and DUST, we set FOTS's time contract 12 times higher above the time limit of other measures. Tab. I gives a summary of the different models that are evaluated and compared throughout our experiments. In order to apply the model UST(UED, GNB), each uncertain feature  vector is flatten such that the first half contains the best guesses and the second half contains the uncertainty deviation.
B. Datasets We used datasets from the well known UCR repository  [7]. Instead of running our experiment on the whole repository, we use only datasets on which shapelet approaches are known to work well. According to  [3] , shapelet approaches are more suitable for electric device, ECG, sensor and simulated datasets. Tab. II gives a summary of the 15 shapelet datasets on which we conducted our experiments. The first column is the name of the dataset, the second is the number of instances in the training/test set, the third is the length of time series and the fourth and last column is the number of different classes in the dataset. Each dataset is already split into the training and the test sets on the repository. Since the datasets in this repository are without uncertainty, we manually add uncertainty in the datasets listed in Tab.
II. Given a dataset, the standard deviation σ i of each timestep is computed. For each time series in the dataset, the added uncertainty for the observation at timestep i follows a normal distribution with mean 0 and standard deviation c × σ, where σ is randomly chosen from a normal distribution with mean 0 and standard deviation σ i. We used different values of c ranging from 0. 1 to 2. The uncertainty result for an instance from the Chinatown dataset is shown by Fig. 2   We implemented UST in the Python programming language, and we used the open source package sktime  [11]. The code and the data used for our experiment are publicly available 1.
The model ST is the classical shapelet approach, in which the Euclidean distance is used. The classifier used is the Gaussian naive bayes. In this model only the best guesses are used, and there is no uncertainty handling at all. For low uncertainty levels, this model is the second best model, behind UST(UED, UGNB). When the uncertainty increases, ST becomes among the worst models, exhibiting the importance of uncertainty handling in time series classification. For instance, on the dataset SmoothSubspace and the uncertainty level of c = 0. 4, ST achieves 47% of accuracy, UST(UED, GNB) achieves 49%, while UST(UED, UGNB) achieves 83%. Training duration: In term of training duration, the UST model that uses FOTS dissimilarity takes in average 128 ± 9 minutes to finish. When using DUST, ED or UED, UST takes in average 10 ± 0.
D. Overall discussion To build the uncertain shapelet transform classification algorithm, we have handled uncertainty in each step of a typical shapelet algorithm. During the first step where shapelets are selected, UED is used to select shapelets while taking uncertainty into account; when two shapelets has the same information gain, the one that is less uncertain is preferred. During the shapelet transform step, the uncertainty is propagated so that the transformed dataset contains uncertainty information. To really take advantage of the propagated uncertainty, a classifier that has been built for uncertain data is used in the last step. Without the use of an uncertain classifier, all the previous steps of uncertainty management are not really worthy. Uncertainty is unpredictable, and because we are dealing with it, it is difficult to identify in which uncertain situation our approach will work well.
For this reason, we use different levels of uncertainty in our experiment, expecting to cover at most possible situations as we can. The uncertainty levels from c = 1 to c = 2 are more likely to be extreme and may not be found in a real application, but it is important to see how the model's behaviour as the uncertainty becomes too large. We manually added uncertainty in our datasets. Applying our model on a real uncertain dataset will strengthen our contribution. Nevertheless, by using different levels of uncertainty in our datasets, we expect to cover any real situation. The uncertain classifier we used is the uncertain naive Bayes. We choose it for its simplicity. There are other uncertain classifiers  [1] ,  [9] , and they can be used in UST, but we did not try them because our goal was to show how important it is to correctly handle uncertainty in the context of uncertain time series classification.
VI. CONCLUSION The goal of this paper was to classify uncertain time series using the shapelet transformation approach. To achieve this goal, we use uncertainty propagation techniques to define an uncertain dissimilarity measure called U ED. Then we adapt the well known shapelet algorithm to the context of uncertain time series using U ED and propose the uncertain shapelet transform algorithm (UST). We have run experiments on state of the art datasets. The results show that propagating uncertainty during the shapelet transformation and then using an uncertain classifier lead to a more accurate model for uncertain time series classification. The idea of uncertainty propagation can be used with any dissimilarity measure, and any uncertain supervised classifier can be used in the classification phase.
GenCand(T, M IN, M AX) which generates every possible uncertain shapelet candidates from the input uncertain time series T. These candidates are uncertain subsequences of T , with length at least M IN and at most M AX. • AssessCand(cands, D) which computes the quality of each candidate in the list of candidates cands. The quality of a candidate is the information gain it produces when used as a separator for the dataset. Cameroun • ExtracBest(C, Q, k) which takes the list of uncertain shapelet candidates C, their associated qualities Q and returns first k uncertain shapelets with highest qualities. In summary, Algo. 1 generates every uncertain subsequences of length at least M IN and at most M AX from the dataset, assesses the quality of each one by computing the information gain obtained when it is used as a separator for the dataset and finally returns the k subsequences that produce the highest information gain.
• GenCand(T, M IN, M AX) which generates every possible uncertain shapelet candidates from the input uncertain time series T. These candidates are uncertain subsequences of T , with length at least M IN and at most M AX. • AssessCand(cands, D) which computes the quality of each candidate in the list of candidates cands. The quality of a candidate is the information gain it produces when used as a separator for the dataset. Cameroun • ExtracBest(C, Q, k) which takes the list of uncertain shapelet candidates C, their associated qualities Q and returns first k uncertain shapelets with highest qualities. In summary, Algo. 1 generates every uncertain subsequences of length at least M IN and at most M AX from the dataset, assesses the quality of each one by computing the information gain obtained when it is used as a separator for the dataset and finally returns the k subsequences that produce the highest information gain.