dataesr/scientific-paragraphs-categorization huggingface dataset:
2A ). The order of the stimuli was randomized across blocks and participants. EEG recording. EEG activity was recorded from 32 electrodes mounted on an elastic cap based on the 10 -20 system (Oxford Instruments) with the addition of extra occipital electrodes using a SynAmps amplifier system (Neuroscan). The ground electrode was placed along the midline, in front of Fz, and impedances were kept Ͻ5 k⍀. Signals were digitized at a sampling rate of 1000 Hz and low-pass filtered at 100 Hz. Potentials were referenced on-line to the Cz electrode and average referenced off-line. EEG data analysis was performed using EEGLAB  (Delorme and Makeig, 2004) , a freely available open source toolbox (http://www. sccn. ucsd. edu/eeglab) running under MATLAB (The Mathworks). First, EEG data were downsampled to 256 Hz and then digitally filtered using a bidirectional linear filter (EEGLAB FIR filter) that preserves the phase information (pass-band 0.
Amplitudes were quantified for each condition as the mean voltage measured within 30 ms windows centered on the grand average peak latencies of the component's maximum amplitude. Peak latency was extracted automatically at the minimum value between 60 and 140 ms for the P100 and 110 and 190 ms for the N170  (Rossion and Caharel, 2011). To estimate reliable differences in peak amplitude or latency while limiting possible confounding issues due to multiple comparisons, we ran a paired two-tailed permutation test based on the t max statistic  (Blair and Karniski, 1993; Maris and Oostenveld, 2007)  using a familywise ␣-level of 0. 05 (32 comparisons) for each component (P100 an N170). All statistic analyses were performed using the Mass Univariate ERP toolbox  (Groppe et al. , 2011)  written in MATLAB.
01;  Barragan-Jason et al. , 2012 , 2013; Besson et al. , 2012). Minimum RTs were estimated by considering the onset of the first significant bin followed by at least 60 ms of significance  (Barragan-Jason et al. , 2012; Besson et al. , 2012). MVPA. MVPA was conducted on single-trial ERPs. A linear classifier was trained to decode the presence of a target versus distractor in single trials from individual time bins of the EEG signal across all electrodes. We derived an accuracy measure by averaging the performance of the classifier over multiple random splits of the data (see below). Such decoding analysis characterizes the temporal evolution of the category signal across the whole brain. Each input feature (electrode potential) was normalized (using a Z-score) across trials, and a linear SVM was used as classifier.
Very few studies have investigated the possibility to read out visual category information from noninvasive human electrophysiological signals. Among them, an MEG study has demonstrated the possible readout of basic object category but with late latencies (incompatible with behavioral results such as those reported in saccadic choice tasks;  Crouzet et al. , 2010)  despite the fact that isolated and cropped stimuli of faces, houses, and other textures were used  (Carlson et al. , 2011). Another EEG study reached higher decoding accuracy for line drawings of animals versus tools  (Simanova et al. , 2010). However, the study used a small number of stimuli with many repetitions and evident low-level visual differences between categories. Here, instead, we used a large database of variable natural scenes without any repetition.
In contrast, end-to-end security gives the control of both data security levels and costs back to users, through classical techniques such as data encryption, anonymization, replication and verification. However, updating and querying secured data in the cloud may turn inefficient and expensive. Thus, specific end-to-end security approaches were designed for distributed/cloud databases (DBs) and data warehouses (DWs)  [15, 18]. The MONOMI system  [20]  notably encrypts both SQL queries and data with multiple cryptographic schemes. However, although MONOMI enforces data privacy, it addresses neither data availability nor integrity issues. In contrast, secret sharing  [16]  simultaneously enforces data privacy, availability and integrity. Secret sharing transforms sensitive data into individually meaningless data pieces (called shares) that are distributed to n CSPs.
Similarly, higher level nodes represent the signatures of table groups, until the root, which stores the whole DB's signature. Signatures are checked before reconstructing data (Section 3. 2. 3). Data integrity can also be verified on-demand. Outer record signatures are created with the help of user-defined one-way functions HF * i(h). Shared record ERijg passes integrity check if s routij0g = HF * i(ERijg). Similarly, shared table ETij passes integrity check if s touti0j = HE * i( er ij g=1 HF * i(ERijg)) , where HE * i(h) are homomorphic functions and erij is the number of records in ETij. Thanks to the homomorphism property  [7] , all tables are correct if a signature stored in a root node equals the sum of the signatures stored in all its child nodes. This allows directly checking a set of records or tables through one node only, and thus speeds up data integrity verification.
Sharing Data Warehouses Since each table of a shared DW is stored in a relational database at a given CSP's and each attribute value in each record is encrypted independently, our approach straightforwardly helps implement any DW logical model, i. e. , star, snowflake and constellation schemas. A shared DW bears the same schema as the original DW's. However, all encrypted attributes are transformed into reals by the sharing process (Section 3. 2). Finally, to improve query performance, computation and data transfer costs when performing Relational OLAP (RO-LAP) operations, we use indices and cloud cubes, which are described below.
Cloud Cubes As in  [2] , our approach supports the storage of data cubes that optimize response time and bandwidth when performing ROLAP operations. In addition, in this work, cubes are directly created in the cloud and refreshed through shares and indices only. Since cloud cubes are built from shares, they are physically stored into tables that must be shared at all n CSPs, because pseudo shares are not available. In addition to customary dimension references and aggregate measures, they can include additional attributes that actually are embedded Type III indices. For example, suppose we need to compute the average of measure M from a cube. Then SUM(M ) and COUNT(M ) must be stored in the cube too, to allow computations on shares without reconstruction. Figure  7  features a cloud cube named Cube-I that sums total prices and numbers of sales by time period and by product.
Data Access Cost Query response time, which is critical in an OLAP context, directly depends on the reconstruction process time complexity, which in turn depends on t and the number of records in the query response, γ (Table  2 ). All secret sharing approaches bear the same reconstruction complexity but  [21]. However, this approach cannot compute aggregations on shares, implying all records involved in aggregations must be reconstructed at the user's, which is more costly than computing the aggregation on shares and only reconstruct the result. Moreover, we expect fVSS to be more efficient than previous approaches because we can directly perform all query types on shared DWs and cubes, in parallel, whereas other approaches cannot and must reconstruct bigger datasets before processing them at the user's.
Many real applications consume data that is intrinsically uncertain, noisy and error-prone. In this study, we investigate the problem of finding the top-k nearest neighbors in uncertain data series, which occur in several different domains. We formalize the top-k nearest neighbor problem for uncertain data series, and describe a model for uncertain data series that captures both uncertainty and correlation. This distinguishes our approach from prior work that compromises the accuracy of the model by assuming independence of the value distribution at neighboring time-stamps. We introduce the Holistic-PkNN algorithm, which uses novel metric bounds for uncertain series and an efficient refinement strategy to reduce the overall number of required probability estimates. We evaluate our proposal under a variety of settings using a combination of synthetic and 45 real datasets from diverse domains.
INTRODUCTION In recent years, the database and data mining community has investigated extensively the problem of modeling and querying uncertain data  [3, 15] , and several probabilistic database systems have been proposed  [16, 6, 28]. Uncertainty can occur for different reasons, including imprecision in the sensor measurements, approximations due to summarization techniques ,privacy-preserving transformations of sensitive records and the limited confidence in the output of predictive models. The problem of identifying the top-k nearest neighbors has been widely studied in traditional database systems  [17] , and has been successfully used to implement classifiers, recommendation engines and location-based services. Similarly, the evaluation of top-k nearest queries has received considerable attention in probabilistic databases  [12, 26, 20, 29, 8, 21, 11].
In this study, we consider the problem of finding the top-k nearest neighbors in uncertain data series, i. e. , in ordered sequences of values that are uncertain  1. Some examples are as follows: • The variations of the soil moisture during one year can be modeled by multiple measurements collected from different nearby field locations at a regular time interval. An uncertain data series can be used to model these sensor measurements to represent the uncertainty of the soil moisture within the investigated area. The type of cultivation can be assigned as class label to the uncertain data series. Nearest neighbor searches on a dataset of uncertain data series representing the soil moisture at different sites can then be used to recommend the type of cultivation in new farm lands. • Trajectories are intrinsically noisy because of imprecisions in the positioning system.
Based on those, we describe an efficient method for the retrieval of the candidate series, using a metric index. • We perform an extensive experimental evaluation, using 45 real datasets from diverse domains and synthetic datasets. The results demonstrate the effectiveness of the proposed techniques and serve as guidelines for the practitioners. This paper is organized as follows. In Section 2, we discuss different alternative models of uncertain data series and formally define our problem. In Section 3, we present our proposal. In Section 4, we discuss the experimental results. In Section 5, we survey prior studies and we conclude in Section 6.
PROBLEM DEFINITION In this section, we formalize the problem after introducing some definitions. A dataset D is a set of N uncertain data series. Similarly to prior works  [12, 8] , we further assume that the uncertain series in D are independent, i. e. , the samples drawn from uncertain series Xi are independent of the samples drawn from uncertain series Xj, ∀i = j. A data series 2  S is an ordered sequence of n real valued numbers S = S[t], 1 ≤ t ≤ n. An uncertain data series X is a data series whose values at each time-stamp are uncertain. We adopt the attribute-uncertainty model under the "possible world" semantics to represent uncertain series. A possible instantiation represents a sample value drawn from the full joint distribution of the uncertain series. We denote the value at time-stamp t of sample j of uncertain series Xi as X j i [t].
The index i may be omitted for ease of exposition. We formalize the uncertain data series model as follows: DEFINITION 2. 1 (UNCERTAIN DATA SERIES MODEL). An uncertain series X of length n is represented by m series samples. A series sample X j is a sample drawn from the full joint distribution of X. Formally, X = {X j : 1 ≤ j ≤ m}. An example of uncertain series represented under the uncertain data series model is shown in Figure  1(b). As discussed in the introduction, the uncertain data series model can represent uncertainty and correlation more accurately than other models that fail to capture the correlation of the value distributions at neighboring time-stamps. The distance between uncertain series X and query Q is uncertain and its distribution is induced by the distance measure. In particular, the distance samples are obtained by evaluating the distance measure between the series instantiations X j as defined under the uncertain data series model and Q:.
DEFINITION 2. 2 (SAMPLE DISTANCE DISTRIBUTION). The sample distance distribution between uncertain series X and query series Q is denoted by Dist(X, Q) and is defined as Dist(X, Q) = {dist(X j , Q) : j ∈ 1,. , m}, where dist(X j , Q) is the distance measure between Q and the jth instance of X. We consider the Euclidean distance as reference implementation of the dist(•) function, however other metric distance measures can be considered as well. Table  1  summarizes the most important symbols used in the rest of the paper. Now we are ready to formulate the problem of top-k nearest neighbor search in uncertain data series. Let D be a dataset of N uncertain series represented by the uncertain data series model with series length n and number of samples m. Given a query series Q, the probability of an uncertain data series Xi to be the NN (Nearest Neighbor), denoted by PNN (Q, Xi), is: PNN (Q, Xi) = P r   Dist(Q, Xi) = s ∧ ∀j =i Dist(Xj, Q) > s   ds (1) Let r(i) be a rank function s.
t. r(i) ≤ r(j) iff PNN (Q, Xi) ≥ PNN (Xj, Q). We can now introduce the definition of the top-k probable nearest neighbors: PROBLEM 2. 1 (TOP-k PROBABLE NEAREST NEIGHBORS). Given a dataset D and query Q, the top-k probable nearest neighbor search Top-k-PNN (D, Q, k) returns the k uncertain series Xi with the largest PNN (Q, Xi) probabilities. Formally, the result set is defined as {X r(1) ,. , X r(k) }. We observe that this problem is computationally bound by the evaluation of the PNN (Q, Xi) probabilities. To this effect, coarse representations of the sample distance distributions are used to refine incrementally the probability bounds. The selection of the refinements is crucial, and can affect significantly the time performance  [12, 20, 8, 11]. In this study, we propose a novel selection strategy that can tighten the probability bounds using a smaller number of iterations, thus reducing the overall number of evaluations of the probability bounds.
LEMMA 2 (DEPENDENCIES IN DISTANCE PARTITIONS). Tightening the PNN probability bounds Bi of candidate Xi ∈ X * may require some refinements in the distance partition Sj, j = i. Uncertain series Xj may not belong to the active set, i. e. , Xj ∈ X *. Demonstration by example. Let D be a dataset with N = 4 and m = 3. Let S1, S2, S3 and S4 be the instantiated distance partitions: S1 = {[2, 2] : 0. 33,  [4, 4]  : 0. 33,  [6, 6]   [5, 5]  : 0. 33,  [9, 9]  : 0. 33} and S4 = {[1, 1] : 0. 33,  [3, 3]  : 0. 33,  [7, 7]  : 0. 33}. : 0. 33}, S2 = {[4, 8] : 1}, S3 = {[1, 1] : 0. 33, The PNN probability estimates determined using the Eq. We want to identify the top-2 most probable nearest neighbors, i. e. , k = 2. Figure  5 (a) and Figure  5 (b) show the corresponding distance partitions Si and the PNN probability bounds Bi, respectively.
In the experimental evaluation we consider different strategies that have been proposed in prior works. The distance partitions Si for all uncertain series Xi are initialized using their spatial or metric bounds in the Holistic-PkNN algorithm using a linear scan on the dataset D. We observe that in the worst case all distance bounds obtained using metric or spatial bounds overlap. If the initial distance bounds overlap then further refinements are needed to discriminate the respective PNN probability bounds. In the following, we discuss how distance partitions are refined incrementally.
EXPERIMENTAL RESULTS In this section we empirically evaluate our proposal under a variety of settings, assessing time performance and accuracy. We implemented all techniques in C++, and ran the experiments on a Linux machine with Intel Xeon 1. 80GHz processors and 64GB of RAM. For all results, we report the averages of the measurements obtained from 10 independent runs, as well as the 95% confidence intervals. Confidence intervals are reported when the y-axis is not in log scale for clearness. Datasets: We consider real and synthetic datasets. Time performance is assessed on synthetic datasets constructed as follows. Let walki be a random walk of length n where the value difference between neighboring time-stamps is a normally distributed random variable with zero mean and unit standard deviation.
The series walki is then normalized  [25] , obtaining a new series denoted by seedi. The l-th sample of uncertain series Xi, X l i , is obtained by adding samples drawn from a normally distributed random variable N (0, σ) to the seedi values. Finally, the samples are normalized again. The procedure is repeated independently for each uncertain series Xi. Please note that the seed series seedi used to generate the samples of uncertain series Xi is different from the other seed series seedj, j = i. Random queries are generated similarly (and independently) to the Xi series samples. Accuracy is assessed on a second different synthetic dataset that allows us to assign class labels to the queries according to the generation model. Uncertain series are derived for a single seed series. The samples of uncertain series Xi are obtained by perturbing the seed series with standard deviation σ = α + iβ.
α ensures a minimum distance to the seed series and β imposes a total order on the distance of the seed series and the uncertain series that we use as ground truth. We observe that series X1 is the NN to the seed series according to this perturbation model, and its seed is used as query. We additionally consider 45 real datasets from the UCR time series collection (described in detail in  [1] ) with class labels. The datasets are divided into two sets, train and test. We assume that these raw series are samples drawn from unknown distributions that may be noisy and error-prone. Similarly to prior works  [8, 11, 12, 21, 31, 7, 27, 14] , uncertain series are constructed from the series in the train set: first, normalized real series are used as seed series seedi. Second, the perturbation standard deviation σ is used to generate positive samples of the normal distribution, then used independently as perturbation standard deviation σ ′ for each sample.
The resulting uncertain series is composed by a set of samples whose perturbation standard deviation varies and is controlled by σ. Evaluation measures: We now describe how accuracy and time performance have been assessed. Given a random query series Q drawn from the test set, the class label associated with the uncertain series identified as the NN in the train set is assigned as label. For each method we compute the confusion matrix M (Mij is the count of query series assigned to class i instead of j). Accuracy is defined as the ratio of true positives for all class labels: Accuracy = 1 |test| Mii, ( 10 ) where |test| is the size of the test set. If all queries are labeled correctly, M is a diagonal matrix. The experiment is repeated several times on each dataset (train and test pair sets) to get statistically significant results.
Effectiveness of Pruning Strategies The tightness of the distance bounds during the initialization of the distance partitions as detailed in Section 3. 5. 1 can greatly reduce the processing time, thanks to the early pruning of a large fraction of the candidate uncertain series. In the first set of experiments, we measure the ratio of candidates that cannot be pruned immediately after the initialization of their distance partitions for the spatial, metric and exact distance bounds on synthetic datasets constructed to evaluate the time performance. Recall that the spatial and metric distance bounds can be estimated efficiently (Section 3. 5), while exact distance bounds require the evaluation of the exact distance samples in Dist(Q, Xi). We stress that the spatial and metric distance bounds lower-and upper-bound the exact distance bounds and the final produced result is exactly the same.
As expected, the CPU cost increases linearly to the dataset size, N. Finally, we evaluated the time performance when pruning the candidates with the metric distance bounds using a linear scan over all candidates and our adaptation of the M-tree index. The M-tree index proved to be competitive to a linear scan only when the perturbation standard deviation σ is low, i. e. , σ = 0. 2. In conclusion, the distance partitions initialized using the metric distance bounds using one pivot series are the best performing. In the rest of this study we initialize the distance partitions Si using the metric distance bounds, initialized through a linear scan over the dataset.
Scalability Finally, we report our results on scalability. Figure  17(a)  shows the time performance for different levels of perturbation standard deviation σ, when varying the number of uncertain series N using the Holistic-PkNN algorithm. We observe that the incurred CPU cost for N = 10, 000 and perturbation standard deviation σ = 0. 3 is similar to the time performance for N = 100, 000 and perturbation standard deviation σ = 0. 1. The size of the dataset N and the perturbation standard deviation σ are two parameters that affect significantly the time performance of the algorithm, and even relatively small datasets are challenging when a large fraction of the distance distributions overlap (i. e. , when σ is large). Figure  17(b)  shows the time performance of Holistic-PkNN for different configurations of the number of uncertain series N and samples m.
Quality results In this section, we report our results on the classification accuracy defined in Eq. 10 on synthetic and real datasets constructed to evaluate the accuracy. Figure  18 (a) reports the accuracy for methods DUST, Euclidean-Avg and Top-k-PNN (D, Q, k) on a synthetic dataset, where the uncertain series are obtained by perturbing the query series with an increasing standard deviation σ ′. As the perturbation increases, the accuracy for DUST and Euclidean-Avg deteriorates, while Top-k-PNN (D, Q, k) manages to maintain a high accuracy. In Figure  18 (b), we present our results on 45 real datasets. The experiment shows the accuracy by varying the perturbation standard deviation σ for the NN classifier defined using the algorithms DUST, Euclidean-Avg and Top-k-PNN (D, Q, k). We observe that, as the perturbation standard deviation increases, the top-1 probable nearest neighbor formulation is more accurate than the DUST and Euclidean-Avg algorithms.
RELATED WORK The problem of modeling, querying and mining uncertain data has been investigated extensively in recent years  [4, 13]. At the same time we have witnessed an increased interest in data series management and processing  [32, 23, 22, 9] , related to data produced by sensors, or scientific experiments. The "possible worlds" model  [2]  formalizes uncertainty by defining the space of the possible instantiations of the database. Instantiations must be consistent with the semantics of the data. For example, in a spatio-temporal database there may be two distinct possible trajectories representing the uncertain trajectory of a moving object, but an object cannot be in two different locations at the same time. In the context of time series databases, a series can be formalized as a point in a high-dimensional space with correlated dimensions.