dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2014). Secondly, they are unevenly distributed over the social spectrum, with notably certain professions and social classes having a more regular use than others  (Preoţiuc-Pietro et al. , 2015). To our knowledge, only one study has used geotagged Twitter data to observe a particular social group in its urban setting. However, the sample used was selected on the basis of a common ethnic and racial background estimated through nicknames and messages analysis  (Luo et al. , 2016). In this article, we identified a social group, the upper middle class, based on its presence in one of its place of leisure. We explore the possibilities offered by these datasets to study a specific social group's activity space. In India, the use of Twitter is particularly well segmented along socio-economic lines, since Twitter requires a good command of the English language and the ownership of a smartphone with 3G or 4G network.
These are two of the most expensive retail destinations in India, with a monthly rental of 1 000 rupees per sq. ft. and 1 250 rupees per sq. ft. , respectively 4. Our study was carried out in two stages. Firstly, in early 2015, we conducted on-site observations and surveys as well as off-site interviews with the users, inquiring about their socio-economic characteristics, place of residence, and places of leisure. The study notably revealed that the two luxury places did not only welcome ultra-highnet-worth individuals, but middle-income consumers as well. Simultaneously, we built a database of luxury shoppers' geotagged locations in Delhi based on a group of people who tweeted at least once in one of the two sites selected for the study. Combining geotagged data and qualitative data, we explored the possibilities of using geotagged Twitter data in researching social groups.
Our study also highlights the drawbacks of Twitter data, especially when not used along with ethnographic research. We will develop our argument in three parts. Firstly, we will thoroughly explain the construction of our database. Secondly, we will critically examine the possibilities it provides for the study of activity space and human mobility. Thirdly, we will demonstrate that the various social motivations to tweet create biases in social groups' representativeness, and eventually argue for the complementary use of geotagged social media and ethnographic data.
THE DATABASE: LOCATION, USER, AND DATE OF TWEETS Twitter is a micro-blogging service on the Internet, where people can send short messages or "tweets". These messages can be private (shared with friends) or public (visible to everyone). Since 2009, it became possible to add the geolocation of the device via "geotagging" of the message, even if this option is blocked by default 5. The Twitter Streaming API 6  allows collecting in real-time of a sample of ~1 % of the total feed of public tweets for free  (Morstatter et al. , 2013; Wang et al. , 2015). In this sample, around 10% of the tweets are geotagged, giving us information on the spatial location of the user, with an accuracy depending on the device -up to 30 metres for a smartphone outdoor  (Zandbergen et Barbeau, 2011) , and up to few kilometres for a computer far from the access point of the Internet service provider.
Consequently, we had to remove the non-human tweets from our database. We based our bot detection algorithm on the speed between two messages sent by a user so that they are slower than a plane speed  (Hawelka et al. , 2014; Jurdak et al. , 2015). But sometimes, two tweets can be sent at the same time from different locations, probably when there are network problems. In that case, the speed is infinite. We considered this bug and chose that users with more than 2% of their tweets sent at a speed higher than 600km/h would be defined as bots. We also excluded users with an average speed higher than 70km/h in urban areas, as this speed is rarely reached in locations like Delhi. We removed all the IDs consisting of 12 hexadecimal digits because they can only be MAC addresses (computers), and all the IDs of 15 hexadecimal digits, which belong to beacons, devices used in geo-marketing.
Eventually, we removed all the users with a very high tweet frequency, i. e. higher than 20 tweets a day on an average, which would mean around 2000 public tweets per day, as we could only collect 1% of the tweets. After removing the robots, we also decided not to consider low activity Twitter users, i. e. with less than 15 active days of tweets, assuming that these users would provide enough locations to perform accurate analysis of the activity spaces. The cleaned database included 5 720 169 tweets for 48 637 unique users accross Indiarespectively 41,8% and 9,58% of the original database. Eventually, in order to keep our focus on Delhi, we selected the tweets that were sent within a 30 km radius of Delhi NCR, generating a final database of 967 379 tweets for 13 349 users.
On the contrary, the Twitter dataset allows to precisely know about the frequency of visits to places whose functions can be identified using OpenStreetMap (OSM), a mapping community project that contributes to the mapping of roads, railways, and all kind of places in the world (www. openstreetmap. org). The OSM database notably helped us to highlight the functions of each user location, which we obtained by aggregating tweets within a spatial radius using the same method as Jurdak et al. (  2015 ) a dbscan approach introduced by Ester et al. , 1996 (described in Figure  2 ). We created clusters of spatial points (tweets) that are all located within a certain distance, 50 meters for this study, implying that in every cluster location, all points should be at an inferior or equal distance to 50 meters.
Drawing on our sample of people who had tweeted at least once in the two luxury commercial places, we were able to identify four shopping places that these users often visit too (see Figure  5 , Figure  6 ), two high-end shopping mall and two high streets. The two high streets (Connaught Place and Hauz Khas village) also include walking spaces, historical monuments, and parks. Consequently, the tweets might not always be sent by consumers but also by visitors and walkers. This bias could be avoided through questionnaires. However, using geotagged Twitter data has the benefit to avoid imposing answers, for instance through the selection of a few places on the assumption that they are the most visited. However, it remains important to look at the configuration of each place to understand discrepancies in results.
Since the Twitter database is not representative of all Delhi inhabitants, this algorithm just provide an estimation of home locations of Twitter users. However, we were able to detect the home of 6324 users in Delhi for 881333 tweets in 130308 locations. If we look at the entire Twitter dataset, we can observe four main poles, namely Gurgaon, South Delhi, East Delhi and West Delhi, with higher densities in South and East Delhi (Figure  7 ), with reducing density in the shopping mall dataset (Figure  7 ). As for the luxury shoppers dataset (Figure  7 ) accounting for only 164 users who tweeted in the Khan Market or in the DLF Emporio, it is noteworthy that two poles appear more clearly in South Delhi and Gurgaon, the most expensive areas of the city. On the contrary, the middle-income areas of West and East Delhi (Noida excepted) are not on the map anymore.
It is relatively small due to the inaccuracy of the locations given by the interviewees. On the other hand, 164 home location were estimated for the Twitter users that visit Khan Market and Emporio. In order to compare the two dataset with Delhi global population, we've estimated the population per colony (as the population is only available ward wise). To do so, we've detect built-up areas (using Kmeans algorithm on Landsat-8 images) and merged them with the 2011 ward-wise census, assuming a homogeneous population per ward. We've created a grid of 250m cells with the population estimation that we've intersected with the colony shapefile. Figure  9  allow to compare the percentage of population from the survey and from the census that lives in a colony with a specific property tax category.
It shows that less of 10% of the Delhiites live in wealthy colonies (A or B), this percentage rise to more 80% for our survey sample, confirming that customers of Khan market and Emporio lives in the most expensive areas of the city. While 70% of Delhi inhabitants stays in quite low property tax colonies (from D to H), it concern only few interviewees, and they lives in wealthy urban villages. If we compare the results of the survey to the Twitter database (Figure  10 ), we can notice that sample of Twitter users is more wide-spread among the different property tax categories. It thus clearly appears that there is an under-representation of high-income users in the Twitter database compared to the interviewees (Figure  10 ). Nevertheless, in both cases, luxury shoppers are over-represented in high-income areas as compared to the actual population who live there.
TWITTER IN CONTEXT: WHO REALLY TWEETS IN LUXURY SHOPPING PLACES? To our knowledge, there has been no sociological research on Twitter users in India, despite one study on the use of social media in South India  (Miller et al. , 2016)  making it difficult to integrate potential biases in the dataset based on age, gender or social categories of the users. We do not have much information on why Indian Twitter users generally post messages. However, studies in other countries have shown that Twitter is mainly used by the younger generations, both as a platform to express opinions and as a social network. The first use likely reduces the number of geotagged tweets people send, since it mostly consists of sharing personal thoughts, general information, or media content. In the other case, when users geotag the tweets they send, we can assume that they are using it as a social network since such information could be only of interest to interpersonal relation circles (Figure  11 ).
CONCLUSION To conclude, we can affirm that the use of social media geotagged data provides us with new perspectives on social groups' activity space and mobility. However, if selected on the basis of the sending of a message from a place, the sample might not be representative of the social group the study initially intended to follow, due to the various social incentives to post on social media and the varying social backgrounds of the individuals. Consequently, there is a need for a mix use of Twitter data and ethnographic methods. First of all, Twitter data can be a major help to the ethnographer, since it facilitates the inclusion of a large variety of locations in a study. This way, there are more possibilities for comparative approaches at various scales. When merged with other spatial information data (such as OpenStreetMap or Google place), such data can also help in a great way in analyzing social groups' activity space and mobility, as well as lifestyles.
For instance, luxury shopping places could seem to be an accessible and easygoing place of study, but it is not. Customers seldom want to spend time answering questions during their leisure moments; their answers are often inaccurate and partial; it consequently takes a lot of time and resources to collect a significant sample of customers; and finally, official authorizations for studies in private places are often difficult to obtain. With Twitter data, the researcher does not need the agreement of the users to inquire about their practices. Even though the Twitter users supposedly know that the information they give out is public since they signed the user agreement, they do not know that this data could serve in tracking their movements, even for scientific purposes. This is an ethical question which remains unsolved in this paper, but would deserve a larger discussion.
A new framework for high cycle fatigue analysis of metallic structures under complex multi-parameter loadings was here developed. This allows to reduce the analysis on a 2-D window with a characterized one-parameter cyclic loading thanks to an equivalence rule relative to damage between any two loadings. The simplified inelastic analysis introduced by J. Zarka [J. Zarka et al. 1990. A new approach in inelastic analysis of structures. CADLM] was used to find the limit state of the structure. A new design rules for fatigue analysis by utilizing automatic learning systems was successfully performed. A database was built by coupling numerical simulations and experimental results on several welded specimens which are considered as a general structure in the proposed approach. This could be possible by the introduction of an intelligent description of a general fatigue case based on the actual theories and models.
A multi-scale elastic analysis is considered, for example for a naval structure (Figure  4 ): (i) at the scale of the hull with rather crude mesh; elastic analysis is performed due to the various loadings, (ii) then at the level of a substructure 3-D with a refined mesh (with the initial loading and the real loading, elastic, elastoplastic or simplified inelastic analysis are performed); the equivalent radial cyclic loading is characterized, and (iii) then at the scale of a 2-D detail (one slice by a plane of the substructure) with a much refined mesh; a mobile window allows to focus at the different hot zones. The materials: base material, weld, and HAZ, are described from the material property database (smooth specimen data). The moving window is similar to a filter. Its size is such that the quantities which are needed become rather insensitive to the errors associated to the mesh size and distribution.
Conclusions From these results, the best window size has to be taken equal to 8 mm during the elastic analysis. Moreover, the simplified and elastoplastic analysis give almost the same reliability than the elastic one. Then only elastic analysis for any new structure with a window size of 8 mm have to be taken. The rules which were generated on this detail, can now be used to analyze any other structure. However, more experimental tests are still necessary to qualify fully our approach. A software, FATPRO, based on this work has been developed at MZ Intelligent Systems, the brochure in  [2].
Acknowledgements. This paper was written in part during the regular visits of the first author to  UCSD's Center of Excellence for Advanced Materials , under ONR contract  N00014-96-1-0631  ( R. Barsoum , Coordinator) to the  University of California San Diego  and for the other part by the second author during his PhD thesis under the sponsorship of Ligeron S. A. ( A. Azarian , Coordinator). We want to thank  Prof S. Nemat-Nasser  for his helpful discussions.
If this reliability is too low, that means that there is not enough data or we have bad or missing intelligent descriptors. 3. To optimize at two levels (Inverse Problems) d Considering the intelligent descriptors as independent; it is possible to get the OPTIMAL SOLUTION satisfying the special required properties and allowing the DISCOVERY OF NEW MECHANISMS, 1. To build a DATABASE of examples i. e. to obtain some experimental, real or simulated results where the EXPERTS indicate all variables or descriptors this may take a part. This is, at first, done with some PRIMITIVE descriptors x, which are usually in a limited number and which are often in a different number and type for each example. d.
Introduction Supervised Classication,  (Apte 2003 , Hand et al. 2001 , Wu et al. 2007) , based on large datasets, plays an important role in many industries, with notable examples being credit scoring  (Baesens et al. 2003) , fraud detection  (Cecchini et al. 2010) , customer targeting  (Archak et al. 2011 , Cui et al. 2006) , and surveillance  (Fang et al. 2013). In Supervised Classication, we are given a set of objects Ω partitioned into classes and the aim is to build a procedure for classifying new objects. In its simplest form, each object i ∈ Ω has associated a pair (x i , y i ), where the feature vector x i takes values on a set X ⊆ R d and y i ∈ {-1, +1} is the class membership of object i. There are several desirable managerial properties in Supervised Classication methods. Incorporating domain knowledge at the time of building the classier is a very appealing property  (Cecchini et al.
2010). When trading o between accuracy and interpretability, another popular approach has been to extract easytounderstand structures from powerful yet blackbox type classiers, such as ifthen rules, decision trees and decision tables  (Baesens et al. 2003 , Bertsimas et al. 2011 , Martens et al. 2007 , Martens and Provost 2013 , Orsenigo and Vercellis 2003 , 2004 ). Yet another way of achieving interpretability is by building discrete linear classiers  (Chevaleyre et al. 2013, Golea and Marchand 1993). Classier interpretability is a major challenge in datasets that contain a huge number of features, where most of these are irrelevant. To address this issue, models have been proposed aimed at increasing the sparsity of the classier, as is done with the Lasso, see  Li et al. (2006)  and  Roth (2004).
2013, Golea and Marchand 1993) , we propose the Discrete Level Support Vector Machines (DILSVM) where the feature scores can only take on a discrete number of levels, dened by the so-called feature rating levels. The DILSVM classier benets from interpretability, as it can be seen as a collection of Likert scales, one for each feature, where we rate the level of agreement with the positive class. We formulate the DILSVM as a Mixed Integer Linear Programming (MILP) problem. The parameters of our model, namely, the tradeo parameter C and the rating levels, may heavily inuence the performance, i. e. , the accuracy and the sparsity, of the DILSVM and, therefore, have to be carefully chosen. Thus, building the DILSVM classier involves solving a series of MILP problems, which, if solved to optimality, may make the overall computational cost high for large datasets.
For this reason we propose three strategies to alleviate the computational burden, with dierent tradeos between performance and reduction in computational cost. Such strategies use the guidance of related but simpler optimization models, and reduce the computational cost associated with each parameter vector and/or the number of parameter vectors to be inspected. In our computational experience, we compare the DILSVM against the SVM classier using ten real-life datasets. We show that the 3-point and 5-point DILSVM classiers, built using the MILP approach, have comparable accuracy to the SVM, with a substan-tial gain in sparsity. Moreover, by the very nature of our procedure (only a few levels, to be interpreted as intensities, are allowed), interpretability is denitely improved allowing us to visualize the classication process via Likert scales.
The tests illustrating the performance of the reduction strategies reveal a clear competitiveness in terms of sparsity, while the accuracy depends on the magnitude of the reduction, being close to the SVM accuracies. In our computational experience, we also compare the DILSVM against the 3-point DILSVM classier with xed parameters using ten real-life datasets. The 3-point DILSVM with xed parameters is inspired by the model in  (Chevaleyre et al. 2013). The results illustrate the relevance of tuning parameters to ensure accuracy and sparsity are not compromised. Likert scale representations allow non-experts to easily understand the classier, and there are fewer relevant features because of the improvement on sparsity. This contributes to the literature on SVM, but more generally, on Data Mining, because it signicantly improves interpretability of learning methods and their visualization, without comprising accuracy.
These advantages are obtained by extending existing SVM models, adding parameters right in the place they are needed to improve sparsity and thus interpretability. The remainder of this paper is organized as follows. In Section 2 we introduce the DILSVM classier. In Section 3 we discuss procedures for building the DILSVM classier. In Section 4 we report our computational results using real-life datasets. We end the paper in Section 5 with some conclusions and directions for future research.
As an illustration, let us consider the well-known German credit dataset, german, which is one of the datasets used in our computational tests in Section 4, with 63 features in total. This is a credit scoring dataset, with good customers dening the positive class, and has been used in the context of Supervised Classication and interpretability, such as in  Baesens et al. (2003)  where rule extraction techniques are studied. Table  5  displays the DILSVM classier with A = {-1, 0, 1} and C/n = 10 6 as a collection of 3-point Likert scales. Let us focus on three of the features, namely `having no debtor', `having a co-applicant' and `having a guarantor'. The only relevant feature is `having a guarantor', strongly contributing to being a good customer, while for the other two features the score is equal to zero.
Reduction Strategies We have formulated the DILSVM (K) as an MILP problem. Solving this MILP formulation to optimality is an N P-Hard task even if we only consider one single rating level, namely K = 1 and a 1 = 1, and C = ∞, as shown in  Chevaleyre et al. (2013). In addition, the performance of the DILSVM (K) classier may be strongly inuenced by the choice of the tradeo parameter C as well as the K rating levels. Thus, building the DILSVM classier involves solving a series of MILPs, which, if solved to optimality, may make the overall computational cost high for large datasets. In this section we present three dierent strategies to alleviate the computational burden of building the DILSVM (K) classier. The proposed strategies use the guidance of related but simpler optimization models, and reduce the computational cost associated with each parameter vector and/or the number of parameter vectors to be inspected.
For each value of C, the SVM classier is obtained, and the rounding procedure is performed using each vector of rating levels. The pseudocode of this reduction strategy is given in Figure  1 , where a 0 = ∞. While this strategy examines all the parameter vectors in the grid, it is appealing since it is cheaper to train an SVM than a DILSVM. In addition, for a given value of C, once the SVM classier has been obtained, the rounding procedure takes O(dK) time for each vector of rating levels. The second strategy is based on the randomized rounding of the LP relaxation of the DILSVM (K). We call this the randomized rounding (RR) strategy. For each parameter vector (C, a 1 ,. , a K ), the RR strategy solves the LP relaxation of the DILSVM (K) , where constraints (9) are relaxed to α + jk , α - jk ∈ [0, 1].
Step 2. Choose the optimal parameter vector using to the assignment constraints, the rounding needs to take place in a predetermined order of the rating levels, such that once a rating level and a sign has been assigned to a feature, we move to the next feature. In the current version of the RR strategy, the rating levels are arranged in decreasing order of max{α + jk , α - jk }. The pseudocode of this reduction strategy can be found in Figure  2 , where rand(p) is a subroutine of random numbers generation, returning the value 1 with probability p and 0 otherwise. K k=1 a k (β + k -β - k ) x + b. In the third strategy, the xing strategy, we use the output of the DILSVM (1) classier to alleviate the burden of building the DILSVM (2) classier. In this case, the reduction is twofold. First, the size of the parameter space is narrowed down.