dataesr/scientific-paragraphs-categorization huggingface dataset:
Acknowledgements This research conducted through the  Structured Operational Research and Training Initiative (SORT IT ), a global partnership led by the  Special Programme for Research and Training in Tropical Diseases at the World Health Organization (WHO/TDR ). The model is based on a course developed jointly by the  International Union Against Tuberculosis and Lung Disease  ( The Union ) and  Medecins Sans Frontieres  ( MSF/Doctors Without Borders ). The specific  SORT IT program  which resulted in this publication was jointly organized and implemented by  The Centre for Operational Research, The Union, Paris, France ;  Department of Medical Research, Ministry of Health and Sports, Yangon; Department of Public Health, Ministry of Health and Sports, Nay Pyi Taw ; The Union Country Office, Mandalay, Myanmar; The Union South-East Asia Office, New Delhi, India; and  London School of Hygiene and Tropical Medicine, London, UK.
On the other hand, strong usage anomalies have been observed in relation to demographic clusters, educational clusters, geographic clusters, and professional clusters. For cellular communications,  Jain et al. (1999)  show that cellular service usage levels differ by customer segments (i. e. , business/professional and personal). However, such segments have not been substantiated in mobile data usage. Amdocs' 2015 State of the RAN (Radio Access Network) reported that 10 percent of mobile users has consumed 80 percent of the world's mobile data traffic and the power users often used as much as 10 times more data than the average mobile subscriber based on 25 million voice and data connections (all with lots of smartphone usage) in major cities around the world. 2 Cisco's Visual Networking Index focused on overall global carrier trends in February 2017 reported that the top 20 percent of mobile users generate 56 percent of mobile data traffic and the top 5 percent of users consume 25 percent of mobile data traffic by September 2016.
We face the same clustering problem as  Santi et al. (2016)  such that all available dissimilarity matrices are used to deal with heterogeneity. Numerous studies use the axiomatic fuzzy set (AFS) clustering methodology (see  Xu et al. , 2009; Xie et al. , 2016; Bagirov and Yearwood, 2006). Kim et al. (2005)  conduct a kernel-based classification with four clustering algorithms (i. e. , K-means, Fuzzy C-means, average linkage, and mountain algorithm) and evaluate their performances for various datasets. Their results indicate that each kernel clustering algorithm evidently performs better than its conventional counterpart. Carrizosa et al. (2014)  propose a variable neighbourhood search method in clustering networks. Bai et al. (2016)  propose a hybrid methodology of fuzzy C-means for decision modelling in green supply chains.
2). The EM algorithm is easy to implement and numerically stable under certain conditions that suffice for reliable global convergence. However, when multiple maxima exist, it may converge slowly without convergence bounded to the global maximum. In addition, the EM algorithm is sensitive to the initial values of w k , µ k and C k that start the search on the likelihood surface  (Bishop, 2006). The main approach to initialize the EM algorithm is K-means, where each cluster is represented by the center of the cluster gravity, but K-means is probably dominated by extreme values in the dataset and therefore results in a singular problem in the EM algorithm. To resolve this issue, we propose a stochastic initialization such that the multiple starting points are chosen and evaluated by their entropy with respect to their ambient values.
Anomalies are those data with extreme values or abnormal distances from most data in the dataset and are not necessarily related to or clustered with each other. Our experience in commercial mobile operations indicates that anomalies do not occupy the main proportion of the dataset. We use the Euclidean distances d i,j to be the measurement between any two data in the dataset. For 1 ≤ i = j ≤ N , we have d i,j = x i -x j 2. ( 3 ) With Equation (3), we identify anomalies in the dataset by discrete entropy. Specifically, we use the histogram approach to approximate the probability density function of the distances from one data to all other data in the dataset and estimate the discrete entropy. The histogram partitions the distances from one data to all other data in the dataset into B disjoint bins, and we therefore have a sequence of distance intervals a 0 , a 1 , • • • , a B.
For every x n , we construct a distance vector d n = [d n,1 , • • • , d n,N ], and then partition these distances into histogram p n = [p n,1 , • • • , p n,B ], where 0 ≤ p n,b ≤ 1 and B b=1 p n,b = 1 for 1 ≤ b ≤ B. The discrete entropy of d n is defined as: H(d n ) = B b=1 p n,b log (p n,b ). (4) Equation (  4 ) is used in this paper to estimate the relative positions of data in the dataset. If x n is in the dense area, the distances from x n to those data belonging to the same cluster or in the adjacent areas contribute to shorter distances. Those data not in the adjacent areas, i. e. , anomalies, result from longer distances. The distribution of p n diversifies and consequently H(d n ) is relatively large. On the other hand, if x n is an anomaly, the distances from x n to all others are only distributed among some specific ranges with large values and H(d n ) is relatively smaller.
If we use order statistics to sort the entropy values and directly select data with the top K entropy values as initial values for µ k , data from the same cluster is very likely to be chosen, as data with similar entropy values are usually clustered in neighbouring regions. Therefore, we use the weighted random selection approach to initialize µ k and give higher priorities to those data with larger entropy values. Imagine a queue with unequal-sized slots. The size of the slot for each data s n to occupy is proportional to the entropy value of the data with respect to the total entropy values of the dataset H(d n ) N m=1 H(d m ) , and each slot is numbered in the corresponding index. In every iteration, we generate a random number r ∈ [0, 1), find out which slot r falls into, and the data with the index will eventually be selected as µ k.
Penalized Likelihood To determine the number of the MGM components to best approximate the true distribution of the dataset, we first specify the range [K min , K max ] for the number of components in the mixture model, construct a candidate pool for all possible numbers K of the MGM components where K min ≤ K ≤ K max , and use the model selection technique to evaluate the performance of all candidate models. This section considers some frequently used information criteria that trade off accuracy and complexity in the model construction. The likelihood of the candidate model expresses the accuracy of the fitting model, and the higher the likelihood, the better the performance fit. The total number of free parameters in the candidate model defines the complexity. At the same likelihood level, a simpler candidate model with better performance should be selected.
(13) We consider AIC, BIC and HQC simultaneously and select the model with the best performance from all candidate models. In addition to using the information criterion to evaluate the performance of candidate models, we also use the F -fold cross validation technique to examine the stability of the candidate models, which randomly partitions the original dataset Θ into F equal-sized subsets Φ f for 1 ≤ f ≤ F. That is Θ = 1≤f ≤F {Φ f }. For every possible K in MGM, the cross validation process is repeatedly executed in F rounds, where every data is tested once in the process as all data are equally important. Every round of cross validation involves training with F -1 subsets Φ T and validation with the remaining subset Φ V and Θ = Φ T ∪ Φ V. In the training stage, we use Φ T to estimate the appropriate K pair parameters, including w k , µ k and C k for 1 ≤ k ≤ K.
Accuracy evaluation This section compares MGM with other previously proposed methods, including K-means, K-means++, Fuzzy C-means (FCM), and normalized cuts (N-Cuts)  (Shi and Malik, 2000; Bai et al. , 2016; Santi et al. , 2016). We use three datasets to examine the clustering accuracy under different cluster characteristics. Since these datasets are generated from the given mixture model information, including the data and the labels that mark the true cluster of each data, it is easy to evaluate the accuracy of our proposed method by checking whether the clustered labels are consistent with the true labels. The first dataset is the stereotype Gaussian mixture model composed of two multivariate Gaussian distributions as per  As the dataset has been labelled for the underlying true clusters, it is easy to identify errors.
We report the clustering error rates with different methods in Table  1  for Dataset-I indicating that our method has the lowest error rates for the three experiments (i. e. , with 2-dimensional, 4-dimensional, and 16-dimensional data). We observe two interesting facts. First, K-means, K-means++ and FCM show almost identical error rates. Second, when the dimension increases, the errors decrease for K-means, K-means++, FCM and MGM. The Dataset-I benchmark data shows strong distance-dependent characteristics, particularly for higher dimensions, namely, by increasing the dimension, the µ k values depart further from each other. N-Cuts do not depend on distance to separate clusters. On the other hand, the K-means, K-means++ and FCM are distance-based clustering methods, and therefore benefit from µ k departure in clustering.
Dataset-II The accuracy of clustering methods is easily dominated by the anomalies in the dataset, particularly for the distance-based methods. For Dataset-II, we follow the simulation method used by  Yang et al. (2012)  to test the clustering performance under the effects of (1) different level of perturbation (anomalies), and (2) overlapping clusters. To examine the robustness of the proposed method, we generate the parameters of the bivariate Gaussian mixture model with different K. We set K min = 3 and K max = 5 and therefore have three test cases (i. e. , K = 3, 4 and 5) in Dataset-II. We first assign K = 3 and apply Algorithm 1 to derive the corresponding parameters, including the mean vectors: µ 1 = (0. 5 0. 5) T , µ 2 = (6 6) T , µ 3 = (10 10)  For each K, we sample 2,500 paired data, including the data and the true labels.
In each test case, we consider the perturbation of anomalies, since extremely large data usages indeed exist in our measured data of the commercial mobile operation dataset. Anomalies are sampled from a uniform distribution in the range  [50, 200]. We gradually increase the occupied ratio of anomalies from 1% to 25% in each test case resulting from our observation of actual consumers' mobile data usages where anomalies did not occupy the main proportion of the dataset. Each ratio of anomalies is run 200 times and we evaluate the clustering accuracy under the predetermined perturbations. We compare our method with other algorithms by mixing 3, 4 and 5 bivariate Gaussian distributions with Dataset-II. For K = 3, the true clusters in the data are 3. Table  2  report the results with different perturbation rates ranged from 1% to 25%.
Dataset-III For Dataset-III, we consider the clustering performance under the effects of (1) the Gamma mixture model, (2) different level of perturbation (anomalies), and (3) overlapping clusters. The most important property of the Gamma distribution is its skewness and kurtosis, which allows a skew center in one cluster and relaxes the constraint that distribution in one cluster should always be symmetric. The shape parameter α and the scale parameter β determine the Gamma distribution, where the mean is αβ and the variance is αβ 2. Like Dataset-II, we determine all parameters of the Gamma mixture model with different K values. When K = 3, we obtain the shape parameters α 1 = 0. 5, α 2 = 4. 8, α 3 = 40/3, and the scale parameters β 1 = 1, β 2 = 1. 25, β 3 = 0. 75. When K = 4, the shape parameters are α 1 = 0.
5, α 2 = 3, α 3 = 6. 25, α 4 = 9. 75 and the scale parameters are β 1 = 1, β 2 = 1, β 3 = 1. 6, β 4 = 2. 56. When K = 5, the shape parameters are α 1 = 0. 5, α 2 = 25/12, α 3 = 4. 8, α 4 = 64/9, α 5 = 16, and the scale parameters are β 1 = 1, β 2 = 1. 2, β 3 = 1. 25, β 4 = 2. 25, β 5 = 2. 5, respectively. Like Dataset-II, we consider the perturbation of anomalies sampled from the uniform distribution over the range  [50, 200]. We gradually increase the occupied ratio of anomalies from 1% to 25% in each test case and check whether the proposed method is robust against perturbations. Our method is compared with other algorithms using 3, 4, and 5 Gamma mixture distributions with Dataset-III. Table  3  summarizes the results with different perturbation rates ranged from 1% to 25%. In comparison with K-means, when K = 3 and the perturbation increases from 1% to 5%, MGM reduces the error rates by 82.
On the other hand, if there are some anomalies in the dataset, the performance is easily influenced by anomalies. Compared with distance-based clustering methods, N-Cut is much closer to spectral clustering methods. The N-Cuts clusters data are not directly based on distances but on measuring the total dissimilarity between different clusters and the total similarity within the clusters. When there are some elongated clusters in the dataset, N-Cuts becomes sensitive to anomalies. Along with the increase in perturbation, our method shows consistently superior performance.
Accuracy evaluation Clustering is fundamental when dealing with high-dimentional data, however, there is distressingly little general theory on it for application to a particular data. When we conduct clustering for big data, difficulties arise due to (1) undeterminable number of clusters, (2) perturbation (or anomalies), and (3) non-spherical and overlapping in a dataset. In practice, we usually observe that when perturbation increases the data points are either elongated in certain directions (i. e. , the data shape is non-spherical) or entangled (i. e. , clusters are overlapping). In our simulation, we assume that the ground-truth number of clusters is determinable. Each clustering algorithm makes specific structural assumptions that need to be considered about the dataset, that is, the shape of the clusters.
Business analytics of real mobile usages Business analytics is a process of analysing data to support decision and evaluate operations. By means of applying descriptive, predictive, and prescriptive analytics, it transforms data to valuable strategic design and provide the logical back end of searching the operational optimisation, see  Kunc and O'Brien (2018)  and references therein. In this section, we conduct a business analytics attempting to provide strategic options of revenue management for sustainability. Following the 3Ps in Jaehn (  2016 ) we hereby interpret the goals of sustainability as follows: stimulating the operator's continuous investments (profit), fostering the consumer's personalized adoption to avoid smartphone addiction (person), and mitigating  Computer-Processed Personal Data Protection Law in Taiwan 17  , they are randomly picked up by CHT from its primary databank and regarded as a representative of the new 4G service without considering any specific features of demographics, psychographics, or sociographics.
We refer to it as the CHT data in this study and treat each monthly usage as a specific feature of usage. In addition, the 12 dimensional features used to characterize the cumulative data consumption are synchronized. Due to the legislation in force, we are not clarified for any labels of these 12 features (e. g. , concrete months of the contractual period). Our experiment is therefore a double-blind test. From practitioner's viewpoint, it is a misconception that many organizations think they need "perfect" data to proceed with analytics. James Guszcza, the Deloitte Consulting chief data scientist pointed out that there's no absolute standard that describes what data is sufficient vs. insufficient and limited data set can help make valuable classifications or predictions. 18 In order to improve the statistical significance, we apply the bootstrapping method of  Sun and Meinl (2012)  to enlarge the sample to 10,000 observations with the original 12 features in our back-testing.
We show the complete procedure in Algorithm 4 in Appendix 2. We refer to this bootstrapped dataset as the augmented CHT data in our study. The advantage of bootstrapping, particularly its contribution to both natural and social sciences, has been addressed in several studies (see the Statistical Science 2003 special issue, vol. 18, no. 2). In addition, bootstrapping techniques can be used for an efficiency measurement  (Fallah-Fini et al. , 2012)  and to obtain a good estimation of the statistical properties of the original population, see  Cerquet et al. (2017)  and references therein. The descriptive statistics of the CHT data and augmented CHT data are shown in Table  6. We recognize that there exists heterogeneity in the usage data. In order to well-characterize them, we apply the density-based subspace clustering proposed in Section 3.
Predictive analytics for formulating strategic options Predictive tools (e. g. , machine learning and simulation) will strengthen formulating strategic options as they provide decision maker with actionable insights from the data, (see  Kunc and O'Brien, 2018). Our  descriptive analytics infers the imperfection of current CHT data plans in matching the user clusters. In this section, we run a predictive analytics that related to sensitivity analysis to predict revenue changes by introducing the MGM based data plan. The current data plans are directly obtained from CHT and listed in Table  9  where six data plans Λ = ∪ 6 k=1 {λ k } are bracketed from 0. 55 GB to 16 GB. In Table  9 , the two-part tariff (a lump-sum fee and a per-unit charge) applied by CHT is shown. The tariff rates Γ = ∪ 6 k=1 {γ k } indicate the basic subscription fees and two options a 1 and a 2 for data overage surcharge: NT$ 100 per 0.
e. , NT$1,336+NT$250×2) by the "billing plan iv" is eliminated when applying the minimum principle. We illustrate the machine learning procedure of determining tariff for the MGM data plans by Algorithm 5 in Appendix 2. The total revenue (Rev) of CHT data plan Λ with rates Γ (see Table  9 ) and estimated overage (see Table  7 ) can be calculated as follows (see Algorithm 6 in Appendix 2): Rev(Θ, Γ, Λ, a i , p i ) = 6 k=1 | θk | n=1 12 m=1 γ k + max 0, min p 1 ceil( x n,m -λ k a 1 ), p 2 ceil( x n,m -λ k a 2 ). ( 14 ) where a i is the overage plan and p i is its rate for i = 1, 2. Θ is the actual data usage whose characteristics are shown in Table  6 , | θk | stands for the corresponding estimated number of users for each data plan, and Θ = 1≤k≤6 { θk }. With the proposed MGM method, after identifying the number of clusters K, the new data plan brackets Λ = ∪ K k=1 {λ k } can be determined by the mean or median of µ k.
The total revenue based on the new basic plan (K, Γ , Λ ) can be calculated by Rev(K, Θ, Γ , Λ , a i , p i ) = K k=1 |θ k | n=1 12 m=1 γ k + max 0, min ∀i∈{1,2} p i ceil( x n,m -λ k a i ) , (15) where |θ k | is the number of users for each MGM based data plan and Θ = 1≤k≤K {θ k }. We propose new data plans by using 3, 4, 5, and 6 multivariate Gaussian distributions based on the descriptive results. In addition, we reduce the 12 dimensions to one dimension with the scalar mean or median of the underlying K univariate mixture Gaussian distributions. for the median-based plan, respectively. Since the tariff rates for the CHT data plans remain unchanged, the unit rates of the MGM based plans are reduced. We then compare the operator's revenue increases after applying the new billing plans by (Revenue MGM -Revenue CHT )/Revenue CHT.
9: BIC f,K ← Φ V to evaluate BIC, see Equation (12). 10: HQC f,K ← Φ V to evaluate HQC, see Equation (  13 ). 11: end for 12: for n = 1 to |Θ| do 4: AIC K ← 1 F F f =1 AIC f,K 13: BIC K ← 1 F F f =1 BIC f,K 14: HQC K ← 1 F F f =1 HQC f, Generating uniformly distributed random number: r = Random(0, 1); γ i ← γ j 4: end for Algorithm 6 Total revenue calculation Input: the dataset Θ; the CHT data allowance Λ; the CHT tariff Γ; the CHT overage plan a i and its rate p i for i = 1, 2 Output: the total revenue Rev(Θ, Γ, Λ, a i , p i ); 1: for n = 1 to N do  n 2 = 0 Initializing the number of a 2 (1 GB); 13: if x > λ then 14: if (x -λ) -x -λ > 2 a 1 then only consider a 2 because of 3 p 1 > p 2 ; 15: n 2 = x -λ 16: else comprising a 1 and a 2 17: n 1 = (x -λ) -x -λ ) a 1 18: n 2 = x -λ 19: end if 20: end if 21: V = p 1 n 1 + p 2 n 2 22: end function.
et al. (2006)  (Dataset-I). The second dataset (Dataset-II) used for clustering analysis follows Yang et al. (2012). 16 The third dataset (Dataset-III) consists of a Gamma mixture model. 4. 1. Synthetic Dataset-IAs Jain (2010) and Zimek et al. (2012)  pointed out, clustering high-dimensional data is a big challenge due to the distance concentration effect, such that irrelevant features conceal relevant information when data dimension increases. Moreover, the vast majority of real world clustering datasets have the overlapping characteristic. In Dataset-I, we check the clustering accuracy of our method under the effects of (1) varying dimensions, and (2) overlapping clusters. The Gaussian distribution dimension varies from 2, 4 to 16 (see Fränti et al. , 2006). Taking the bivariate Gaussian mixture model as an example, there are16 Clustering benchmark datasets: http://cs.
uef. fi/sipu/datasets/ 12 10 different test cases as shown in Figure1, where µ 1 and µ 2 are always located in the same positions but the value of the covariance matrix gradually increases in range from 10 to 100 along with the index increasing from 1 to 10. The overlapping region of two clusters also increases. For each test case, there are 2,048 paired data including the data values and the true labels. With 3 different Gaussian distribution dimensions, there are 30 test cases in Dataset-I.
Algorithms Algorithm 1 Initialization algorithm Input: the dataset Θ; the number of clusters K; the number of histogram bins B; Output: initial parameters for Gaussian mixture model, including µ k , C k and w k for 1 ≤ k ≤ K 1:for i = 1 to N do i ) = B b=1 p i,b log (p i,b) 9: end for 10: for n = 1 to N do 11:s n = H(d n ) N i=1H(d i ) 12: end for 13: for k = 1 to K do x i *. 17: end for 18: for k = 1 to K do 19:θ k = {x : xµ k 2 ≤ xµ j 2 ∀j = k, 1 ≤ j ≤ K and x ∈ Θ} 20: ∀x∈θ k (x -µ k ) (x -µ k ) T 22: end forAlgorithm 2 EM algorithm Input: the dataset Φ ∈ Θ; the initial parameters derived from Algorithm 1, including µ k , C k and w k for 1 ≤ k ≤ K. Output: the refined parameters for the mixture Gaussian model: µ k , C k , w k ; and θ k for 1 ≤ k ≤ K. 1: repeat 2:.
5: until L (Φ) is converged. 6: for m = 1 to |Φ| do 7: δ m ← argmax 1≤k≤K w k,m with Equation (7) 8: end for 9: for k = 1 to K do 10: for m = 1 to |Φ| do 11:θ k = δm=k {x m } 12:end for 13: end for Algorithm 3 Estimating the optimal number of components in MGM and their parameters Input: the dataset Θ; the number of partitions in cross validation F ; the range of candidate components for MGM [K min , K max ] ; Output: the parameters for Gaussian mixture models, including the number of componentsK, µ k , C k and w k for 1 ≤ k ≤ K 1: Randomly partition Θ into F disjoint subsets Φ f for 1 ≤ f ≤ F 2: for K = K min to K max doUsing Φ T to initialize parameters µ k , C k and w k with Algorithm 1.