A Survey on Data Mining Techniques Applied to Energy Time Series Forecasting

Seediscussions,stats,andauthorprofilesforthispublicationat:https://www.researchgate.net/publication/283513131 Asurveyondataminingtechniquesappliedto energytimeseriesforecasting ARTICLEinENERGIES·NOVEMBER2015 ImpactFactor:2.07 READS 60 4AUTHORS,INCLUDING: JoséCRiquelme UniversidaddeSevilla 225PUBLICATIONS1,401CITATIONS SEEPROFILE Availablefrom:FranciscoMartínez-Álvarez Retrievedon:06April2016 Submitted to Energies. Pages 1 - 41.OPEN ACCESS energies ISSN 1996-1073 www.mdpi.com/journal/energies Article A SURVEY ON DATA MINING TECHNIQUES APPLIED TO ENERGY TIME SERIES FORECASTING F. Martínez-Álvarez 1,†*, A. Troncoso 1,†, G. Asencio-Cortés 1and J. C. Riquelme 2 1Department of Computer Science, Pablo de Olavide University, Seville, Spain 2Department of Computer Science, University of Seville, Seville, Spain †These authors contributed equally to this work. Version November 6, 2015 submitted to Energies. Typeset by L A T EX using class file mdpi.cls Abstract: Data mining has become an essential tool during the last decade to analyze large1 sets of data. The variety of techniques it includes and the successful results obtained in2 many application fields, make this family of approaches powerful and widely used. In3 particular, this work explores the application of these techniques to time series forecasting.4 Although classical statistical-based methods provides reasonably good results, the result of5 the application of data mining outperforms those of classical ones. Hence, this work faces6 two main challenges: i) to provide a compact mathematical formulation of the mainly used7 techniques, ii) to review the latest works of time series forecasting and, as case study, those8 related to electricity price and demand markets.9 Keywords: Energy; time series; forecasting; data mining10 1. Introduction11 The prediction of the future has fascinated the human being since its early existence. Actually, many12 of these efforts can be noticed in everyday events such as energy management [1], telecommunications13 [2], pollution [3], bioinformatics [4], earthquakes [5], and so forth. Accurate predictions are essential in14 economical activities as remarkable forecasting errors in certain areas may involve large loss of money.15 Given this situation, the successful analysis of temporal data has been a challenging task for many16 researchers during the last decades and, indeed, it is difficult to figure out any scientific branch with no17 time-dependant variables.18 A thorough review of the existing techniques devoted to forecast time series is provided in this19 survey. Although a description of classical Box-Jenkins methodology is also discussed, this text is20 particularly focused on those methodologies that make use of data mining techniques. Moreover, a21 Version November 6, 2015 submitted to Energies 2 of 41 family of energy-related time series are examined due to the scientific relevance exhibited during the last22 decade: electricity price and demand time series. These series have been chosen since they present some23 peculiarities such as nonconstant mean and variance, high volatility or presence of outliers, that turns the24 forecasting process into a particularly difficult task to fulfil.25 Actually, the electric power markets have become competitive markets due to the deregulation carried26 out in the last years, allowing the participation of all producers, investors, traders or qualified buyers.27 Thus, the price of the electricity is determined on the basis of this buying/selling system. Consequently,28 a will of obtaining optimized bidding strategies has arisen in the electricity-producer companies [6],29 needing both insight into future electricity prices and assessment of the risk of trusting in predicted30 prices.31 On the other hand, the process of forecasting the quantity of electricity required for a specific32 geographical area during a time period is called load forecasting or demand forecasting. This process33 is key since current technology allows to store only little amount of electricity in batteries. Therefore,34 the demand forecasting plays an important role for electricity power suppliers because both excess and35 insufficient energy production may lead to large costs and significative reduction of benefits.36 Some works have already reviewed electricity price time series forecasting techniques. For instance,37 [7] collates a massive review of artificial neural networks, but it barely reviews other data mining38 techniques. Also, Weron [8] presented an excellent review, describing many different approaches for39 several markets. However, none of them are focused on the whole data mining paradigm. Moreover,40 they do not provide mathematical foundations for all the methods they evaluated. And this is maybe the41 most significative strength of the paper, since information relating to underlying mathematics is provided,42 as well as an exhaustive description of the measures typically used to evaluate the performance. In short,43 this survey is to provide the reader with a general overview of current data mining techniques used in44 time series analysis and to highlight all the skills these techniques are exhibiting nowadays. As case45 study, their application to a real-world energy-related set of series is reported.46 As it will be shown in subsequent sections, the majority of the techniques have been applied to47 Pennsylvania-New Jersey-Maryland (PJM) [9], New York (NYSIO) [10] and Spain (OMEL) [11]48 electricity markets. This is due to their standard market design structure, which is basically a49 two-settlement market comprising a day-ahead market and a real-time intraday market. By contrast,50 both Australian National Electricity Market (ANEM) [12] and Ontario [13] follow a single settlement51 real-time structure and few researchers have dealt with such markets. ANEM is also well-known for52 its volatility and its frequent appearance of outliers, turning this market into a perfect target for robust53 forecasting. Additionally, the Californian electricity market (CAISO) [14] has also been widely analyzed54 because of the well-known problems that it experienced in the second half of 2000’s. Some other markets55 appear in this work, given the relevance of the model applied. Such are the cases for the UK, India,56 Malaysia, Finland, Turkey, Egypt, Nord Pool, Brazil, Jordan, China, Taiwan or Greece. Note that most57 of them provide public access to data.58 The remainder of this work is structured as follows. Section 2provides a formal description of a time59 series and describes its main features.60 Section 3describes statistical indicators and errors typically used in this field. Also, the concept of61 persistence model and forecasting skill is here described.62 Version November 6, 2015 submitted to Energies 3 of 41 In particular, Section 4describes the approaches based on linear methods. Classical Box and63 Jenkins-based methods such as AR, MA, ARMA, ARIMA, ARCH, GARCH or VAR are thus reviewed.64 Note that from this section on, all sections consist of a brief mathematical description of the technique65 analyzed and a review of the most representative works.66 As for Section 5, it is a compendium of the non-linear forecasting techniques currently in use in the67 data mining domain. In particular, these methods are divided into global (neural networks, support vector68 machines, genetic programming) and local (nearest neighbors).69 In Section 6, rule-based forecasting methods are analyzed, providing a brief explanation of what a70 decision rule is, and revisiting the latest and most relevant works in this domain.71 The use of wavelets, as relevant method for hybridization, is detailed in Section 7as well as discussing72 the most relevant improvements achieved by means of these techniques.73 A compilation of several works that cannot be classified in none of the aforementioned groups is74 described in Section 8. Thus, forecasting approaches based on Markov processes, on Grey models, on75 Pattern-Sequence similarity or on manifold dimensionality reduction, are there detailed.76 Due to the large amount of ensemble models that are being used nowadays, Section 9is devoted to77 cover these methods.78 Finally, the conclusions drawn from the exploration of all existing techniques are summarized in79 Section 10.80 2. Time series description81 This section is to describe temporal data features as well as to provide mathematical description for82 such a kind of data. Thus, a time series can be understood as a sequence of values observed over time83 and chronologically ordered. Time is a continuous variable, however, samples are recorded at constant84 intervals in practice. When the time is considered as a continuous variable, the discipline is commonly85 referred as functional data analysis [15]. The description of this category is out of scope in this survey.86 Let yt, t = 1,2, ..., T be the historical data of a given time series. This series is thus formed by87 Tsamples, where each yirepresents the recorded value of the variable yat time i. Therefore, the88 forecasting process consists in estimating the value of yT+1 (ˆyT+1) and, the goal, to minimize the error,89 which is typically represented as a function of yT+1 −ˆyT+1. This estimation can be extended when the90 horizon of prediction is greater than one, that is, when the objective is to predict a sample at a time91 T+h(ˆyT+h). In this situation, the best prediction is reached when a function of ∑h i=1(yT+i−ˆyT+i)is92 minimized.93 Time series can be graphically represented. In particular, the x–axis identifies the time (t= 1,2, ..., T)94 whereas the y–axis the values recorded at punctual time stamps (yt). This representation allows the visual95 detection of the most highlighting features of a series, such as oscillations amplitude, existing seasons96 and cycles or the existence of anomalous data or outliers. Figure 1illustrates, as example, the price97 evolution for a particular period of 2006 in the Spanish electricity market.98 An usual strategy to analyze time series is to decompose them in three main components [16,17]:99 trend, seasonality and irregular components, also known as residuals.100 Version November 6, 2015 submitted to Energies 4 of 41 0 100 200 300 400 500 600 700 0 20 40 60 80 100 120 140 Time (hours) Electricity price Figure 1. Time series example. 1. Trend. It is the general movement that the variable exhibits during the observation period, without101 considering seasonality and irregulars. Some authors prefer to refer the trend as the long–term102 movement that a time series shows. Trends can present different profiles such as linear, exponential103 or parabolic.104 2. Seasonality. This component typically represents periodical fluctuations of the variable subjected105 to analysis. It consists of the effects reasonably stable along with the time, magnitude and106 direction. It can arise from several factors such as weather conditions, economical cycles or107 holidays.108 3. Residuals. Once the trend and cyclic oscillations have been calculated and removed, some residual109 values remain. These values can be, sometimes, high enough to mask the trend and the seasonality.110 In this case, the term outlier is used to refer these residuals, and robust statistics are usually applied111 to cope with them [18]. These fluctuations can be of diverse origin, which makes the prediction112 almost impossible. However, if by any chance, this origin can be detected or modeled, they can be113 thought of precursors in trend changes.114 Figure 2depicts how a time series can be decomposed in the variables above described.115 Obviously, real-world time series present a meaningful irregular component, which makes their116 prediction a especially hard task to fulfil. Some forecasting techniques are focused on detecting trend117 and seasonality (especially traditional classical methods), however, residuals are the most challenging118 component to be predicted. The effectiveness of one technique or another is assessed according to its119 capability of forecasting this particular component. It is for the analysis of this component where data120 mining-based techniques has been shown to be particularly powerful, as this survey will attempt to show121 in next sections.122 3. Accuracy measures123 Version November 6, 2015 submitted to Energies 5 of 41 0 10 20 30 40 50 60 70 80 90 100 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time series Time Magnitude 0 10 20 30 40 50 60 70 80 90 100 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Trend Time Magnitude 0 10 20 30 40 50 60 70 80 90 100 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 Seasonality Time Magnitude 0 10 20 30 40 50 60 70 80 90 100 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 Time Magnitude Residuals Figure 2. Time series main components decomposition. The purpose of error measures is to obtain a clear and robust summary of the error distribution. It is124 common practice to calculate error measures by first calculating a loss function (usually eliminating the125 sign of the single errors) and then computing an average. Let in the following ytbe the observed value126 at time t, also called the reference value, and let ˆytbe the forecast for yt. The error Etis then computed127 by yt−ˆyt. Hyndman and Koehler [19] give a detailed review of different accuracy measures used in128 forecasting and classify the measures into the groups detailed in subsequent sections.129 3.1. Scale-dependent measures130 There are some commonly used accuracy measures whose scale depends on the scale of the data.131 These are useful when comparing different methods on the same set of data, but should not be used, for132 example, when comparing across data sets that have different scales.133 The most commonly used scale-dependent measures are based on the absolute error AEt=|yt−ˆyt|134 or squared error SEt= (yt−ˆyt)2. These errors are averaged by arithmetic mean or median, leading to135 the mean absolute error (MAE, Eq. (1)), the median absolute error (MDAE, Eq. (2)), the mean squared136 error (MSE, Eq. (3)) or the root mean squared error (RMSE, Eq. (4)).137 MAE =1 n n ∑ t=1 |yt−ˆyt|(1) MDAE =median(|yt−ˆyt|)(2) MSE =1 n n ∑ t=1 (yt−ˆyt)2(3) Version November 6, 2015 submitted to Energies 6 of 41 RMSE =v u u t 1 n n ∑ t=1 (yt−ˆyt)2(4) When comparing forecast methods on a single data set, the MAE is popular as it is easy to understand138 and compute. While MAE do not penalize extreme forecast errors, MSE and RMSE emphasize the fact139 that the total forecast error is in fact much affected by large individual errors, i.e. large errors are much140 expensive than small errors. Often, the RMSE is preferred to the MSE as it is on the same scale as the141 data. However, MSE and RMSE are more sensitive to outliers than MAE or MDAE.142 3.2. Percentage errors143 To address the scale-dependency, the error can be divided by the reference value. Thus, the percentage144 error (PE) is given by 100(yt−ˆyt)/(yt). Percentage errors have the advantage of being scale-independent145 and, therefore, they are frequently used to compare forecast performance across different data sets. The146 most commonly used measure is the Mean Absolute Percentage Error (MAPE, Eq. (5)).147 MAPE =1 n n ∑ t=1  100yt−ˆyt yt (5) These measures have the disadvantage of being infinite or undefined if yt= 0 for any t in the period148 of interest, and having an extremely skewed distribution when any ytis close to zero. Where the data149 involves small counts (which is common with intermittent demand data) it is impossible to use these150 measures as occurrences of zero values of ytoccur frequently.151 By using the median for averaging these problems are easier to deal with, as single infinite or152 undefined values do not necessarily result in an infinite or undefined measure. However, they also153 have the disadvantage that they put a heavier penalty on positive errors than on negative errors. This154 observation led to the use of the so-called symmetric measures sMAPE and sMdAPE, defined in Eq. (6)155 and Eq. (7).156 sMAPE =1 n n ∑ t=1 200 |yt−ˆyt| |yt|+|ˆyt|(6) sMdAPE =median (200 |yt−ˆyt| |yt|+|ˆyt|)(7) 3.3. Relative errors157 An alternative way of scaling is to divide each error by the error obtained using another standard158 method of forecasting as benchmark. Let rt=et/e∗ tdenote the relative error where e∗ tis the forecast159 error obtained from the benchmark method. Usually, the benchmark method is the random walk where160 ˆytis equal to the last observation. Then we can define Mean Relative Absolute Error (MRAE, Eq. (8))161 and Median Relative Absolute Error (MdRAE, Eq. (9)).162 MRAE =mean(|rt|)(8) Version November 6, 2015 submitted to Energies 7 of 41 MdRAE =median(|rt|)(9) A serious deficiency in relative error measures is that e∗ tcan be small. In fact, rthas infinite variance163 because e∗ thas positive probability density at 0. One common special case is when etand e∗ tare normally164 distributed, in which case rthas a Cauchy distribution.165 3.4. Relative measures166 Rather than use relative errors, one can use relative measures. For example, let MAEbdenote the167 MAE from the benchmark method. Then, a relative MAE is given by:168 RelMAE =MAE/MAEb(10) Similar measures can be defined using RMSE, MDAE or MAPE. An advantage of these methods is169 their interpretability. For example relative MAE measures the possible improvement from the proposed170 forecast method relative to the benchmark forecast method. When RelMAE < 1, the proposed method171 is better than the benchmark method and when RelMAE > 1, the proposed method is worse than the172 benchmark method.173 When the benchmark method is a random walk, and the forecasts are all one-step forecasts, the relative174 RMSE is the Theil’s U statistic, as defined in Eq. (11). The random walk (where ˆytis equal to the last175 observation) is the most common benchmark method for such calculations.176 U=√1 n∑n t=1 (yt−ˆyt)2 √1 n∑n t=1 y2 t√1 n∑n t=1 ˆy2 t (11) The Theil’s U statistic is a normalized measure of total forecasting error and 0≤U≤1. This177 measure is affected by change of scale and data transformations. For assessing good forecast accuracy,178 it is desirable that the Theil’s U statistic is close to zero. U= 0 means a perfect fit.179 3.5. Persistence model180 The persistence model is an important dynamic property of any time series and usually related to181 memory properties. Specifically, a time series is a persistent process if the effect of infinitesimally small182 shock will influence future predictions of the time series for a very long time. Thus the longer the183 influence time the longer is the persistence.184 If a series suffers an external shock, the persistence degree provides information about the impact of185 the shock on such series, whether it will soon revert to its mean path or it will be further pushed away186 from the mean path. In case of a highly persistence series, a shock to the series tends to persist for long187 and the series drifts away from its historical mean path. On the contrary, for the case of a time series188 with low persistence degree after a shock, the time series tends to get back to its historical mean path.189 The persistence of a time series model has been measured by different ways in literature [20].190 Version November 6, 2015 submitted to Energies 8 of 41 3.6. Forecasting skill191 The forecasting skill is a type of measures that scores the ability of a forecasting method to predict192 future values of a time series with respect to a reference model as benchmark. The forecasting skill is a193 scaled representation of the relative forecasting error and its purpose is the same of the relative measures194 introduced in subsection 3.4.195 The most commonly used forecasting skill measure is shown in Eq. (12) and it is based on the196 previously introduced mean squared error (MSE, see Eq. (3)). MSE is the error of the tested forecasting197 method and MSEbis the error of the reference benchmark.198 SS = 1 −MSE MSEb (12) A perfect forecast skill implies SS = 1, a forecast with similar skill to the benchmark forecast199 produces a SS close to 0, and a forecast which is less skillful than the benchmark would produce a200 negative SS value.201 4. Forecasting based on linear methods202 There exist real complex phenomena that cannot be represented by means of linear difference equations203 since they are not fully deterministic. Therefore, it may be desirable to insert a random component in204 order to allow a higher flexibility on its analysis.205 Linear forecasting methods are those that try to model a time series behavior by means of a linear206 function. From all the existing techniques, seven of them are quite popular: AR, VAR, MA, ARMA,207 ARIMA, ARCH and GARCH. These models follow a common methodology, whose application to time208 series analysis was first introduced by Box and Jenkins. The original work has been extended and209 published many times since its first apparition in 1970, but the newest version can be found in [21].210 Autoregressive –AR(p)–, moving average –MA(q)–, mixed –ARMA(p, q)– autoregressive211 integrated moving average –ARIMA(p, d, q)– autoregressive conditional heteroskedastic –ARCH(q)–212 and generalized autoregressive conditional heteroskedastic –GARCH(p, q)– models were described213 following this idea, where pis the number of autoregressive parameters, qis the number of moving214 average parameters and dis the number of differentiations for the series to be stationary. Vector215 autoregressive models –V AR(p)– are the natural extension for AR models to multivariate time series,216 where pdenotes the number of lags considered in the system.217 4.1. Autoregressive processes218 An autoregressive process (AR) is denoted by AR(p), where pis the order of the AR process. This219 process assumes that every ytcan be expressed as a linear combination of some past values. It is a simple220 model but that adequately describes many real complex phenomena. The generalized AR model of order221 pis described by:222 yt= p ∑ i=1 αiyt−i+ϵt(13) Version November 6, 2015 submitted to Energies 15 of 41 Figure 4. Mathematical model of an ANN. recurrent if they keep feedback links between neurons in different layers, neurons in the same layer385 or in the same neuron. Finally, the connection grade can be totally connected if all neurons in a386 layer are connected with the neurons in the next layer (feedforward networks) or with the neurons387 in the last layer (recurrent networks) and, otherwise, partially connected networks in cases where388 there is not total connection among neurons from different layers.389 2. Learning paradigm. The learning is a process that consists in modifying the weights of the ANN,390 according to the input information. The changes that can be carried out during the learning process391 are removing (the weight is set to zero), adding (conversion of a weight equal to zero to a weight392 different to zero) or modifying neurons connections. The learning process is said to be finished or,393 in other words, the network has learnt when the values assigned to the weights remain unchanged.394 3. Representation of the input/output information. ANN can be also classified according to395 the way in which information relative to both input and output data is represented. Thus, in a396 great number of networks input and output data are analog which entails activation functions also397 analogs, either linear or sigmoidal. In contrast, there are some networks that only allow discrete398 or even binary values as input data. In this situation, the neurons are activated by means of an399 echelon function. Finally, hybrid ANNs can be found in which input data may accept continuous400 values and output data would provide discrete values or viceversa.401 5.1.1.2. Extreme Learning Machine402 Extreme Learning Machine (ELM) [46] is a feedforward neural network with an only hidden layer403 that uses a method for the training faster than the classical ANNs. Namely, the ELM randomly generates404 the weights W1that connect the input layer with the hidden layer and computes the weights W2that405 connect the hidden layer with the output using a simple matrix computation. Thus, the output yis406 defined by the following model:407 y=W2ϕ(W1x)(24) where ϕis the activation function and xis the input vector.408 Version November 6, 2015 submitted to Energies 16 of 41 The training consists in computing the weights W2as follows:409 H=ϕ(W1xi)(25) W2=H+yi(26) where (xi, yi)are the points of the training set and H+represents the pseudoinverse of the matrix H.410 5.1.1.3. Self Organizing Maps411 The learning in ANN can be either supervised (perceptron and backpropagation [47] techniques) or412 unsupervised, from which the self-organizing Kohonen’s maps (SOM) [48] stands out.413 SOM have been mainly applied to discover patterns in data. The learning paradigm is based on414 a competitive learning, that is the neurons compete among them and win the neuron with the nearest415 weights to the input vector. Then, all neurons near to the win neuron update their weights according to a416 specific rule defined by:417 wj n+1 =wj n+µn(x−wj n)(27) where wj nis the weight associated to the neuron jat the n-th iteration, µnis the learning factor and xis418 the input vector.419 The neurons that are not neighbors to the win neuron do not update their weights. Finally, a clustering420 of the data is obtained when the training phase ends.421 5.1.1.4. Related work422 Many references proposing the use of ANNs, or a variation of them, as a powerful tool to forecast423 time series, can be found in the literature. The most important works are detailed below. Furthermore,424 the creation of hybrid methods that highlight most of the strengths of each technique is currently the425 most popular work among the researchers. However, from all of them, the combination of ANN and426 fuzzy set theory has become a new tool to be explored.427 Rodríguez and Anders [49] presented a method to predict electricity prices by means of an ANN428 and fuzzy logic, as well as a combination of both. The basic selected network configuration consisted429 of a back propagation neural network with one hidden layer that used a sigmoid transfer function and430 a one-neuron output layer with a linear transfer function. They also reported the results of applying431 different regression-based techniques over the Ontario market.432 A hybrid model which used ANNs and fuzzy logic was introduced in [50]. As regards the neural433 network presented, it had a feed-forward architecture and three layers, where the hidden nodes of the434 proposed fuzzy neural network performed the fuzzyfication process. The approach was tested over the435 Spanish electricity price market and showed to be better than many other techniques such as ARIMA or436 MLP.437 Taylor et al. [51] compared six univariate time series methods to forecast electricity load for Rio de438 Janeiro and England and Wales markets. These methods were an ARIMA model and an exponential439 smoothing (both for double seasonality), an artificial neural network, a regression model with a previous440 principal component analysis and two naive approaches as reference methods. The best method was the441 Version November 6, 2015 submitted to Energies 17 of 41 proposed exponential smoothing and the regression model showed a good performance for the England442 and Wales demand.443 Another neural network-based approach was introduced in [52] in which multiple combinations were444 considered. These combinations consisted of networks with different number of hidden layers, different445 number of units in each layer and several types of transfer functions. The authors evaluated the accuracy446 of the approach reporting the results from the electricity markets of mainland Spain and California.447 The use of ANN for forecasting electricity prices in the Spanish market was also proposed in [53].448 The main novelty of this work lies on the proposed training method for ANN, which is based on making449 a previous selection for the MLP training samples, using an ART-type [54] neural network.450 In [55], the authors discussed and presented results by using an ANN to forecast the Jordanian451 electricity demand, which is trained by a particle swarm optimization technique. They also showed the452 performance obtained by using a back propagation algorithm (BP) and autoregressive moving average453 models.454 Neupane et al. [56] used an ANN model with carefully selected inputs. Such inputs were selected by455 means of a wrapper method for feature selection. The proposal was applied to data from Australia, New456 York and Spain electricity markets, outperforming the PSF algorithm performance.457 The feature selection problem to obtain optimal inputs for load forecasting has also been addressed458 by means of ANN [57]. The authors evaluated the performance of four feature selection methods in459 conjunction with state-of-the-art prediction algorithms, using two years of Australian data. The results460 outperformed those of exponential smoothing prediction models.461 In spite of the widespread use of the ANNs, the ELM has not been too explored to predict energy time462 series. An ELM and bootstrapping to predict probabilistic intervals for Australian electricity market was463 proposed in [58]. First, an ELM was applied to obtain point forecasts, and later, a bootstrap method was464 used for uncertainty estimations. The results were compared with two ANNs, namely a back-propagation465 ANN and a radial basis function neural network, showing that ELM outperforms other methods in most466 of the test sets. For the same market, prediction intervals (PI) were also obtained in [59]. In this case, a467 maximum likelihood method was used to estimate the noise variance indeed of a bootstrap method. The468 results were compared to a random walk (RW), and both traditional ANN and ELM with a bootstrap469 method. The proposed method provided the best training time and errors.470 In [60] five recent methods to train radial-basis function (RBF) networks were applied to obtain471 the short-term load forecasting in New England. These method were SVR, ELM, decay RBF neural472 networks, improved second order and error correction. The best results regarding the training, errors,473 network size, and computational time were obtained with the error correction.474 Li et al [61] presented a wavelet transform to deal with the nonstationary of the load time series and475 an ELM with weights initially computed by an artificial bee colony algorithm to predict the load time476 series in New England and North American from the wavelet series. The authors showed that the use of477 an optimization algorithm to set the weights in ELM improves the forecasting errors.478 Most approaches based on SOMs published in the literature for forecasting tasks, use the SOM to479 group the data in an initial stage, and later obtain a prediction model for each group. In [62] the authors480 propose to combine SOM and support vector machines to predict hourly electricity prices for next-day.481 First, they applied a SOM to split the data into groups, and then, a support vector machine model for each482 Version November 6, 2015 submitted to Energies 18 of 41 group is used to obtain the prediction of the prices in the New England electricity market. In this work,483 two months were used to validate the method, which provided errors of 7% approximately. Likewise,484 a SOM along with an ANN was applied to forecast the prices for Australian and New York electricity485 markets [63]. In this case, the ANN predicted the nearest cluster and the prediction was obtained by486 the centroid of the cluster. The errors reported for the year 2006 were around a 1.76% and 2.88% for487 Australian and New York markets, respectively. A SOM without combining with another technique was488 presented in [64] to predict the prices for the Spanish electricity market. A preprocessing to select the489 input variables was proposed as a previous step to the prediction, which was obtained from the prices of490 the nearest centroid to the input data. The proposed SOM obtained forecasts with an error of 2.32% for491 the daily market.492 Table 2summarizes the content of this section. Table 2. Summary on ANN, SOM and ELM for electricity forecasting. Reference Technique Outperforms Metrics Horizon Year Market [49] Hybrid ANN 5+ models MAPE 1 day 2002 Ontario [50] Hybrid ANN MLP/ARIMA/RBF MRE 1 day 2002 OMEL [51] ANN 5+ models RMSE/MAE 1 day 2003 Brazil [52] ANN ARIMA/Naive MAPE 1 day 2000/2002 CAISO/OMEL [53] ART-NN ARIMA/ANN MAPE 1 day 2003 OMEL [55] ANN ARMA/BP RMSE/MAPE 1 day 2004 Jordan [56] ANN PSF MRE/MAPE 1 day 2006 NYISO/ANEM/OMEL [57] ANN Smoothing MAE/MAPE 1 day 2007 ANEM [58] ELM 5+ models MAE/MAPE/RMSE 1 day 2006/07 ANEM [59] ELM RW/ANN PI 1 day 2007/09 ANEM [60] ELM RBF/SVR MAPE 1 day 2011 ANEM [61] ELM 5+ models MAPE 1 day 2006 NYISO/ANEM [62] SOM SVM MAE/MAPE 1 day 2005 ANEM [63] SOM PSF MRE/MAPE 1 day 2006 NYISO/ANEM/OMEL [64] SOM 5+ models MAPE 1 day 2011 OMEL 493 5.1.2. Genetic programming494 5.1.2.1. Fundamentals495 A genetic algorithm (GA) [65] is a kind of searching stochastic algorithm based on natural selecting496 procedures. Such algorithms try to imitate the biological evolutive process since they combine the497 survival of the best individuals in a set, by means of an structured and random process of information498 exchange.499 Every time the process iterates, a new set of data structures is generated gathering just the best500 individuals of older generations. Thus, the GA are evolutionary algorithms due to their capacity to501 efficiently exploit the information relating to past generations. This fact allows the speculation about502 new searching points in the solution space, trying to obtain better models thanks to its evolution.503 Many genetic operators can be defined. However, selection, crossover and mutation are the most504 relevant and used and are now going to be briefly described.505 Version November 6, 2015 submitted to Energies 19 of 41 1. Selection. During each successive generation, a proportion of the existing population is selected to506 breed a new generation. Individual solutions are selected through a fitness-based process, where507 fitter solutions (as measured by a fitness function) are typically more likely to be selected. Certain508 selection methods rate the fitness of each solution and preferentially select the best solutions. Other509 methods rate only a random sample of the population, as this process may be very time-consuming.510 Most functions are stochastic and designed so that a small proportion of less fit solutions are511 selected. This helps keep the diversity of the population large, preventing premature convergence512 on poor solutions. Popular and well-studied selection methods include roulette wheel selection513 and tournament selection.514 2. Crossover. Just after two parents are selected by any selection method, crossover takes place.515 Crossover is an operator that mates these two parents to produce offspring. The newborn516 individuals may be better than their parents and the evolution process may continue. In most517 crossover operators, two individuals are randomly selected and recombined with a crossover518 probability, pc. That is, an uniform number ris generated and if r≤pcthe two randomly selected519 individuals undergo recombination. Otherwise, the offspring can be sheer copies of their parents.520 The value of pccan either be set experimentally or set based on schema-theorem principles [65].521 3. Mutation. Mutation is the genetic operator that randomly changes one or more of the individuals’522 genes. The purpose of the mutation operator is to prevent the genetic population from converging523 to a local minimum and to introduce to the population new possible solutions.524 Genetic programming (GP) is a natural evolution of GA and its first apparition in the literature dates525 of 1992 [66]. It is a specialization of genetic algorithms where each individual is a computer program.526 Therefore it is used to optimize a population of computer programs according to a fitness landscape527 determined by a program’s ability to perform a given computational task. Hence, specialized genetic528 operator that generalize crossover and mutation are used for tree-structured programs.529 The main steps to be followed when using GP are now summarized. Obviously, depending on the530 type of the application, these steps may change in order to be adapted to the particular problem to be531 dealt with.532 1. Random generation of an initial population, that is, programs.533 2. Iterative execution until the stop condition –to be determined in each situation– is fulfilled:534 (a) To execute each program of the population and to assign an aptitude value, according to their535 behavior in relation with the problem.536 (b) To create new programs by applying different primary operations to the programs.537 i. To copy an existing program in the new generation.538 ii. To create two programs from two existing ones, genetically and randomly recombining539 some chosen parts of both programs, making use of the crossover operator, which will540 also be randomly chosen for each program.541 iii. To create a program from another randomly chosen by randomly changing a gene.542 Version November 6, 2015 submitted to Energies 20 of 41 3. The program identified as possessing the best aptitude (the best for the last generation) is the543 designed result of the GP running.544 5.1.2.2. Related work545 The viability of forecasting the electricity demand via linear GP is analyzed in [67]. Hence, the546 authors considered load demand patterns for ten consecutive months, observed every thirty minutes for547 the Victoria State of Australia. The performance was compared with an ANN and a neuro-fuzzy system548 (EFuNN) and the system delivered best results in terms of accuracy and computational cost.549 An evolutionary technique applied to the optimal short-term scheduling of the electric energy550 production was presented in [68]. The equations that define the problem led to a nonlinear mixed-integer551 programming problem with a high number of real and integer variables. The required heuristics,552 introduced to assure the feasibility of the constraints, are analyzed, along with a brief description of553 the proposed GA. Results from the Spanish power system were reported and compared to dynamic554 regression (DR).555 Another price forecasting strategy was proposed in [69]. In fact the authors presented a mutual556 information-based feature selection technique (MI) in which the prediction part was a cascaded557 neuro-evolutionary algorithm. The accuracy was largely evaluated since they compared their results558 –obtained from Pennsylvania-New Jersey-Maryland and Spanish electricity markets– with seven559 different models.560 The electricity energy consumption is forecasted by using genetic algorithms in Turkey [70]. The561 results were compared with conventional regression techniques, and the estimated values of the Turkish562 Ministry of Energy and Natural Resources (TMENR). An estimation for the electricity demand in the563 year 2020 is also provided.564 A variant of genetic programming, Multi-Gene Genetic Programming (MGGP), was introduced in565 [71] and applied to Egypt load forecasting. The method was compared with RBF network and the566 standard genetic programming.567 A variant of genetic programming, improved by incorporating semantic awareness in algorithm, for568 short term load forecasting is described in [72]. The authors analyzed South Italy data and outperformed569 standard GP and some other machine learning methods.570 Finally, Table 3summarizes all the methods reviewed in this section. Table 3. Summary on GP for electricity forecasting. Reference Technique Outperforms Metrics Horizon Year Market [67] Linear GP ANN/EFuNN RMSE 2 days 1995 ANEM [68] GP DR MRE/MAE 1 day 2002 OMEL [69] MI GP 5+ models MAE/MSRE 1 day 2007 PJM/OMEL [70] GP TMENR MSE 1 day 2020 Turkey [71] MGGP RBF/GP MAPE 1 day 2012 Egypt [72] Semantic GP 5+ models MAE/MSRE 1 day 2009/10 Italy 571 Version November 6, 2015 submitted to Energies 21 of 41 5.1.3. Support vector machines572 5.1.3.1. Fundamentals573 The support vector machine (SVM) model the way is nowadays understood, initially appeared in574 1992 in the Computational Learning Theory (COLT) Conference and it has been subsequently studied575 and extended [73,74]. The interest for this learning model is continuously increasing and it is considered576 an emerging and successful technique nowadays. Thus, it has become to a widely accepted standard in577 machine learning and data mining disciplines.578 The learning process in SVM represents an optimization problem under constraints that can be solved579 by means of quadratic programming. The convexity guarantees a single solution which is an advantage580 with regard to the classical model of ANN. Furthermore, current implementations provide moderate581 efficiency for real-world problems with thousands of samples and attributes.582 Support vector machines aims at separating points by means of what they defined as hyperplane, which are just linear separators with a high dimensionality whose functions are defined according to different kernels. Formally, a hyperplane in a D-dimensional space is defined as follows: h(x) =< w, x > +b(28) where xis the sample, wϵRDis the orthogonal vector to the hyperplane, bϵR,wis the weight vector, b583 is the bias or threshold decision and < w, x > expresses the scalar product in RD.584 In case of a binary classifier is required, the equation can be reformulated as: f(x) = sign (h(x)) (29) where the sign function is defined as: sign(x) = {+1, if x ≥0 −1, if x < 0(30) There exist many algorithms directed to create hyperplanes (w, b)given a dataset linearly separable.585 These algorithms guarantee the convergency to a solution hyperplane although particularities of all of586 them will lead to slightly different solutions. Note that there can be infinity hyperplanes that perform587 adequate separations. So the key problem for the SVM is to choose the best hyperplane, in other words,588 the hyperplane that maximizes the minimum distance (or geometric margin) between the samples in the589 dataset and the hyperplane itself.590 Another peculiarity of SVM is that only take into consideration those points belonging to the frontiers591 of the region of decision, which are the points that do not clearly belong to a class or to another. Such592 points are named support vectors. Figure 5illustrates a bidimensional representation of an hyperplane593 equidistant to two classes, as well as showing the support vectors and the existing margin.594 If non linear transformation is carried out from the input space to the feature space, non linear595 separators-based learning is reached with SVM. Kernel functions are used thus in order to estimate596 the scalar product of two vectors in the features space. Consequently the election of an adequate kernel597 function is crucial and a priori knowledge of problem is required for a proper application of SVM.598 Nevertheless, the samples may not be linearly separable (see Figure 6) even in the features space.599 Version November 6, 2015 submitted to Energies 22 of 41 Figure 5. Hyperplane (w, b)equidistant to two classes, margin and support vectors. Figure 6. Non linearly separable dataset. Trying to classify properly all the samples can seriously compromise the generalization of the600 classifier. This problem is known as overfitting. In such situations it is desirable to admit that some601 samples will be misclassified in exchange for having more promising and general separators. This602 behavior is reached by inserting soft margin in the model, whose objective function is composed by the603 addition of two terms: the geometric margin and the regularization term. The importance of both terms604 is pondered by means of a typically called parameter C. This model appeared in 1999 [75], and it was605 the model that really allowed the practical use that SVMs have nowadays, since it provided robustness606 against the noise.607 On the other hand, SVMs can be easily adapted to solve regression problems by means of the608 introduction of a loss function. SVMs are commonly called Support Vector Regression (SVR) for time609 series forecasting. Now, the problem consists in finding a non linear function fthat minimizes the610 forecasting error for the training set. The ϵ-insensitive loss function Lϵdefined by Eq. (31) is typically611 used due to a reduced number of support vectors is obtained. The ϵparameter represents the error612 allowed for each point of the training set.613 Lϵ(y) =      0if |y−f(x)| ≤ ϵ |y−f(x)|−ϵ otherwise (31) Version November 6, 2015 submitted to Energies 23 of 41 To approximate all data of the training set with an error less than ϵis not always possible in practice.614 For this reason, slack variables ξiand ξ∗ iare inserted to allow errors greater. Thus, the SVR model615 consists in solving the following problem:616 minimize 1 2||w||2+C∑ i (ξi+ξ∗ i) subject to yi−f(xi)≤ϵ+ξi f(xi)−yi≤ϵ+ξ∗ i (32) where (xi, yi)are the points of the training set, wis the margin and Cis the regularization parameter.617 Once the optimization problem has been solved, the following function is obtained:618 f(x) = n ∑ i=1 (α+ i−α− i)K(x, xi)(33) where α+ iand α− iare the multipliers of Lagrange of the dual optimization problem and K is the kernel619 function.620 5.1.3.2. Related work621 Many works have been focussed on forecasting time series by applying SVM. Hence, the study carried622 out in [76] analyzed the suitability of applying SVM to forecast the electric load for the Taiwanese623 market. The results were compared to that of linear regressions and ANN. The same time series type, but624 related to the Chinese market, was forecasted in [77], in which the authors reached a globally optimized625 prediction by applying a SVM.626 The occurrence of outliers (also called spike prices) or prices significantly larger than the expected627 values is an usual feature found in these time series. With the aim of dealing with this feature, the authors628 in [78] proposed a data mining framework based on both SVM and probability classifiers.629 The research published in [79] proposed a new prediction approach based on SVM and rough sets630 techniques (RS) with a previous selection of features from data sets by using an evolutionary method.631 The approach improved the forecasting quality, reduced the speed of convergence and the computational632 cost as regards a conventional SVM and a hybrid model formed by a SVM and simulated annealing633 algorithms (SAA).634 The Taiwanese electricity market was forecasted by means of SVR in [80]. The author proposed a635 novel initialization of the SVR by using particle swarm optimization. The results were compared to other636 SVR but with different initialization strategies, mainly, the least-squares (LS) method.637 A two-stage multiple SVM based model for midterm electricity price forecasting was proposed in638 [81].The first stage was used to separate input data into different price zones, and was carried out by639 means of a single SVM. Then, four parallel designed SVM were applied to forecast the electricity price.640 The method was applied to PJM market and the results compared to the standard SVM.641 Finally, Table 4summarizes all the methods reviewed in this section. Note the GRNN stands for642 general regression neural networks.643 Version November 6, 2015 submitted to Energies 24 of 41 Table 4. Summary on SVM for electricity forecasting. Reference Technique Outperforms Metrics Horizon Year Market [76] SAA-SVM ARIMA/GRNN MAE/MSRE 1 day 2004 China [77] SVM ANN MAPE 1 day 2005 China [78] M-SVM SVM MAE/MSRE 1 day 2006 ANEM [79] RS-SVM SAA-SVM MAE/MSRE 1 day 2007 NYISO [80] PSO-SVM LS-SVM MSE 1 day 2009 Taiwan [81] M-SVM SVM MAE/MSRE 1 day 2009/10 PJM 5.2. Forecasting based on local methods644 Due to the complexity to find a global function that models the whole system, the local models emerge645 as learning methods for time series forecasting. Conversely to global methods, a local model does not646 use the input data to predict the output but only the points close to the point to forecast. In general, global647 models have a lower computational cost than local models, since the latter have to be rebuilt for each648 point of the test set. But, the accuracy achieved by local methods is usually better than that of global649 methods. The main local methods for prediction tasks are the methods based on nearest neighbors.650 5.2.1. Forecasting based on nearest neighbors651 5.2.1.1. Fundamentals652 One of the most popular way of either predicting or classifying a new data, based on past and known653 observations, it the nearest neighbors technique (NN), that was first formulated by Cover and Hart in654 1967 [82]. The classical example to illustrate the application of NN refers to a doctor that tries to655 predict the result of a surgical procedure by comparing it with the obtained result from the most similar656 patient subjected to the same operation. However, a single case in which surgery had failed may have657 an excessive influence over other slightly different cases in which the operation had successfully carried658 out. For this reason, the NN algorithm is generalized with the knearest neighbors, kNN. Thus, a simple659 election of the knearest neighbors generates a prediction for every cases. Moreover, this rule can be660 extended by weighting the importance of the neighbors, giving a larger weight to the really nearest661 neighbors.662 The search of the nearest neighbor process can be defined as follows:663 Definition. Given a dataset P=p1, ..., pnin a metric espace Xof distance d, two different type of664 queries are wanted to be answered:665 •Nearest neighbor: find the point in Pnearest to qϵX666 •Range: given a point qϵX and r > 0, return all the points pϵP that satisfy d(p, q)≤r667 Figure 7illustrates an example in which k is set to three (three nearest neighbors are searched for)668 and an Euclidean metric is used.669 Formally, the classification rule is formulated as follows:670 Version November 6, 2015 submitted to Energies 31 of 41 patterns in the Spanish market. Later, these patterns were used to transform the time series into834 a sequence of labels showing the benefits of using this information as previous step in time series835 forecasting [118]. Finally, an extended and improved approach, PSF, was introduced in [119], where836 New York, Australian and Spanish electricity and demand time series were successfully forecasted,837 showing remarkable performance compared to classical methods. The same method was adapted to838 forecast outliers (o-PSF) for the same markets in [120].839 A method using a principal component analysis (PCA) network was introduced in [121] to forecast840 day-ahead prices. The PCA network extracts essential features from periodic information in the market.841 Later, these features are used as inputs in a multilayer feedforward network. PJM market was used to842 test the proposed method and the results compared to ARIMA models.843 Finally, Table 8summarizes all the methods reviewed in this section.844 Table 8. Summary on other models for electricity forecasting. Reference Technique Outperforms Metrics Horizon Year Market [111] TFM ARIMA RMSE/MAPE 1 day 2003 PJM [112] BH NGT RMSE 1 year 2002/03 UK [113] FIS ARMA/GARCH RMSE/MAPE 1 day 2003/04 PJM [114] MFL ARIMA/Holt MSE up to 1 month 2010 NYISO [115] Grey-Markov Grey MRE 1 day 2005/06 Shangai [119] PSF 5+ methods MRE/MAPE 1 day 2006 NYISO/ANEM/OMEL [120] o-PSF 5+ methods MRE/MAPE 1 day 2006 NYISO/ANEM/OMEL [121] PCA ANN MAE 1 day 2008 PJM 9. Ensemble models845 Recently, ensemble models are beginning to receive attention from the research community due to the846 good performance obtained for classification problems [122,123]. In general, ensemble models consists847 in combining different models in order to improve the accuracy of the individual models. In most of848 works, the combination is usually based on a system of majority votes (bagging) or weighted majority849 votes (boosting).850 In the last years, ensemble techniques have been also applied to the prediction of energy time series.851 Fan et al. [124] proposed a machine learning model based on Bayesian Clustering by Dynamics (BCD)852 and SVM. First, Bayesian clustering techniques were used to split the input data into 24 subsets. Then,853 SVM methods were applied to each subset to obtain the forecasts of the hourly electricity load for the854 city of New York.855 The work in [125] introduced a price forecasting method based on wavelet transform combined with856 ARIMA and GARCH models. The method was assessed on Spanish and PJM electricity markets and857 compared to some other forecasting methods.858 An ensemble of RBF neural networks for short-term load forecasting in seven buildings from Italy859 can be found in [126]. The main novelty of this work is the introduction of a new term in the objective860 function to minimize the correlation between the error of a network with the errors of the rest of861 Version November 6, 2015 submitted to Energies 32 of 41 networks of the ensemble. In this case, the results were compared to SARIMA, which proved to be862 more competitive in most of the buildings.863 An ensemble of ELM was presented in [127] to short-term load forecasting of Australian electricity864 market. Both the weights of the input layer and the number of nodes in hidden layer for each ELM were865 randomly set. The median of the outputs generated for each ELM was the final prediction. The results866 reported an error of 1.82% for the year 2010 versus 2.89%, 2.93%, and 2.86% obtained by a single ELM,867 a back-propagation ANN and a RBF neural network, respectively.868 Many ensembles of ANN have been recently published in the literature with the purpose of electricity869 prices or load forecasting. In fact, most of the proposed ensemble techniques for regression tasks have870 been ensembles of ANN. For instance, the authors in [128] proposed the hybrid method PSF-NN, which871 combines pattern sequence similarity with neural networks. The results show that the use of ensemble872 of NNs instead of a single NN in the NN component of the PSF-NN prediction method is beneficial873 considering that it produces better accuracy at acceptable computational cost.874 Another ensemble based on PSF was introduced in [129]. In this case, five forecasting models using875 different clustering techniques: K-means, SOM, Hierarchical Clustering, K-medoids model, and Fuzzy876 C-means were used. The ensemble model was implemented with an iterative prediction procedure. The877 method was applied to New York, Australia and Spain markets, and the results compared to those of the878 original PSF algorithm.879 The performance of an ensemble of ANN was compared with a Seasonal Autoregressive Integrated880 Moving Average (SARIMA) model, a Seasonal Autoregressive Moving Average (SARMA), a Random881 Forest, a Double Exponential Smoothing and Multiple Regression in [130], providing the best results.882 The ANNs composing of the ensemble were trained with different subsets provided by a previous883 clustering.884 An ensemble was proposed in [131] to predict the load in California for the next day. The authors885 used a reference forecast made by the system operator as input variable of the proposed method, and this886 prediction was improved by means of two Box-Jenkins time series models. Then, the forecasts provided887 by these two models were combined to obtain the final prediction. The weights of the combination888 were optimized by means of least square method, and moreover, the authors built different ensembles889 considering global weights or weights depending on the hour or the day.890 Finally, Table 9summarizes all the methods reviewed in this section.891 Table 9. Summary on ensembles for electricity forecasting. Reference Technique Outperforms Metrics Horizon Year Market [124] BCD+SVM SVR MAPE 1 day 2001-2003 NYISO [125] WL+GARCH 5+ models RMSE/MAPE 1 day 2002 OMEL/PJM [126] ANN SARIMA MSE/MAE/MAPE 1 day 2010 Italy [127] ELM ANN/RBF MAE/MAPE 1 day 2010 ANEM [128] PSF+ANN 5+ models MAE/MAPE 1 day 2010 ANEM [129] PSF+Clust PSF MRE/MAPE 1 day 2006 NYISO/ANEM/OMEL [130] ANN SARIMA MAPE 1 day 2012 C&I [131] ARIMA 5+ models RMSE/MAE/MAPE 1 day 2013 CAISO/ERCOT Version November 6, 2015 submitted to Energies 33 of 41 10. Conclusions892 It is expected that this work serve as initial guide for those researchers interested in time series893 forecasting and, in particular, in forecasting based on data mining approaches. Thus, a brief but rigorous894 mathematical description of the main existing data mining techniques that have been applied to forecast895 time series is reported. Due to the wide variety of application of such techniques, one case study has been896 selected: The analysis of energy-related time series (electricity price and demand). The large amount897 of works carried out during the last decade in this topic highlights the strengths that data mining had898 already exhibit in other fields.899 With reference to the type of prediction, it can be concluded that almost all methods use a horizon900 of prediction equals to one day. There are few works forecasting recent years since, for comparative901 purposes, they prefer to use older data. Moreover, there are several techniques that have been rarely used902 so far in this research areas: nearest-neighbors and genetic programming. This fact suggests that much903 work is still remaining for such models. On the contrary, ANN and SVM have been extensively used904 for this forecasting task. Linear models are still being used, but mainly to be used as baselines, since905 most of the data mining approaches outperform them in terms of accuracy. Wavelets and rule-based906 methods are mainly used in hybrid approaches and are causing significative accuracy improvement when907 properly combined. The accuracy measures mainly used are MAPE and RMSE. Finally, the current trend908 in electricity forecasting points to the development of ensembles, thus highlighting single strengths of909 every method.910 Acknowledgments911 The authors would like to thank Spanish Ministry of Economy and Competitiveness, Junta de912 Andalucía and Pablo de Olavide University for the support under projects TIN2014-55894-C2-R,913 P12-TIC-1728 and APPB813097, respectively.914 Author Contributions915 F. Martínez-Álvarez and A. Troncoso conceived the paper. J. C. Riquelme and G. Asencio-Cortés916 proposed the paper structure. 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