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Time-series clustering is the process of grouping time series with respect to their similarity or characteristics. Previous approaches usually combine a specific distance measure for time series and a standard clustering method. However, these approaches do not take the similarity of the different subsequences of each time series into account, which can be used to better compare the time-series objects of the dataset. In this article, we propose a novel technique of time-series clustering consisting of two clustering stages. In a first step, a least-squares polynomial segmentation procedure is applied to each time series, which is based on a growing window technique that returns different-length segments. Then, all of the segments are projected into the same dimensional space, based on the coefficients of the model that approximates the segment and a set of statistical features. After mapping, a first hierarchical clustering phase is applied to all mapped segments, returning groups of segments for each time series. These clusters are used to represent all time series in the same dimensional space, after defining another specific mapping process. In a second and final clustering stage, all the time-series objects are grouped. We consider internal clustering quality to automatically adjust the main parameter of the algorithm, which is an error threshold for the segmentation. The results obtained on 84 datasets from the UCR Time Series Classification Archive have been compared against three state-of-the-art methods, showing that the performance of this methodology is very promising, especially on larger datasets.

Emerging technologies have led to the creation of huge databases that require reducing their high dimensionality to be analysed. Many suboptimal methods have been proposed for this purpose. On the other hand, few efficient optimal methods have been proposed due to their high computational complexity. However, these methods are necessary to evaluate the performance of suboptimal methods. This paper proposes a new optimal approach, called OSTS, to improve the segmentation of time series. The proposed method is based on A* algorithm and it uses an improved version of the well-known Salotti method for obtaining optimal polygonal approximations. Firstly, a suboptimal method for time-series segmentation is applied to obtain pruning values. In this case, a suboptimal method based on Bottom-Up technique is selected. Then, the results of the suboptimal method are used as pruning values to reduce the computational time of the proposed method. The proposal has been compared to other suboptimal methods and the results have shown that the method is optimal, and, in some cases, the computational time is similar to other suboptimal methods.

Large time series are difficult to be mined and preprocessed, hence reducing their number of points with minimum information loss is an active field of study. This paper proposes new methods based on time series segmentation, including the adaptation of the particle swarm optimisation algorithm (PSO) to this problem, and more advanced PSO versions, such as barebones PSO (BBPSO) and its exploitation version (BBePSO). Moreover, a novel algorithm is derived, referred to as dynamic exploitation barebones PSO (DBBePSO), which updates the importance of the social and cognitive components throughout the generations. All these algorithms are further improved by considering a final local search step based on the combination of two well-known standard segmentation algorithms (Bottom-Up and Top-Down). The performance of the different methods is evaluated using 15 time series from various application fields, and the results show that the novel algorithm (DBBePSO) and its hybrid version (HDBBePSO) outperform the rest of segmentation techniques.

The huge amount of data chronologically collected in short periods of time by different devices and technologies is an important challenge in the analysis of times series. This problem has produced the development of new automatic techniques to reduce the number of points in the resulting time series, in order to facilitate their processing and analysis. In this paper, we propose a new modification of a coral reefs optimization algorithm (CRO) to tackle the problem of reducing the size of the time series minimizing the approximation error. The modification includes a memetization procedure (hybridization with a local search procedure) of the standard algorithm to improve its quality when finding a promising solution in a given searching area. The memetization process is applied to the worse individuals of the algorithm at the beginning, and only to the best ones at the end of the algorithm’s convergence, resulting in a dynamical search approach called dynamic memetic CRO (DMCRO). The proposed DMCRO performance is compared in this paper against other state-of-the-art CRO algorithms, such as the standard one, its statistically driven version (SCRO) and two different hybrid versions (HCRO and HSCRO, respectively), and the standard memetic version (MCRO). All the algorithms compared have been tested in 15 time series approximation, collected from different sources, including financial problems, oceanography data, and cardiology signals, among others, showing that the best results are obtained by DMCRO.

La Ciencia de Datos es el área que comprende el desarrollo de métodos científicos, procesos y sistemas para extraer conocimiento a partir de datos recopilados previamente, con el objetivo de analizar los procedimientos llevados a cabo actualmente. El perfil profesional asociado a este campo es el del Científico de Datos, generalmente llevado a cabo por Ingenieros Informáticos gracias a que las aptitudes y competencias adquiridas durante su formación se ajustan perfectamente a lo requerido en este puesto laboral. Debido a la necesidad de formación de nuevos Científicos de Datos, entre otros fines, surgen plataformas en las que éstos pueden adquirir una amplia experiencia, como es el caso de Kaggle. El principal objetivo de esta experiencia docente es proporcionar al alumnado una experiencia práctica con un problema real, así como la posibilidad de cooperar y competir al mismo tiempo. Así, la adquisición y el desarrollo de las competencias necesarias en Ciencia de Datos se realiza en un entorno altamente motivador. La realización de actividades relacionadas con este perfil ha tenido una repercusión directa sobre el alumnado, siendo fundamental la motivación, la capacidad de aprendizaje y el reciclaje continuo de conocimientos a los que se someten los Ingenieros Informáticos. Data Science is the area that comprises the development of scientific methods, processes, and systems for extracting knowledge from previously collected data, aiming to analyse the procedures being carried out currently. The professional profile associated with this field is the Data Scientist, generally carried out by Computer Engineers as the skills and competencies acquired during their training are perfectly suited to what this job requires. Due to the need for training new Data Scientists, among other goals, there are different emerging platforms where they can acquire extensive experience, such as Kaggle. The main objective of this teaching experience is to provide students with practical experience on a real problem, as well as the possibility of cooperating and competing at the same time. Thus, the acquisition and development of the necessary competencies in Data Science are carried out in a highly motivating environment. The development of activities related to this profile has had a direct impact on the students, being fundamental the motivation, the learning capacity and the continuous recycling of knowledge to which Computer Engineers are subjected.

Parkinson’s disease is characterised by a decrease in the density of presynaptic dopamine transporters in the striatum. Frequently, the corresponding diagnosis is performed using a qualitative analysis of the 3D-images obtained after the administration of $$^{123}$$ 123 I-ioflupane, considering a binary classification problem (absence or existence of Parkinson’s disease). In this work, we propose a new methodology for classifying this kind of images in three classes depending on the level of severity of the disease in the image. To tackle this problem, we use an ordinal classifier given the natural order of the class labels. A novel strategy to perform feature selection is developed because of the large number of voxels in the image, and a method for generating synthetic images is proposed to improve the quality of the classifier. The methodology is tested on 434 studies conducted between September 2015 and January 2019, divided into three groups: 271 without alteration of the presynaptic nigrostriatal pathway, 73 with a slight alteration and 90 with severe alteration. Results confirm that the methodology improves the state-of-the-art algorithms, and that it is able to find informative voxels outside the standard regions of interest used for this problem. The differences are assessed by statistical tests which show that the proposed image ordinal classification could be considered as a decision support system in medicine.

This paper proposes the application of novel artificial neural networks with evolutionary training and different basic functions (sigmoidal, product and radial), for a real problem of fog events classification from meteorological input variables. Specifically, a Multiobjective Evolutionary Algorithm is considered as artificial neural network training mechanism in order to obtain a binary classification model for the detection of fog events at Valladolid airport (Spain). The evolutionary neural models developed are based on two-dimensional performance measures: traditional accuracy and the minimum sensitivity, as the lowest percentage of examples correctly predicted as belonging to each class with respect to the total number of examples in the corresponding class. These performance measures are directly related to features associated with any classifier: its global performance and the rate of the worst classified class. These two objectives are usually in conflict when the optimization process tries to construct models with a high classification rate level in the generalization dataset, and also with a good classification level for each class or minimum sensitivity. A sensitivity analysis of the proposed models is carried out, and thus the subjacent relations between the input variables and the output classification target can be better understood.

Time series segmentation is aimed at representing a time series by using a set of segments. Some researchers perform segmentation by approximating each segment with a simple model (e.g. a linear interpolation), while others focus their efforts on obtaining homogeneous groups of segments, so that common patterns or behaviours can be detected. The main hypothesis of this paper is that both objectives are conflicting, so time series segmentation is proposed to be tackled from a multiobjective perspective, where both objectives are simultaneously considered, and the expert can choose the desired solution from a Pareto Front of different segmentations. A specific multiobjective evolutionary algorithm is designed for the purpose of deciding the cut points of the segments, integrating a clustering algorithm for fitness evaluation. The experimental validation of the methodology includes three synthetic time series and three time series from real-world problems. Nine clustering quality assessment metrics are experimentally compared to decide the most suitable one for the algorithm. The proposed algorithm shows good performance for both clustering quality and reconstruction error, improving the results of other mono-objective alternatives of the state-of-the-art and showing better results than a simple weighted linear combination of both corresponding fitness functions.

This paper is focused on reducing the number of elements in time series with minimum information loss, with specific applications on time series segmentation. A modification of the coral reefs optimization metaheuristic (CRO) is proposed for this purpose, which is called statistical CRO (SCRO), where the main parameters of the algorithm are adjusted based on the mean and standard deviation associated with the fitness distribution. Moreover, the algorithm is combined with the Bottom-Up and Top-Down methodologies (traditional local search methods for time series segmentation), resulting in a hybrid methodology (HSCRO). We evaluate the performance of these algorithms using 16 time series from different application areas. The statistically-driven version of CRO is shown to improve the results of the standard CRO, eliminating the necessity of manually adjusting the main parameters of the algorithm and dynamically adjusting these parameters throughout the evolution. Moreover, when compared with other local search methods and metaheuristics from the state of the art, HSCRO shows robust segmentation results, consistently obtaining lower approximation errors.

Piecewise Linear Approximation is one of the most commonly used strategies to represent time series effectively and approximately. This approximation divides the time series into non-overlapping segments and approximates each segment with a straight line. Many suboptimal methods were proposed for this purpose. This paper proposes a new optimal approach, called OSFS, based on feasible space (FS) Liu et al. (2008)[1], that minimizes the number of segments of the approximation and guarantees the error bound using the L ∞ -norm. On the other hand, a new performance measure combined with the OSFS method has been used to evaluate the performance of some suboptimal methods and that of the optimal method that minimizes the holistic approximation error ( L 2 -norm). The results have shown that the OSFS method is optimal and demonstrates the advantages of L ∞ -norm over L 2 -norm.

This paper presents a methodology for the detection and prediction of Segments containing very high Significant Wave Height (SSWH) values in oceans. This kind of prediction is needed in order to account for potential changes in a long-term future operational environment of marine and coastal structures. The methodology firstly characterizes the wave height time series by approximating it using a sequence of labeled segments, and then a binary classifier is trained to predict the occurrence of SSWH periods based on past height values. A genetic algorithm (GA) combined with a likelihood-based local search is proposed for the first stage (detection), and the second stage (prediction) is tackled by an Artificial Neural Network (ANN) trained with a Multiobjective Evolutionary Algorithm (MOEA). Given the unbalanced nature of the dataset (SSWH are rarer than non SSWH), the MOEA is specifically designed to obtain a balance between global accuracy and individual sensitivities for both classes. The results obtained show that the GA is able to group SSWH in a specific cluster of segments and that the MOEA obtains ANN models able to perform an acceptable prediction of these SSWH.

The discovery of useful patterns embodied in a time series is of fundamental relevance in many real applications. Repetitive structures and common type of segments can also provide very useful information of patterns in financial time series. In this paper, we introduce a time series segmentation and characterization methodology combining a hybrid genetic algorithm and a clustering technique to automatically group common patterns from this kind of financial time series and address the problem of identifying stock market prices trends. This hybrid genetic algorithm includes a local search method aimed to improve the quality of the final solution. The local search algorithm is based on maximizing a likelihood ratio, assuming normality for the series and the subseries in which the original one is segmented. To do so, we select two stock market index time series: IBEX35 Spanish index (closing prices) and a weighted average time series of the IBEX35 (Spanish), BEL20 (Belgian), CAC40 (French) and DAX (German) indexes. These are processed to obtain segments that are mapped into a five dimensional space composed of five statistical measures, with the purpose of grouping them according to their statistical properties. Experimental results show that it is possible to discover homogeneous patterns in both time series.

This paper presents four configurations of a genetic algorithm (GA) combined with a local search (LS) method for time series segmentation with the purpose of correctly recognising extreme values. The LS method is based on likelihood maximisation of a beta distribution. The proposal is tested on three real ocean wave height time series, where extreme values are frequently found. Concretely, the time series are taken from two oceanographic buoys in the Gulf of Alaska, and another one from Puerto Rico. The results show that the different combinations of LS improve the results of the GA. Furthermore, the algorithm provides segmentations where extreme values are grouped in a well-defined cluster, which allows the study of the characteristics of this type of events.

In this paper we tackle the problem of massive missing data reconstruction in ocean buoys, with an evolutionary product unit neural network (EPUNN). When considering a large number of buoys to reconstruct missing data, it is sometimes difficult to find a common period of completeness (without missing data on it) in the data to form a proper training and test set. In this paper we solve this issue by using partial reconstruction, which are then used as inputs of the EPUNN, with linear models. Missing data reconstruction in several phases or steps is then proposed. In this work we also show the potential of EPUNN to obtain simple, interpretable models in spite of the non-linear characteristic of the neural network, much simpler than the commonly used sigmoid-based neural systems. In the experimental section of the paper we show the performance of the proposed approach in a real case of massive missing data reconstruction in 6 wave-rider buoys at the Gulf of Alaska.

This paper evaluates the performance of different evolutionary neural network models in a problem of solar radiation prediction at Toledo, Spain. The prediction problem has been tackled exclusively from satellite-based measurements and variables, which avoids the use of data from ground stations or atmospheric soundings. Specifically, three types of neural computation approaches are considered: neural networks with sigmoid-based neurons, radial basis function units and product units. In all cases these neural computation algorithms are trained by means of evolutionary algorithms, leading to robust and accurate models for solar radiation prediction. The results obtained in the solar radiation estimation at the radiometric station of Toledo show an excellent performance of evolutionary neural networks tested. The structure sigmoid unit-product unit with evolutionary training has been shown as the best model among all tested in this paper, able to obtain an extremely accurate prediction of the solar radiation from satellite images data, and outperforming all other evolutionary neural networks tested, and alternative Machine Learning approaches such as Support Vector Regressors or Extreme Learning Machines.

Wave height prediction is an important task for ocean and marine resource management. Traditionally, regression techniques are used for this prediction, but estimating continuous changes in the corresponding time series can be very difficult. With the purpose of simplifying the prediction, wave height can be discretised in consecutive intervals, resulting in a set of ordinal categories. Despite this discretisation could be performed using the criterion of an expert, the prediction could be biased to the opinion of the expert, and the obtained categories could be unrepresentative of the data recorded. In this paper, we propose a novel automated method to categorise the wave height based on selecting the most appropriate distribution from a set of well-suited candidates. Moreover, given that the categories resulting from the discretisation show a clear natural order, we propose to use different ordinal classifiers instead of nominal ones. The methodology is tested in real wave height data collected from two buoys located in the Gulf of Alaska and South Kodiak. We also incorporate reanalysis data in order to increase the accuracy of the predictors. The results confirm that this kind of discretisation is suitable for the time series considered and that the ordinal classifiers achieve outstanding results in comparison with nominal techniques.

The amount of data available in time series is recently increasing in an exponential way, making difficult time series preprocessing and analysis. This paper adapts different methods for time series representation, which are based on time series segmentation. Specifically, we consider a particle swarm optimization algorithm (PSO) and its barebones exploitation version (BBePSO). Moreover, a new variant of the BBePSO algorithm is proposed, which takes into account the positions of the particles throughout the generations, where those close in time are given more importance. This methodology is referred to as weighted BBePSO (WBBePSO). The solutions obtained by all the algorithms are finally hybridised with a local search algorithm, combining simple segmentation strategies (Top-Down and Bottom-Up). WBBePSO is tested in 13 time series and compared against the rest of algorithms, showing that it leads to the best results and obtains consistent representations.

Recent studies propose that different dynamical systems, such as climate, ecological and financial systems, among others, present critical transition points named to as tipping points (TPs). Climate TPs can severely affect millions of lives on Earth so that an active scientific community is working on finding early warning signals. This paper deals with the development of a time series segmentation algorithm for paleoclimate data in order to find segments sharing common statistical patterns. The proposed algorithm uses a clustering-based approach for evaluating the solutions and six statistical features, most of which have been previously considered in the detection of early warning signals in paleoclimate TPs. Due to the limitations of classical statistical methods, we propose the use of a genetic algorithm to automatically segment the series, together with a method to compare the segmentations. The final segments provided by the algorithm are used to construct a prediction model, whose promising results show the importance of segmentation for improving the understanding of a time series.

This paper presents a local search (LS) method based on the beta distribution for time series segmentation with the purpose of correctly representing extreme values of the underlying variable studied. The LS procedure is combined with an evolutionary algorithm (EA) which segments time series trying to obtain a given number of homogeneous groups of segments. The proposal is tested on a real problem of wave height estimation, where extreme high waves are frequently found. The results show that the LS is able to significantly improve the clustering quality of the solutions obtained by the EA. Moreover, the best segmentation clearly groups extreme waves in a separate cluster and characterizes them according to their centroid.

Time series representation can be approached by segmentation genetic algorithms (GAs) with the purpose of automatically finding segments approximating the time series with the lowest possible error. Although this is an interesting data mining field, obtaining the optimal segmentation of time series in different scopes is a very challenging task. In this way, very accurate algorithms are needed. On the other hand, it is well-known that GAs are relatively poor when finding the precise optimum solution in the region where they converge. Thus, this paper presents a hybrid GA algorithm including a local search method, aimed to improve the quality of the final solution. The local search algorithm is based on two well-known algorithms: Bottom-Up and Top-Down. A real-world time series in the Spanish Stock Market field (IBEX35) and a synthetic database (Donoho-Johnstone) used in other researches were used to test the proposed methodology.

This paper proposes a reservoir computing architecture for predicting wind power ramp events (WPREs), which are strong increases or decreases of wind speed in a short period of time. This is a problem of high interest, because WPREs increases the maintenance costs of wind farms and hinders the energy production. The standard echo state network architecture is modified by replacing the linear regression used to compute the reservoir outputs by a nonlinear support vector machine, and past ramp function values are combined with reanalysis data to perform the prediction. Another novelty of the study is that we will predict three type of events (negative ramps, non-ramps and positive ramps), instead of binary classification of ramps, given that the type of ramp can be crucial for the correct maintenance of the farm. The model proposed obtains satisfying results, being able to correctly predict around \(70\,\%\) of WPREs and outperforming other models.

Time-series segmentation can be approached by combining a clustering technique and genetic algorithm (GA) with the purpose of automatically finding segments and patterns of a time series. This is an interesting data mining field, but its application to the optimal segmentation of financial time series is a very challenging task, so accurate algorithms are needed. In this sense, GAs are relatively poor at finding the precise optimum solution in the region where the algorithm converges. Thus, this work presents a hybrid GA algorithm including a local search method, aimed to improve the quality of the final solution. The local search algorithm is based on maximizing a likelihood ratio, assuming normality for the series and the subseries in which the original one is segmented. A real-world time series in the Spanish Stock Market field was used to test this methodology.