Time series data mining: preprocessing, analysis, segmentation and prediction. Applications

Currently, the amount of data which is produced for any information system is increasing exponentially. This motivates the development of automatic techniques to process and mine these data correctly. Specifically, in this Thesis, we tackled these problems for time series data, that is, temporal data which is collected chronologically. This kind of data can be found in many fields of science, such as palaeoclimatology, hydrology, financial problems, etc. TSDM consists of several tasks which try to achieve different objectives, such as, classification, segmentation, clustering, prediction, analysis, etc. However, in this Thesis, we focus on time series preprocessing, segmentation and prediction. Time series preprocessing is a prerequisite for other posterior tasks: for example, the reconstruction of missing values in incomplete parts of time series can be essential for clustering them. In this Thesis, we tackled the problem of massive missing data reconstruction in SWH time series from the Gulf of Alaska. It is very common that buoys stop working for different periods, what it is usually related to malfunctioning or bad weather conditions. The relation of the time series of each buoy is analysed and exploited to reconstruct the whole missing time series. In this context, EANNs with PUs are trained, showing that the resulting models are simple and able to recover these values with high precision. In the case of time series segmentation, the procedure consists in dividing the time series into different subsequences to achieve different purposes. This segmentation can be done trying to find useful patterns in the time series. In this Thesis, we have developed novel bioinspired algorithms in this context. For instance, for paleoclimate data, an initial genetic algorithm was proposed to discover early warning signals of TPs, whose detection was supported by expert opinions. However, given that the expert had to individually evaluate every solution given by the algorithm, the evaluation of the results was very tedious. This led to an improvement in the body of the GA to evaluate the procedure automatically. For significant wave height time series, the objective was the detection of groups which contains extreme waves, i.e. those which are relatively large with respect other waves close in time. The main motivation is to design alert systems. This was done using an HA, where an LS process was included by using a likelihood-based segmentation, assuming that the points follow a beta distribution. Finally, the analysis of similarities in different periods of European stock markets was also tackled with the aim of evaluating the influence of different markets in Europe. When segmenting time series with the aim of reducing the number of points, different techniques have been proposed. However, it is an open challenge given the difficulty to operate with large amounts of data in different applications. In this work, we propose a novel statistically-driven CRO algorithm (SCRO), which automatically adapts its parameters during the evolution, taking into account the statistical distribution of the population fitness. This algorithm improves the state-of-the-art with respect to accuracy and robustness. Also, this problem has been tackled using an improvement of the BBPSO algorithm, which includes a dynamical update of the cognitive and social components in the evolution, combined with mathematical tricks to obtain the fitness of the solutions, which significantly reduces the computational cost of previously proposed coral reef methods. Also, the optimisation of both objectives (clustering quality and approximation quality), which are in conflict, could be an interesting open challenge, which will be tackled in this Thesis. For that, an MOEA for time series segmentation is developed, improving the clustering quality of the solutions and their approximation. The prediction in time series is the estimation of future values by observing and studying the previous ones. In this context, we solve this task by applying prediction over high-order representations of the elements of the time series, i.e. the segments obtained by time series segmentation. This is applied to two challenging problems, i.e. the prediction of extreme wave height and fog prediction. On the one hand, the number of extreme values in SWH time series is less with respect to the number of standard values. In this way, the prediction of these values cannot be done using standard algorithms without taking into account the imbalanced ratio of the dataset. For that, an algorithm that automatically finds the set of segments and then applies EANNs is developed, showing the high ability of the algorithm to detect and predict these special events. On the other hand, fog prediction is affected by the same problem, that is, the number of fog events is much lower tan that of non-fog events, requiring a special treatment too. A preprocessing of different data coming from sensors situated in different parts of the Valladolid airport are used for making a simple ANN model, which is physically corroborated and discussed. The last challenge which opens new horizons is the estimation of the statistical distribution of time series to guide different methodologies. For this, the estimation of a mixed distribution for SWH time series is then used for fixing the threshold of POT approaches. Also, the determination of the fittest distribution for the time series is used for discretising it and making a prediction which treats the problem as ordinal classification. The work developed in this Thesis is supported by twelve papers in international journals, seven papers in international conferences, and four papers in national conferences