The problem of early classification of time series appears naturally in contexts where the data, of temporal nature, is collected over time, and early class predictions are interesting or even required. The objective is to classify the incoming sequence as soon as possible, while maintaining suitable levels of accuracy in the predictions. Thus, we can say that the problem of early classification consists in optimizing two objectives simultaneously: accuracy and earliness. In this context, we present a method for early classification of time series based on combining a set of probabilistic classifiers together with a stopping rule. This stopping rule will act as a trigger and will tell us when to output a prediction or when to wait for more data, and it's main novelty lies in the fact that it is built by explicitly optimizing a cost function based on accuracy and earliness. We have selected a large set of benchmark datasets and 4 other state-ofthe-art early classification methods and we have evaluated and compared our framework obtaining superior results in terms of both earliness and accuracy.

Recent advances in technology have brought major breakthroughs in data collection, enabling a large amount of data to be gathered over time and thus generating time series. Mining this data has become an important task for researchers and practitioners in the past few years, including the detection of outliers or anomalies that may represent errors or events of interest. This review aims to provide a structured and comprehensive state-of-the-art on unsupervised outlier detection techniques in the context of time series. To this end, a taxonomy is presented based on the main aspects that characterize an outlier detection technique.

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Time series classification is an increasing research topic due to the vast amount of time series data that are being created over a wide variety of fields. The particularity of the data makes it a challenging task and different approaches have been taken, including the distance based approach. 1-NN has been a widely used method within distance based time series classification due to it simplicity but still good performance. However, its supremacy may be attributed to being able to use specific distances for time series within the classification process and not to the classifier itself. With the aim of exploiting these distances within more complex classifiers, new approaches have arisen in the past few years that are competitive or which outperform the 1-NN based approaches. In some cases, these new methods use the distance measure to transform the series into feature vectors, bridging the gap between time series and traditional classifiers. In other cases, the distances are employed to obtain a time series kernel and enable the use of kernel methods for time series classification. One of the main challenges is that a kernel function must be positive semi-definite, a matter that is also addressed within this review. The presented review includes a taxonomy of all those methods that aim to classify time series using a distance based approach, as well as a discussion of the strengths and weaknesses of each method.

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