To extract knowledge from time series data, classical mathematical analysis methods can be used. For example, the Fourier analysis is a method in widespread use. Due to an increase of computing power, ever-growing amounts of data can be saved and processed. As an alternative to writing explicit software that defines mathematical rules to solve problems, machine learning can be employed for data-driven knowledge discovery. For tasks like regression (e.g. physical modeling), classification (see below fig. 1), anomaly detection (see below fig. 2) and forecasting (see below fig. 3) machine learning is the preferred method. Especially when these tasks are non-trivial to solve with classical methods or when classical methods are computationally too costly, machine learning is the state of the art. Depending on the difficulty of the problem, the model complexity ranges from simple linear models to complex deep neural network architectures.
In Time Series data mining, a good baseline is automatic feature extraction in combination with classic machine learning models. Another time series specific property is that relatively strong distance metrics for one dimensional data over time are available. This means that the similarity of two time series can be assessed relatively well using an Euclidean distance combined with dynamic time warping. Both in time series classification and in univariate anomaly detection this similarity measure proofed to be competitive. Another class of machine learning models is designed specifically for time series data. Some of these models limit the complexity of time series data by introducing a quantization or by down-sampling the data. With the same goal in mind, deep neural network architectures have also been adapted to meet the specific challenges of time series data. Famous examples of deep learning architectures adapted to time series data are Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs) or, more recently, the Transformer architectures.