In this section, we include explanatory examples of the interpretability of shapelets for the experimental cases included in the work.

In Figure 1, we show a time series of each class for the problem generated from random sequences of 0 and 1 processed by 4 ARIMA models. In addition, we show the first shapelets found for each class in the search process. One shapelet for each class. The tree generated by the search algorithm can be found in the online resource. The objective of this graph is to show the characteristic patterns extracted from each class, allowing us to observe what behaviors of time series differentiate one class from another. The difference between class 3 and the others is clear, a positive tend. The class 0 has slightly steep climbs and a characteristic shape. Class 1 consists of stepped climbs and smooth descents. Class 2 presents continuous oscillations. The use of the shapelets allows users to extract interpretable information about the behavior of each class and the characteristics that differentiate them from each other.

 4ARIMAs_shapelets_example

Figure 1.- Example of interpretability on ARIMAs problem.

 

In Figure 2, we show an example of the type of time series that makes up each class, followed by the first shapelet found for each class. The complete shapelet tree can be found in the online resource. The first shapelets of classes 1 and 3 are formed by the original time series. The series included in these classes are very similar to each other, within the same class. The high threshold distance of these shapelets shows the high difference in behavior between the time series of these classes and those of the rest of the classes. Class 1 is composed of the outline of the phalanges of different users, so it is a particular problem with characteristic patterns. Class 3 corresponds to the evolution of the X-axis when a person makes the gesture of removing and keeping a weapon, which also generates a specific pattern of this problem. Class 0 is composed of electrocardiograms. The main characteristic of this type of signals is found in the registered patterns of beats, both in the ascents and the descents. Class 2 is characterized by the presence of square pulses of different amplitude and duration, which have been correctly identified by the extracted shapelets. Class 4 has the measurements of a sensor during the processing of a wafer, characterized by the presence of variations between 2 levels and long periods of permanence in one of them. Class 5 is composed of the records of different sensors in a house, in order to identify the use that is made of electricity. In this case

 6Class-Datasets_shapelets_example

Figure 2.- Example of interpretability on 6 Datasets-Class problem.