Generating Synthetic Time Series to Augment Sparse Datasets

Abstract

In machine learning, data augmentation is the process of creating synthetic examples in order to augment a dataset used to learn a model. One motivation for data augmentation is to reduce the variance of a classifier, thereby reducing error. In this paper, we propose new data augmentation techniques specifically designed for time series classification, where the space in which they are embedded is induced by Dynamic Time Warping (DTW). The main idea of our approach is to average a set of time series and use the average time series as a new synthetic example. The proposed methods rely on an extension of DTW Barycentric Averaging (DBA), the averaging technique that is specifically developed for DTW. In this paper, we extend DBA to be able to calculate a weighted average of time series under DTW. In this case, instead of each time series contributing equally to the final average, some can contribute more than others. This extension allows us to generate an infinite number of new examples from any set of given time series. To this end, we propose three methods that choose the weights associated to the time series of the dataset. We carry out experiments on the 85 datasets of the UCR archive and demonstrate that our method is particularly useful when the number of available examples is limited (e.g. 2 to 6 examples per class) using a 1-NN DTW classifier. Furthermore, we show that augmenting full datasets is beneficial in most cases, as we observed an increase of accuracy on 56 datasets, no effect on 7 and a slight decrease on only 22.

Deep learning for time series classification: a review

“…Finally, we showed how the blackbox effect of deep models which renders them uninterpretable, can be mitigated with a Class Activation Map visualization that highlights which parts of the input time series, contributed the most to a certain class identification. Although we have conducted an extensive experimental evaluation, deep learning for time series classification, unlike for computer vision and NLP tasks, still lacks a thorough study of data augmentation (Ismail Fawaz et al, 2018a;Forestier et al, 2017) and transfer learning (Ismail Fawaz et al, 2018c;Serrà et al, 2018). In addition, the time series community would benefit from an extension of this empirical study that compares in addition to accuracy, the training and testing time of these deep learning models.…”

“…We implemented our framework using the open source deep learning library Keras (Chollet, 2015) with the Tensorflow (Abadi et al, 2015) back-end 1 . Following Lucas et al (2018);Forestier et al (2017); Petitjean et al (2016); Grabocka et al (2014) we used the mean accuracy measure averaged over the 10 runs on the test set. When comparing with the state-of-the-art results published in Bagnall et al (2017) we averaged the accuracy using the median test error.…”

Adversarial Attacks on Deep Neural Networks for Time Series Classification

“…We used Multi-Dimensional Scaling (MDS) [31], [32] with the objective to gain some insights on the spatial distribution of the perturbed time series compared to the original ones. MDS uses a pairwise distance matrix as input and aims at placing each object in an N-dimensional space such as the betweenobject distances are preserved as well as possible.…”

Data Augmentation with Suboptimal Warping for Time-Series Classification

“…Other such techniques involve the addition of noise, rotation, and scaling of the values in sequences [4]. A more advanced method, DTW Barycentric Averaging (DBA) [9], generates time-series as weighted averages of multiply aligned time-series. In that method, a time-series is selected and used for aligning the remaining samples.…”

“…Therefore, time-series augmentation techniques generate new examples by randomly stretching, shrinking, removing their parts [4], or perturbing them [7]. Also, weighted aligned averages [8,9] or generative models [10] are used.…”