Abstract
Time series data play an important role in many applications and their analysis reveals crucial information for understanding the underlying processes. Among the many time series learning tasks of great importance, we here focus on semi-supervised learning based on a graph representation of the data. Two main aspects are studied in this paper. Namely, suitable distance measures to evaluate the similarities between different time series, and the choice of learning method to make predictions based on a given number of pre-labeled data points. However, the relationship between the two aspects has never been studied systematically in the context of graph-based learning. We describe four different distance measures, including (Soft) DTW and MPDist, a distance measure based on the Matrix Profile, as well as four successful semi-supervised learning methods, including the recently introduced graph Allen–Cahn method and Graph Convolutional Neural Network method. We provide results for the novel combination of these distance measures with both the Allen-Cahn method and the GCN algorithm for binary semi-supervised learning tasks for various time-series data sets. In our findings we compare the chosen graph-based methods using all distance measures and observe that the results vary strongly with respect to the accuracy. We then observe that no clear best combination to employ in all cases is found. Our study provides a reproducible framework for future work in the direction of semi-supervised learning for time series with a focus on graph representations.
Highlights
Many processes for which data are collected are time-dependent and as a result the study of time series data is a subject of great importance [1,2,3]
Each time series becomes a node within a weighted undirected graph and the edge-weight is proportional to the similarity between different time series
Our motivation follows that of [32, 33], where many methods for supervised learning in the context of time series were compared, namely that we aim to provide a wide-ranging overview of recent methods based on a graph representation of the data and combined with several distance measures
Summary
Many processes for which data are collected are time-dependent and as a result the study of time series data is a subject of great importance [1,2,3]. We here focus on the task of classification of time series [11,12,13,14,15,16] in the context of semi-supervised learning [17, 18] where we want to label all data points based on the fact that only a small portion of the data is already pre-labeled. The Laplacian is the representation of the network that is utilized from machine learning to mathematical imaging It has been used network-Lasso-based learning approaches focusing on data with an inherent network structure, see e.g., [26, 27]. The computation of the distance between time series or subsequences becomes a crucial task and this will be reflected in our choice of weight function. We consider several distance measures such as dynamic time warping DTW [28], soft DTW [29], and matrix profile [30]
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