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 which benefits of a graph representation of the data. Two main aspects are involved in this task : A suitable distance measure to evaluate the similarities between time series, and a learning method to make predictions based on these distances. However, the relationship between the two aspects has never been studied systematically  . We describe four different distance measures, including (Soft) DTW and  Matrix Profile, as well as four successful semi-supervised learning methods, including the graph Allen- Cahn method and a Graph Convolutional Neural Network. We then compare the performance of the algorithms on standard data sets. Our findings show that all measures and methods vary strongly in accuracybetween data sets and that there is no clear best combination to employ in all cases  .
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 involved in this task . A suitable distance measure to evaluate the similarities between time series, and a learning method to make predictions based on these distances. 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 graph Allen--Cahn method and a Graph Convolutional Neural Network. We then compare the performance of the algorithms on binary classification 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. As predicted by the ``no free lunch'' theorem, 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 .
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which benefits of
based on
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:
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in the context of graph-based learning
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MPDist, a distance measure based on the
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Allen- Cahn
Allen--Cahn
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standard
binary classification
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Our findings show that all measures and methods vary strongly in accuracybetween data sets and that there is no
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. As predicted by the ``no free lunch'' theorem, no
A
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