  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.
