An Empirical Study of Graph-Based Approaches for Semi-Supervised Time Series Classification

TL;DR

This paper systematically evaluates various graph-based semi-supervised learning methods for time series classification, analyzing how different distance measures impact performance and providing a framework for future research.

Contribution

It offers a comprehensive comparison of four distance measures and four semi-supervised learning methods for graph-based time series classification, highlighting the variability in results.

Findings

Performance varies significantly with different method and distance measure combinations.

No single best approach is identified across all datasets, confirming the 'no free lunch' theorem.

Provides a reproducible framework for future research in semi-supervised time series learning.

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 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.